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open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
You are Dastan, the great Prince of Persia!
After searching long for the mysterious 'Sands of Time', you have finally arrived at the gates of the city that hosts the ancient temple of the gods. However, the gate is locked and it can only be opened with a secret code, which you need to obtain by solving the following puzzle:
There is a table in front of you, with $N$ coins placed in a row and numbered $1$ through $N$ from left to right. For each coin, you know whether it is initially showing heads or tails. You have to perform exactly $K$ operations. In one operation, you should remove the rightmost coin present on the table, and if this coin was showing heads right before it was removed, then you should also flip all the remaining coins. (If a coin was showing heads, then after it is flipped, it is showing tails, and vice versa.)
The code needed to enter the temple is the number of coins which, after these $K$ operations are performed, have not been removed and are showing heads. Can you find this number? The fate of Persia lies in your handsβ¦
-----Input-----
- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
- The first line of each test case contains two space-separated integers $N$ and $K$.
- The second line contains $N$ space-separated characters. For each valid $i$, the $i$-th of these characters is 'H' if the $i$-th coin is initially showing heads or 'T' if it is showing tails.
-----Output-----
For each test case, print a single line containing one integer β the number of coins that are showing heads after $K$ operations.
-----Constraints-----
- $1 \le T \le 200$
- $1 \le K < N \le 100$
-----Subtasks-----
Subtask #1 (100 points): original constraints
-----Example Input-----
3
5 3
H T T H T
7 4
H H T T T H H
6 1
T H T H T T
-----Example Output-----
1
2
2
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
t=int(input())
for i in range(t):
n,k=[int(i) for i in input().split()]
l=input().split()
for i in range(k):
if l.pop()=='H':
for ind,j in enumerate(l):
if j=='H':
l[ind]='T'
else:
l[ind]='H'
print(sum([1 for i in l if i=='H']))
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Suppose you are performing the following algorithm. There is an array $v_1, v_2, \dots, v_n$ filled with zeroes at start. The following operation is applied to the array several times β at $i$-th step ($0$-indexed) you can: either choose position $pos$ ($1 \le pos \le n$) and increase $v_{pos}$ by $k^i$; or not choose any position and skip this step.
You can choose how the algorithm would behave on each step and when to stop it. The question is: can you make array $v$ equal to the given array $a$ ($v_j = a_j$ for each $j$) after some step?
-----Input-----
The first line contains one integer $T$ ($1 \le T \le 1000$) β the number of test cases. Next $2T$ lines contain test cases β two lines per test case.
The first line of each test case contains two integers $n$ and $k$ ($1 \le n \le 30$, $2 \le k \le 100$) β the size of arrays $v$ and $a$ and value $k$ used in the algorithm.
The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($0 \le a_i \le 10^{16}$) β the array you'd like to achieve.
-----Output-----
For each test case print YES (case insensitive) if you can achieve the array $a$ after some step or NO (case insensitive) otherwise.
-----Example-----
Input
5
4 100
0 0 0 0
1 2
1
3 4
1 4 1
3 2
0 1 3
3 9
0 59049 810
Output
YES
YES
NO
NO
YES
-----Note-----
In the first test case, you can stop the algorithm before the $0$-th step, or don't choose any position several times and stop the algorithm.
In the second test case, you can add $k^0$ to $v_1$ and stop the algorithm.
In the third test case, you can't make two $1$ in the array $v$.
In the fifth test case, you can skip $9^0$ and $9^1$, then add $9^2$ and $9^3$ to $v_3$, skip $9^4$ and finally, add $9^5$ to $v_2$.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
t = int(input())
for _ in range(t):
n,k = list(map(int,input().split()))
a = list(map(int,input().split()))
for i in range(60, -1, -1):
m = k ** i
for j in range(n):
if a[j] >= m:
a[j] -= m
break
if all(i == 0 for i in a):
print('YES')
else:
print('NO')
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Little kids, Jack and Evan like playing their favorite game Glass-and-Stone. Today they want to play something new and came across Twitter on their father's laptop.
They saw it for the first time but were already getting bored to see a bunch of sentences having at most 140 characters each. The only thing they liked to play with it is, closing and opening tweets.
There are N tweets on the page and each tweet can be opened by clicking on it, to see some statistics related to that tweet. Initially all the tweets are closed. Clicking on an open tweet closes it and clicking on a closed tweet opens it. There is also a button to close all the open tweets. Given a sequence of K clicks by Jack, Evan has to guess the total number of open tweets just after each click. Please help Evan in this game.
-----Input-----
First line contains two integers N K, the number of tweets (numbered 1 to N) and the number of clicks respectively (1 β€ N, K β€ 1000). Each of the following K lines has one of the following.
- CLICK X , where X is the tweet number (1 β€ X β€ N)
- CLOSEALL
-----Output-----
Output K lines, where the ith line should contain the number of open tweets just after the ith click.
-----Example-----
Input:
3 6
CLICK 1
CLICK 2
CLICK 3
CLICK 2
CLOSEALL
CLICK 1
Output:
1
2
3
2
0
1
Explanation:
Let open[x] = 1 if the xth tweet is open and 0 if its closed.
Initially open[1..3] = { 0 , 0 , 0 }. Here is the state of open[1..3] after each click and corresponding count of open tweets.
CLICK 1 : { 1, 0, 0 }, open count = 1
CLICK 2 : { 1, 1, 0 }, open count = 2
CLICK 3 : { 1, 1, 1 }, open count = 3
CLICK 2 : { 1, 0, 1 }, open count = 2
CLOSEALL : { 0, 0, 0 }, open count = 0
CLICK 1 : { 1, 0, 0 }, open count = 1
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
def getInput():
N_k = input().split()
N =int(N_k[0])
k =int(N_k[1])
list = []
output = []
count = 0
for i in range(0,k):
val = input()
if(val!="CLOSEALL"):
val=val.split()
val = int (val[1])
if val not in list:
count= count +1
list.append(val)
else:
list.remove(val)
count= count -1
else:
count =0
while len(list) > 0:
list.pop()
output.append(count)
for each in output:
print(each)
getInput()
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Who's interested in football?
Rayne Wooney has been one of the top players for his football club for the last few years. But unfortunately, he got injured during a game a few months back and has been out of play ever since.
He's got proper treatment and is eager to go out and play for his team again. Before doing that, he has to prove to his fitness to the coach and manager of the team. Rayne has been playing practice matches for the past few days. He's played N practice matches in all.
He wants to convince the coach and the manager that he's improved over time and that his injury no longer affects his game. To increase his chances of getting back into the team, he's decided to show them stats of any 2 of his practice games. The coach and manager will look into the goals scored in both the games and see how much he's improved. If the number of goals scored in the 2nd game(the game which took place later) is greater than that in 1st, then he has a chance of getting in. Tell Rayne what is the maximum improvement in terms of goal difference that he can show to maximize his chances of getting into the team. If he hasn't improved over time, he's not fit to play. Scoring equal number of goals in 2 matches will not be considered an improvement. Also, he will be declared unfit if he doesn't have enough matches to show an improvement.
-----Input:-----
The first line of the input contains a single integer T, the number of test cases.
Each test case begins with a single integer N, the number of practice matches Rayne has played.
The next line contains N integers. The ith integer, gi, on this line represents the number of goals Rayne scored in his ith practice match. The matches are given in chronological order i.e. j > i means match number j took place after match number i.
-----Output:-----
For each test case output a single line containing the maximum goal difference that Rayne can show to his coach and manager. If he's not fit yet, print "UNFIT".
-----Constraints:-----
1<=T<=10
1<=N<=100000
0<=gi<=1000000 (Well, Rayne's a legend! You can expect him to score so many goals!)
-----Example:-----Input:
3
6
3 7 1 4 2 4
5
5 4 3 2 1
5
4 3 2 2 3
Output:
4
UNFIT
1
Explanation:
In the first test case, Rayne can choose the first and second game. Thus he gets a difference of 7-3=4 goals. Any other pair would give him a lower improvement.
In the second test case, Rayne has not been improving in any match. Thus he's declared UNFIT.
Note: Large input data. Use faster I/O methods. Prefer scanf,printf over cin/cout.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
T = int(input())
for j in range(0,T):
line1, line2 = input(), input()
seq = line2.split()
current_min = 1000001
current_max = 0
max_spread = 0
for i in range(0,len(seq)):
current_value = int(seq[i])
if current_min > current_value:
current_min = current_value
current_max = current_value
elif current_max < current_value:
current_max = current_value
if max_spread < (current_max - current_min):
max_spread = current_max - current_min
if max_spread > 0:
print(max_spread)
else:
print("UNFIT")
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Today Sonya learned about long integers and invited all her friends to share the fun. Sonya has an initially empty multiset with integers. Friends give her t queries, each of one of the following type: + a_{i}Β β add non-negative integer a_{i} to the multiset. Note, that she has a multiset, thus there may be many occurrences of the same integer. - a_{i}Β β delete a single occurrence of non-negative integer a_{i} from the multiset. It's guaranteed, that there is at least one a_{i} in the multiset. ? sΒ β count the number of integers in the multiset (with repetitions) that match some pattern s consisting of 0 and 1. In the pattern, 0 stands for the even digits, while 1 stands for the odd. Integer x matches the pattern s, if the parity of the i-th from the right digit in decimal notation matches the i-th from the right digit of the pattern. If the pattern is shorter than this integer, it's supplemented with 0-s from the left. Similarly, if the integer is shorter than the pattern its decimal notation is supplemented with the 0-s from the left.
For example, if the pattern is s = 010, than integers 92, 2212, 50 and 414 match the pattern, while integers 3, 110, 25 and 1030 do not.
-----Input-----
The first line of the input contains an integer t (1 β€ t β€ 100 000)Β β the number of operation Sonya has to perform.
Next t lines provide the descriptions of the queries in order they appear in the input file. The i-th row starts with a character c_{i}Β β the type of the corresponding operation. If c_{i} is equal to '+' or '-' then it's followed by a space and an integer a_{i} (0 β€ a_{i} < 10^18) given without leading zeroes (unless it's 0). If c_{i} equals '?' then it's followed by a space and a sequence of zeroes and onse, giving the pattern of length no more than 18.
It's guaranteed that there will be at least one query of type '?'.
It's guaranteed that any time some integer is removed from the multiset, there will be at least one occurrence of this integer in it.
-----Output-----
For each query of the third type print the number of integers matching the given pattern. Each integer is counted as many times, as it appears in the multiset at this moment of time.
-----Examples-----
Input
12
+ 1
+ 241
? 1
+ 361
- 241
? 0101
+ 101
? 101
- 101
? 101
+ 4000
? 0
Output
2
1
2
1
1
Input
4
+ 200
+ 200
- 200
? 0
Output
1
-----Note-----
Consider the integers matching the patterns from the queries of the third type. Queries are numbered in the order they appear in the input. 1 and 241. 361. 101 and 361. 361. 4000.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
from sys import stdin
def main():
cnt = [0] * 2 ** 18
t = str.maketrans("0123456789", "0101010101")
_, *l = stdin.read().splitlines()
for sign, s in map(str.split, l):
if sign == '?':
print(cnt[int(s, 2)])
else:
cnt[int(s.translate(t), 2)] += 1 if sign == '+' else -1
def __starting_point():
main()
__starting_point()
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
A string a of length m is called antipalindromic iff m is even, and for each i (1 β€ i β€ m) a_{i} β a_{m} - i + 1.
Ivan has a string s consisting of n lowercase Latin letters; n is even. He wants to form some string t that will be an antipalindromic permutation of s. Also Ivan has denoted the beauty of index i as b_{i}, and the beauty of t as the sum of b_{i} among all indices i such that s_{i} = t_{i}.
Help Ivan to determine maximum possible beauty of t he can get.
-----Input-----
The first line contains one integer n (2 β€ n β€ 100, n is even) β the number of characters in s.
The second line contains the string s itself. It consists of only lowercase Latin letters, and it is guaranteed that its letters can be reordered to form an antipalindromic string.
The third line contains n integer numbers b_1, b_2, ..., b_{n} (1 β€ b_{i} β€ 100), where b_{i} is the beauty of index i.
-----Output-----
Print one number β the maximum possible beauty of t.
-----Examples-----
Input
8
abacabac
1 1 1 1 1 1 1 1
Output
8
Input
8
abaccaba
1 2 3 4 5 6 7 8
Output
26
Input
8
abacabca
1 2 3 4 4 3 2 1
Output
17
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
from collections import Counter
r = lambda: list(map(int, input().split()))
def main():
n, = r()
s = input()
cost = list(r())
ans = 0
cnt = Counter()
for i in range(n // 2):
if s[i] == s[n - 1 - i]:
ans += min(cost[i], cost[n - 1 - i])
cnt[s[i]] += 1
total = sum(cnt.values())
if total > 0:
ch, occ = cnt.most_common(1)[0]
avail = []
if occ > total - occ:
for i in range(n // 2):
if s[i] != s[n - 1 - i] and s[i] != ch and s[n - 1 - i] != ch:
avail.append(min(cost[i], cost[n - 1 - i]))
avail.sort()
ans += sum(avail[:2 * occ - total])
print(sum(cost) - ans)
main()
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
You are given a set of n pens, each of them can be red, blue, green, orange, and violet in color. Count a minimum number of pens that should be taken out from the set so that any two neighboring pens have different colors. Pens are considered to be neighboring if there are no other pens between them.
-----Input:-----
-
The first line contains t denoting the number of test cases.
-
The first line of each test case will contain a single integer n.
-
The second line of each test case will contain a string s.
(s contains only 'R', 'B', 'G', 'O', and 'V' characters denoting red, blue, green, orange, and violet respectively)
-----Output:-----
For each test case, print single line containing one integer - The minimum number of pens that need to be taken out.
-----Constraints-----
- $1 \leq T \leq 100$
- $1 \leq n \leq 1000$
-----Sample Input:-----
2
5
RBBRG
5
RBGOV
-----Sample Output:-----
1
0
-----EXPLANATION:-----
In first test case, two blue pens are neighboring each other, if we take out any one of them then the string will be RBRG in which each pen has different neighbors.
In second test case, no pen needs to be taken out as each pen has different neighbors.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
t = int(input())
for _ in range(t):
n = int(input())
a = input().strip()
prev = a[0]
ans = -1
for i in a:
if prev == i:
ans += 1
prev = i
print(ans)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Indian National Olympiad in Informatics 2014
Due to resurfacing work, all north-south traffic on the highway is being diverted through the town of Siruseri. Siruseri is a modern, planned town and the section of roads used for the diversion forms a rectangular grid where all cars enter at the top-left intersection (north- west) and leave at the bottom-right intersection (south-east). All roads within the grid are one-way, allowing traffic to move north to south (up-down) and west to east (left-right) only.
The town authorities are concerned about highway drivers overspeeding through the town. To slow them down, they have made a rule that no car may travel more than d consecutive road segments in the same direction without turning. (Closed-circuit TV cameras have been installed to enforce this rule.)
Of course, there is also repair work going on within the town, so some intersections are blocked and cars cannot pass through these.
You are given the layout of the rectangular grid of roads within Siruseri and the constraint on how many consecutive road segments you may travel in the same direction. Your task is to compute the total number of paths from the entry (top-left) to the exit (bottom-right).
For instance, suppose there are 3 rows and 4 columns of intersec- tions, numbered from (1,1) at the top-left to (3,4) at the bottom-right, as shown on the right. Intersection (2,1) in the second row, first column is blocked, and no car may travel more than 2 consecutive road seg- ments in the same direction.
Here, (1,1) β (1,2) β (2,2) β (3,2) β (3,3) β (3,4) is a valid path from (1,1) to (3,4), but (1,1) β (1,2) β (1,3) β (1,4) β (2,4) β (3,4) is not, because this involves 3 consecutive road segments from left to right. The path (1, 1) β (2, 1) β (2, 2) β (2, 3) β (3, 3) β (3, 4) is ruled out because it goes through a blocked intersection. In this example, you can check that the total number of valid paths is 5.
-----Input format-----
β’ Line 1: Three space-separated integers, R, C and d, where R is the number of rows in the grid, C is the number of columns in the grid and d is the maximum number of consecutive segments you can travel in any direction.
β’ Lines 2 to R+1: Each line contains C integers, each of which is 0 or 1, describing one row of intersections in the grid. An intersection marked 0 is blocked and an intersection marked 1 is available to pass through. The start (top-left) and finish (bottom-right) intersections are always marked 1.
-----Output format-----
A single integerβthe number of paths from the top-left intersection to the bottom-right intersection that go only down and right, and obey the d constraint.
Since the final answer may not fit in a variable of type int, report your answer modulo 20011. Be careful to avoid overflows in intermediate computations.
-----Test Data-----
The testdata is grouped into three subtasks. In all subtasks, 1 β€ R β€ 300, 1 β€ C β€ 300 and 1 β€ d β€ 300. In addition, each subtask has the following constraints on the inputs.
β’ Subtask 1 [20 points]: d = max(R, C) β 1. (In other words, there is no limit on the number of consecutive segments you can travel in one direction.)
β’ Subtask 2 [30 points]: d=2.
β’ Subtask 3 [50 points]: No additional constraint on d.
-----Example-----
Here is the sample input and output corresponding to the example above.
-----Sample input-----
3 4 2
1 1 1 1
0 1 1 1
1 1 1 1
-----Sample output-----
5
Note: Your program should not print anything other than what is specified in the output format. Please remove all diagnostic print statements before making your final submission. A program with extraneous output will be treated as incorrect!
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
class PathNode:
def __init__(self, row, col, st_x, st_y, p_count=0):
self.x = row
self.y = col
self.pathCount = p_count
def __str__(self):
return str(self.x) + " | " + str(self.y) + " | " + str(self.pathCount)
class GraphUtil:
def __init__(self, mat, R,C, d):
self.mat = mat
self.R = R
self.C = C
self.d = d
self.tab = {}
def isValidMove(self, r, c, blockVal):
return r < self.R and c < self.C and self.mat[r][c] != blockVal
def possbilePathUtil(self, r, c, blockVal, step,direction):
if(not self.isValidMove(r, c, 0)):
return 0
if (r == self.R - 1 and c == self.C - 1):
return 1
if ((r,c,step,direction) in self.tab):
return self.tab[(r,c,step,direction)]
result = 0
if direction == 1:
if step < self.d:
result = (result + self.possbilePathUtil(r, c + 1, blockVal, step + 1,1)) % 20011
result = (result + self.possbilePathUtil(r+1, c, blockVal, 1,2)) % 20011
else:
if step < self.d:
result = (result + self.possbilePathUtil(r + 1, c, blockVal, step + 1, 2)) % 20011
result = (result + self.possbilePathUtil(r, c + 1, blockVal, 1,1)) % 20011
self.tab[(r,c,step,direction)] = result
return result
def possbilePath(self):
if (not self.mat or len(self.mat) < 1):
return 0
return self.possbilePathUtil(0, 0, 0,0,2)
numbers = [int(n) for n in input().split()]
mat = [[int(n) for n in input().split()] for r in range(0, numbers[0])]
result = GraphUtil(mat, numbers[0], numbers[1], numbers[2])
print(result.possbilePath())
# print(result.count)# cook your dish here
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Polycarpus is a system administrator. There are two servers under his strict guidance β a and b. To stay informed about the servers' performance, Polycarpus executes commands "ping a" and "ping b". Each ping command sends exactly ten packets to the server specified in the argument of the command. Executing a program results in two integers x and y (x + y = 10;Β x, y β₯ 0). These numbers mean that x packets successfully reached the corresponding server through the network and y packets were lost.
Today Polycarpus has performed overall n ping commands during his workday. Now for each server Polycarpus wants to know whether the server is "alive" or not. Polycarpus thinks that the server is "alive", if at least half of the packets that we send to this server reached it successfully along the network.
Help Polycarpus, determine for each server, whether it is "alive" or not by the given commands and their results.
-----Input-----
The first line contains a single integer n (2 β€ n β€ 1000) β the number of commands Polycarpus has fulfilled. Each of the following n lines contains three integers β the description of the commands. The i-th of these lines contains three space-separated integers t_{i}, x_{i}, y_{i} (1 β€ t_{i} β€ 2;Β x_{i}, y_{i} β₯ 0;Β x_{i} + y_{i} = 10). If t_{i} = 1, then the i-th command is "ping a", otherwise the i-th command is "ping b". Numbers x_{i}, y_{i} represent the result of executing this command, that is, x_{i} packets reached the corresponding server successfully and y_{i} packets were lost.
It is guaranteed that the input has at least one "ping a" command and at least one "ping b" command.
-----Output-----
In the first line print string "LIVE" (without the quotes) if server a is "alive", otherwise print "DEAD" (without the quotes).
In the second line print the state of server b in the similar format.
-----Examples-----
Input
2
1 5 5
2 6 4
Output
LIVE
LIVE
Input
3
1 0 10
2 0 10
1 10 0
Output
LIVE
DEAD
-----Note-----
Consider the first test case. There 10 packets were sent to server a, 5 of them reached it. Therefore, at least half of all packets sent to this server successfully reached it through the network. Overall there were 10 packets sent to server b, 6 of them reached it. Therefore, at least half of all packets sent to this server successfully reached it through the network.
Consider the second test case. There were overall 20 packages sent to server a, 10 of them reached it. Therefore, at least half of all packets sent to this server successfully reached it through the network. Overall 10 packets were sent to server b, 0 of them reached it. Therefore, less than half of all packets sent to this server successfully reached it through the network.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
n=int(input())
ta,tb,da,db=[0]*4
for i in range (n):
t,x,y=list(map(int,input().split()))
if t==1:
ta+=(x+y)
da+=y
if (t==2):
tb+=(x+y)
db+=y
if (ta-da>=0.5*ta):
print ('LIVE')
else :
print ('DEAD')
if (tb-db>=0.5*tb):
print ('LIVE')
else :
print ('DEAD')
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Chef and his friend Miron were getting bored and decided to play a game.
Miron thinks of a sequence of N integers (A1, A2, β¦., AN) and gives Chef a matrix B, where Bi,j = |Ai - Aj|. He further tells Chef that A1 = 0. The game is for Chef to guess the sequence that Miron thought of.
But Miron is an adversarial player. Every time Chef tries to guess the sequence, he makes a change to the matrix. He makes such a change Q times. Each time, he replaces an entry in some row and the corresponding column with a new one leaving Chef to guess the sequence after each change.
Chef needs a friend to help him against such an adversarial player. Can you be that friend and help Chef find a suitable sequence A for the initial matrix B and also after each change Miron makes?
Note that if several answers exist, then print the lexicographically smallest answer. Further, the numbers in the sequence can be negative.
-----Input-----
The first line contains two space-separated integers N, Q. Each of the N subsequent lines contains N space-separated integers, denoting the matrix B.
Q queries follow. Each query has two lines. The first line of each query contains an integer p, denoting the number of row and column that is changed. The second line of each query contains N space-separated integers F1, F2, F3, ... FN, denoting the new values to the corresponding cells of the matrix (you should make the following assignments Bi,p = Bp,i = Fi for all valid i).
-----Output-----
Print Q + 1 lines which contain N space-separated integers, Miron's initial array and Miron's array after each query.
-----Constraints-----
- 3 β€ N β€ 1000
- 1 β€ Q β€ 1000
- 0 β€ Bi,j β€ 5000
- 1 β€ p β€ n
- 0 β€ Fi β€ 5000
- it's guaranteed there's always an answer
-----Example-----
Input:
3 2
0 1 2
1 0 1
2 1 0
1
0 4 3
2
4 0 7
Output:
0 -1 -2
0 -4 -3
0 -4 3
-----Explanation-----
Example case 1. Initially, sequence {0, 1, 2} is also suitable, but {0, -1, -2} is lexicografically smaller.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
def update_B(B, query):
p, R = query
for i in range(len(R)):
B[p][i] = R[i]
B[i][p] = R[i]
def get_A(B):
N = len(B)
A = [0] * N
i = 0
for j in range(N):
if B[0][j] != 0:
i = j
A[i] = -B[0][i]
break
for j in range(i + 1, N):
if abs(A[i] - B[0][j]) == B[i][j]:
A[j] = B[0][j]
else:
A[j] = -B[0][j]
return A
def print_list(A):
print(' '.join([str(a) for a in get_A(B)]))
N, Q = [int(x) for x in input().rstrip().split()]
B = []
for i in range(N):
B += [[int(x) for x in input().rstrip().split()]]
queries = []
for i in range(Q):
p = int(input()) - 1
arr = input().rstrip().split()
queries += [(p, [int(x) for x in arr])]
print_list(get_A(B))
for q in queries:
update_B(B, q)
print_list(' '.join([str(a) for a in get_A(B)]))
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
You are given $N$ gears numbered $1$ through $N$. For each valid $i$, gear $i$ has $A_i$ teeth. In the beginning, no gear is connected to any other. Your task is to process $M$ queries and simulate the gears' mechanism. There are three types of queries:
- Type 1: Change the number of teeth of gear $X$ to $C$.
- Type 2: Connect two gears $X$ and $Y$.
- Type 3: Find the speed of rotation of gear $Y$ if gear $X$ rotates with speed $V$.
It is known that if gear $i$ is directly connected to gear $j$ and gear $i$ rotates with speed $V$, then gear $j$ will rotate with speed $-V A_i / A_j$, where the sign of rotation speed denotes the direction of rotation (so minus here denotes rotation in the opposite direction). You may also notice that gears can be blocked in some cases. This happens when some gear would have to rotate in different directions. If a gear is connected to any blocked gear, it is also blocked. For example, if three gears are connected to each other, this configuration can not rotate at all, and if we connect a fourth gear to these three, it will also be blocked and not rotate.
-----Input-----
- The first line of the input contains two space-separated integers $N$ and $M$.
- The second line contains $N$ space-separated integers $A_1, A_2, \dots, A_N$.
- The following $M$ lines describe queries. Each of these lines begins with an integer $T$ denoting the type of the current query.
- If $T = 1$, it is followed by a space and two space-separated integers $X$ and $C$.
- If $T = 2$, it is followed by a space and two space-separated integers $X$ and $Y$.
- If $T = 3$, it is followed by a space and three space-separated integers $X$, $Y$ and $V$.
-----Output-----
For each query of type 3, print a single line containing two integers separated by a slash '/' β the numerator and denominator of the rotation speed of the given gear expressed as an irreducible fraction (even if this speed is an integer), or $0$ if the gear does not rotate at all.
-----Constraints-----
- $1 \le N \le 10^5$
- $1 \le M \le 2\cdot 10^5$
- $6 \le A_i \le 10^6$ for each valid $i$
- $1 \le X, Y \le N$
- $1 \le C, V \le 10^6$
-----Subtasks-----
Subtask #1 (30 points):
- $N \le 2,000$
- $M \le 5,000$
Subtask #2 (70 points): original constraints
-----Example Input-----
4 10
6 8 10 13
3 1 2 2
2 1 2
3 1 2 3
2 2 3
1 1 7
3 1 3 10
2 3 1
3 1 3 2
2 1 4
3 1 4 6
-----Example Output-----
0
-9/4
7/1
0
0
-----Explanation-----
For the first query of type 3, there are no connections between gears, so the answer is $0$.
For the second query of type 3, we can calculate the rotation speed using the formula $-3\cdot\frac{6}{8} = \frac{-9}{4}$.
For the third query of type 3, we can use the formula twice, so the speed of the second gear is $-10\cdot\frac{7}{8} = -\frac{35}{4}$, and the speed of the third gear is $-(-\frac{35}{4})\frac{8}{10} = \frac{7}{1}$.
For the last query of type 3, all gears are blocked.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
class Dsu:
def __init__(self, v, s):
self.par = s
self.v = v
self.dr = [1] * v
self.zero = [False] * v
self.speed = []
for i in range(v):
self.speed.append([])
self.speed[i].append(i)
def find(self, i):
# if parent[i] == -1:
# return i
# else: return self.find_parent(parent, parent[i])
if i != self.par[i][0]:
org = self.par[i][0]
self.par[i][0] = self.find(self.par[i][0])
if self.zero[i] or self.zero[self.par[i][0]] or self.zero[org]:
self.zero[i] = self.zero[self.par[i][0]] = self.zero[org] = True
if org != self.par[i][0]:
self.speed[self.par[i][0]].append(i)
return self.par[i][0]
def union(self, x, y):
# def union(self, parent, x, y):
# x_set = self.find_parent(parent, x)
# y_set = self.find_parent(parent, y)
# parent[x_set] = y_set
self.rx = self.find(x)
self.ry = self.find(y)
self.sign = -self.dr[x] * self.dr[y]
if self.rx != self.ry:
if (self.par[self.rx][1]<self.par[self.ry][1]):
mx=self.ry
mn=self.rx
if (self.par[self.rx][1]>self.par[self.ry][1]):
mx=self.rx
mn=self.ry
if self.par[self.rx][1] != self.par[self.ry][1]:
self.par[mn][0] = mx
if self.zero[mn] or self.zero[mx] or self.zero[x] or self.zero[y]:
self.zero[mn] = self.zero[mx] = self.zero[x] = self.zero[y] = True
else:
for i in range(len(self.speed[mn])):
self.dr[self.speed[mn][i]] *= self.sign
org = self.par[self.speed[mn][i]][0]
if org != mx:
self.par[self.speed[mn][i]][0] = mx
self.speed[mx].append(self.speed[mn][i])
self.speed[mx].append(mn)
else:
self.par[self.ry][0] = self.rx
self.par[self.rx][1] += 1
if self.zero[self.rx] or self.zero[self.ry] or self.zero[x] or self.zero[y]:
self.zero[self.rx] = self.zero[self.ry] = self.zero[x] = self.zero[y] = True
else:
for i in range(len(self.speed[self.ry])):
self.dr[self.speed[self.ry][i]] *= self.sign
org = self.par[self.speed[self.ry][i]][0]
if org != self.rx:
self.par[self.speed[self.ry][i]][0] = self.rx
self.speed[self.rx].append(self.speed[self.ry][i])
self.speed[self.rx].append(self.ry)
else:
return
def optwo(x, y, D):
if (D.find(x) == D.find(y) and D.dr[x] == D.dr[y]):
D.zero[x] = D.zero[y] = True
D.union(x, y)
def gcd(a, b):
if a == 0:
return b
else:
return gcd(b % a, a)
def opthree(x, y, v, D):
if (D.find(x) != D.find(y)) or (D.zero[D.par[y][0]]):
print(0)
else:
g = gcd(v * speed[x], speed[y])
flag=(D.dr[x] * D.dr[y])//abs(D.dr[x] * D.dr[y])
print(str(flag * v * speed[x] // g) + "/" + str(speed[y] // g))
n, M = map(int, input().split())
speed = list(map(int, input().split()))
s = []
for i in range(n):
s.append([i, 0])
D = Dsu(n, s)
for i in range(M):
T = list(map(int, input().split()))
if (T[0] == 1):
speed[T[1] - 1] = T[2]
elif (T[0] == 2):
optwo(T[1] - 1, T[2] - 1, D)
elif (T[0] == 3):
opthree(T[1] - 1, T[2] - 1, T[3], D)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Chef works in a similar way to a travelling salesman β he always travels to new cities in order to sell his delicious dishes.
Today, Chef is planning to visit $N$ cities (numbered $1$ through $N$). There is a direct way to travel between each pair of cities. Each city has a specific temperature; let's denote the temperature in the $i$-th city by $C_i$. Chef has a fixed temperature tolerance $D$ with the following meaning: for each pair of cities $a$ and $b$, he may travel from city $a$ directly to city $b$ only if $|C_a-C_b| \le D$, otherwise he would catch a heavy flu because of the sudden change in temperature.
Chef starts from city $1$. Is he able to visit all $N$ cities in such a way that each city is visited exactly once?
Notes:
- Chef is not able to travel through a city without visiting it.
- City $1$ is visited at the beginning.
- It is not necessary to be able to travel directly to city $1$ from the last city Chef visits.
-----Input-----
- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
- The first line of each test case contains two space-separated integers $N$ and $D$.
- The second line contains $N$ space-separated integers $C_1, C_2, \ldots, C_N$.
-----Output-----
For each test case, print a single line containing the string "YES" (without quotes) if Chef can visit all cities or "NO" (without quotes) if he cannot.
-----Constraints-----
- $1 \le T \le 1,000$
- $2 \le N \le 10^5$
- $0 \le D \le 10^9$
- $0 \le C_i \le 10^9$ for each valid $i$
- the sum of $N$ over all test cases does not exceed $10^6$
-----Subtasks-----
Subtask #1 (20 points):
- $N \le 1,000$
- the sum of $N$ over all test cases does not exceed $10,000$
Subtask #2 (80 points): original constraints
-----Example Input-----
2
5 3
3 2 1 4 5
5 4
10 1 3 2 9
-----Example Output-----
YES
NO
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
# cook your dish here
def solution(b,n1,d):
first=b[0]
b.sort()
for j in range(n1-1):
if(a[j+1]-a[j]>d):
return "NO"
for j in range(n1):
if(b[j]==first):
pos=j
if(pos==0 or pos==n1-1):
return "YES"
rec=1
for j in range(pos-1,n1-2):
if(a[j+2]-a[j]>d):
rec=0
break
if(rec):
return "YES"
rec=1
for j in range(pos+1,1,-1):
if(a[j]-a[j-2]>d):
rec=0
break
if(rec):
return "YES"
else:
return "NO"
testcase=int(input())
for i in range(testcase):
n,d=list(map(int,input().split()))
a=list(map(int,input().split()))
print(solution(a,n,d))
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Maxim always goes to the supermarket on Sundays. Today the supermarket has a special offer of discount systems.
There are m types of discounts. We assume that the discounts are indexed from 1 to m. To use the discount number i, the customer takes a special basket, where he puts exactly q_{i} items he buys. Under the terms of the discount system, in addition to the items in the cart the customer can receive at most two items from the supermarket for free. The number of the "free items" (0, 1 or 2) to give is selected by the customer. The only condition imposed on the selected "free items" is as follows: each of them mustn't be more expensive than the cheapest item out of the q_{i} items in the cart.
Maxim now needs to buy n items in the shop. Count the minimum sum of money that Maxim needs to buy them, if he use the discount system optimally well.
Please assume that the supermarket has enough carts for any actions. Maxim can use the same discount multiple times. Of course, Maxim can buy items without any discounts.
-----Input-----
The first line contains integer m (1 β€ m β€ 10^5) β the number of discount types. The second line contains m integers: q_1, q_2, ..., q_{m} (1 β€ q_{i} β€ 10^5).
The third line contains integer n (1 β€ n β€ 10^5) β the number of items Maxim needs. The fourth line contains n integers: a_1, a_2, ..., a_{n} (1 β€ a_{i} β€ 10^4) β the items' prices.
The numbers in the lines are separated by single spaces.
-----Output-----
In a single line print a single integer β the answer to the problem.
-----Examples-----
Input
1
2
4
50 50 100 100
Output
200
Input
2
2 3
5
50 50 50 50 50
Output
150
Input
1
1
7
1 1 1 1 1 1 1
Output
3
-----Note-----
In the first sample Maxim needs to buy two items that cost 100 and get a discount for two free items that cost 50. In that case, Maxim is going to pay 200.
In the second sample the best strategy for Maxim is to buy 3 items and get 2 items for free using the discount. In that case, Maxim is going to pay 150.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
import sys
n_discounts = int(sys.stdin.readline())
discount_values = [int(x) for x in sys.stdin.readline().split()]
n_items = int(sys.stdin.readline())
item_values = [int(x) for x in sys.stdin.readline().split()]
min_discount_req = 10000000
for discount_value in discount_values:
min_discount_req = min(min_discount_req, discount_value)
item_values.sort(reverse=True)
index = 0
overall_price = 0
while index < n_items:
n_left = min(min_discount_req, n_items - index)
for i in range(n_left):
overall_price += item_values[index+i]
index += n_left + 2
print(overall_price)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
-----Problem Statement-----
Harry Potter has one biscuit and zero rupee in his pocket. He will perform the following operations exactly $K$ times in total, in the order he likes:
- Hit his pocket, which magically increases the number of biscuits by one.
- Exchange $A$ biscuits to $1$ rupee.
- Exchange $1$ rupee to $B$ biscuits.
Find the maximum possible number of biscuits in Harry's pocket after $K$ operations.
-----Input-----
Input is given in the following format:
K A B
-----Output-----
Print the maximum possible number of biscuits in Harry's pocket after $K$operations.
-----Constraints-----
- $1 \leq K, A, B \leq 10^9$
- $K$, $A$ and are integers.
-----Sample Input-----
4 2 6
-----Sample Output-----
7
-----EXPLANATION-----
The number of biscuits in Harry's pocket after $K$ operations is maximized as follows:
- Hit his pocket. Now he has $2$ biscuits and $0$ rupee.
- Exchange $2$ biscuits to $1$ rupee in his pocket .Now he has $0$ biscuits and $1$ rupee.
- Hit his pocket. Now he has $1$ biscuits and $1$ rupee.
- Exchange $1$ rupee to $6$ biscuits. his pocket. Now he has $7$ biscuits and $0$ rupee.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
K,A,B = map(int,input().split())
if A + 2 > B:
print(K + 1)
return
start = A - 1
K -= start
ans = K//2 * (B-A) + K%2 + start + 1
print(ans)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Most problems on CodeChef highlight chef's love for food and cooking but little is known about his love for racing sports. He is an avid Formula 1 fan. He went to watch this year's Indian Grand Prix at New Delhi. He noticed that one segment of the circuit was a long straight road. It was impossible for a car to overtake other cars on this segment. Therefore, a car had to lower down its speed if there was a slower car in front of it. While watching the race, Chef started to wonder how many cars were moving at their maximum speed.
Formally, you're given the maximum speed of N cars in the order they entered the long straight segment of the circuit. Each car prefers to move at its maximum speed. If that's not possible because of the front car being slow, it might have to lower its speed. It still moves at the fastest possible speed while avoiding any collisions. For the purpose of this problem, you can assume that the straight segment is infinitely long.
Count the number of cars which were moving at their maximum speed on the straight segment.
-----Input-----
The first line of the input contains a single integer T denoting the number of test cases to follow. Description of each test case contains 2 lines. The first of these lines contain a single integer N, the number of cars. The second line contains N space separated integers, denoting the maximum speed of the cars in the order they entered the long straight segment.
-----Output-----
For each test case, output a single line containing the number of cars which were moving at their maximum speed on the segment.
-----Example-----
Input:
3
1
10
3
8 3 6
5
4 5 1 2 3
Output:
1
2
2
-----Constraints-----
1 β€ T β€ 100
1 β€ N β€ 10,000
All speeds are distinct positive integers that fit in a 32 bit signed integer.
Each input file will not be larger than 4 MB (4,000,000,000 bytes) in size.
WARNING! The input files are very large. Use faster I/O.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
for _ in range(int(input())):
n = int(input())
l = list(map(int,input().split()))
ans = 1
l1 = l[0]
for i in range(1,n):
if l[i] <= l1:
l1 = l[i]
ans = ans + 1
print(ans)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
There is a beautiful garden of stones in Innopolis.
Its most beautiful place is the $n$ piles with stones numbered from $1$ to $n$.
EJOI participants have visited this place twice.
When they first visited it, the number of stones in piles was $x_1, x_2, \ldots, x_n$, correspondingly. One of the participants wrote down this sequence in a notebook.
They visited it again the following day, and the number of stones in piles was equal to $y_1, y_2, \ldots, y_n$. One of the participants also wrote it down in a notebook.
It is well known that every member of the EJOI jury during the night either sits in the room $108$ or comes to the place with stones. Each jury member who comes there either takes one stone for himself or moves one stone from one pile to another. We can assume that there is an unlimited number of jury members. No one except the jury goes to the place with stones at night.
Participants want to know whether their notes can be correct or they are sure to have made a mistake.
-----Input-----
The first line of the input file contains a single integer $n$, the number of piles with stones in the garden ($1 \leq n \leq 50$).
The second line contains $n$ integers separated by spaces $x_1, x_2, \ldots, x_n$, the number of stones in piles recorded in the notebook when the participants came to the place with stones for the first time ($0 \leq x_i \leq 1000$).
The third line contains $n$ integers separated by spaces $y_1, y_2, \ldots, y_n$, the number of stones in piles recorded in the notebook when the participants came to the place with stones for the second time ($0 \leq y_i \leq 1000$).
-----Output-----
If the records can be consistent output "Yes", otherwise output "No" (quotes for clarity).
-----Examples-----
Input
5
1 2 3 4 5
2 1 4 3 5
Output
Yes
Input
5
1 1 1 1 1
1 0 1 0 1
Output
Yes
Input
3
2 3 9
1 7 9
Output
No
-----Note-----
In the first example, the following could have happened during the night: one of the jury members moved one stone from the second pile to the first pile, and the other jury member moved one stone from the fourth pile to the third pile.
In the second example, the jury took stones from the second and fourth piles.
It can be proved that it is impossible for the jury members to move and took stones to convert the first array into the second array.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
n = int(input())
a = list(map(int, input().split()))
b = list(map(int, input().split()))
c = sum(a)
d = sum(b)
if c >= d:
print('Yes')
else:
print('No')
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Two players decided to play one interesting card game.
There is a deck of $n$ cards, with values from $1$ to $n$. The values of cards are pairwise different (this means that no two different cards have equal values). At the beginning of the game, the deck is completely distributed between players such that each player has at least one card.
The game goes as follows: on each turn, each player chooses one of their cards (whichever they want) and puts on the table, so that the other player doesn't see which card they chose. After that, both cards are revealed, and the player, value of whose card was larger, takes both cards in his hand. Note that as all cards have different values, one of the cards will be strictly larger than the other one. Every card may be played any amount of times. The player loses if he doesn't have any cards.
For example, suppose that $n = 5$, the first player has cards with values $2$ and $3$, and the second player has cards with values $1$, $4$, $5$. Then one possible flow of the game is:
The first player chooses the card $3$. The second player chooses the card $1$. As $3>1$, the first player gets both cards. Now the first player has cards $1$, $2$, $3$, the second player has cards $4$, $5$.
The first player chooses the card $3$. The second player chooses the card $4$. As $3<4$, the second player gets both cards. Now the first player has cards $1$, $2$. The second player has cards $3$, $4$, $5$.
The first player chooses the card $1$. The second player chooses the card $3$. As $1<3$, the second player gets both cards. Now the first player has only the card $2$. The second player has cards $1$, $3$, $4$, $5$.
The first player chooses the card $2$. The second player chooses the card $4$. As $2<4$, the second player gets both cards. Now the first player is out of cards and loses. Therefore, the second player wins.
Who will win if both players are playing optimally? It can be shown that one of the players has a winning strategy.
-----Input-----
Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 100$). The description of the test cases follows.
The first line of each test case contains three integers $n$, $k_1$, $k_2$ ($2 \le n \le 100, 1 \le k_1 \le n - 1, 1 \le k_2 \le n - 1, k_1 + k_2 = n$)Β β the number of cards, number of cards owned by the first player and second player correspondingly.
The second line of each test case contains $k_1$ integers $a_1, \dots, a_{k_1}$ ($1 \le a_i \le n$)Β β the values of cards of the first player.
The third line of each test case contains $k_2$ integers $b_1, \dots, b_{k_2}$ ($1 \le b_i \le n$)Β β the values of cards of the second player.
It is guaranteed that the values of all cards are different.
-----Output-----
For each test case, output "YES" in a separate line, if the first player wins. Otherwise, output "NO" in a separate line. You can print each letter in any case (upper or lower).
-----Example-----
Input
2
2 1 1
2
1
5 2 3
2 3
1 4 5
Output
YES
NO
-----Note-----
In the first test case of the example, there is only one possible move for every player: the first player will put $2$, the second player will put $1$. $2>1$, so the first player will get both cards and will win.
In the second test case of the example, it can be shown that it is the second player who has a winning strategy. One possible flow of the game is illustrated in the statement.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
q = int(input())
for z in range(q):
n, k1, k2 = map(int, input().split())
arr1 = list(map(int, input().split()))
arr2 = list(map(int, input().split()))
if max(arr1) > max(arr2):
print('YES')
else:
print('NO')
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Chef has $N$ markers. There is a cap on each marker. For each valid $i$, the $i$-th marker has colour $a_i$. Initially, for each valid $i$, the colour of the cap on the $i$-th marker is also $a_i$.
Chef wants to rearrange the caps in such a way that no marker has the same colour as its cap. (Obviously, each marker must have exactly one cap.) Can he do that? If he can, find one such way to rearrange the caps. If there are multiple solutions, you may find any one.
-----Input-----
- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
- The first line of each test case contains a single integer $N$.
- The second line contains $N$ space-separated integers $a_1, a_2, \ldots, a_N$.
-----Output-----
- For each test case:
- If Chef cannot successfully rearrange the caps, print a single line containing the string "No" (without quotes).
- Otherwise, print two lines. The first line should contain the string "Yes" (without quotes). The second line should contain $N$ space-separated integers describing a valid rearrangement of caps. For each valid $i$, the $i$-th of these integers should denote the final colour of the cap on the $i$-th marker.
-----Constraints-----
- $1 \le T \le 10$
- $1 \le N \le 10^5$
- $1 \le a_i \le 10^9$ for each valid $i$
-----Example Input-----
2
9
1 1 1 2 2 2 3 3 3
2
1 1
-----Example Output-----
Yes
2 2 2 3 3 3 1 1 1
No
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
# cook your dish here
from collections import Counter,defaultdict
for i in range(int(input())):
n=int(input())
arr=list(map(int,input().split()))
coun=Counter(arr)
check=True
for j in coun:
if coun[j]>n//2:
print("No")
check=False
break
if check==True:
print("Yes")
narr=sorted(arr)
dic=defaultdict()
j=0
for j in range(len(narr)):
if narr[j] not in dic:
dic[narr[j]]=j
ans=[0]*n
for j in range(len(arr)):
ans[j]=narr[(dic[arr[j]]+n//2)%n]
if coun[arr[j]]!=1:
dic[arr[j]]+=1
print(*ans)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
This problem is actually a subproblem of problem G from the same contest.
There are $n$ candies in a candy box. The type of the $i$-th candy is $a_i$ ($1 \le a_i \le n$).
You have to prepare a gift using some of these candies with the following restriction: the numbers of candies of each type presented in a gift should be all distinct (i. e. for example, a gift having two candies of type $1$ and two candies of type $2$ is bad).
It is possible that multiple types of candies are completely absent from the gift. It is also possible that not all candies of some types will be taken to a gift.
Your task is to find out the maximum possible size of the single gift you can prepare using the candies you have.
You have to answer $q$ independent queries.
If you are Python programmer, consider using PyPy instead of Python when you submit your code.
-----Input-----
The first line of the input contains one integer $q$ ($1 \le q \le 2 \cdot 10^5$) β the number of queries. Each query is represented by two lines.
The first line of each query contains one integer $n$ ($1 \le n \le 2 \cdot 10^5$) β the number of candies.
The second line of each query contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le n$), where $a_i$ is the type of the $i$-th candy in the box.
It is guaranteed that the sum of $n$ over all queries does not exceed $2 \cdot 10^5$.
-----Output-----
For each query print one integer β the maximum possible size of the single gift you can compose using candies you got in this query with the restriction described in the problem statement.
-----Example-----
Input
3
8
1 4 8 4 5 6 3 8
16
2 1 3 3 4 3 4 4 1 3 2 2 2 4 1 1
9
2 2 4 4 4 7 7 7 7
Output
3
10
9
-----Note-----
In the first query, you can prepare a gift with two candies of type $8$ and one candy of type $5$, totalling to $3$ candies.
Note that this is not the only possible solution β taking two candies of type $4$ and one candy of type $6$ is also valid.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
import sys
input = sys.stdin.readline
Q = int(input())
for _ in range(Q):
N = int(input())
A = [int(a) for a in input().split()]
X = {}
for a in A:
if a in X:
X[a] += 1
else:
X[a] = 1
Y = []
for x in X:
Y.append(X[x])
Y = sorted(Y)[::-1]
prev = Y[0] + 1
su = 0
for i in range(len(Y)):
ne = min(prev-1, Y[i])
if ne <= 0:
break
su += ne
prev = ne
print(su)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
You are given a string S constisting of uppercase Latin letters. Is it possible to reorder the characters in this string to get a string with prefix "LTIME" and suffix "EMITL"?
We remind you that a prefix of a string is any substring which contains its first character, while a suffix of a string is substring containing its last character.
-----Input-----
The first line contains a single integer T, denoting the number of testcases. The descriptions of T test cases follow.
The first and only line of the test case description has one non-empty string S consisting of uppercase Latin letters only.
-----Output-----
For each testcase output a single line containing the string "YES" (without quotes) if it's possible to reorder the characters to get the required prefix and suffix, or "NO" (without quotes) otherwise.
-----Constraints-----
- Subtask 1 (23 points) : 1 β€ T β€ 100, 1 β€ |S| β€ 9
- Subtask 2 (77 points) : 1 β€ T β€ 1000, 1 β€ |S| β€ 100
-----Example-----
Input:3
LTIMEAZAZAITLME
LLLTTTIIIMMMEEEAHA
LTIMEM
Output:YES
YES
NO
-----Explanation-----
Test case 1: we can permute the last 5 letters and get LTIMEAZAZAEMITL
Test case 2: we have 3 copies of each of the letters 'L', 'T', 'I', 'M', 'E' so we can leave 5 of them in the beginning and move 5 of them to the end.
Test case 3: we have only one letter 'L' so we can't make necessary prefix and suffix at the same time.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
# cook your dish here
from collections import Counter
for i in range(int(input())):
s=input().upper()
res=Counter(s)
if res["L"]>=2 and res["T"]>=2 and res["I"]>=2 and res["M"]>=2 :
if len(s)==9:
if res["E"] >=1 :
print("YES")
else:
print("NO")
elif len(s)>9:
if res["E"]>=2:
print("YES")
else:
print("NO")
else:
print("NO")
else:
print("NO")
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Salmon runs a fish delivery company in Fish City. Fish City has $N$ vertical roads numbered $1, 2, ..., N$ from left to right, each spaced 1 unit apart; similarly, there are $M$ horizontal roads numbered $1, 2, ..., M$ from bottom to top, each spaced 1 unit apart. We will denote the intersection between the $x$-th vertical road and the $y$-th horizontal road as $(x, y)$.
Salmon has to make $K$ deliveries, with the $i$-th delivery starting at $(x_i, y_i)$ and ending at $(x'_i, y'_i)$. He can also travel every road with speed $0.5$ (meaning it would take him $2$ units of time to travel $1$ unit of distance). However, Salmon can bribe the mayor of Fish City and make the mayor change exactly one horizontal road to a highway, meaning the speed on that road would increase to $1$.
He wants to choose a road to be a highway such that the sum of durations of all the deliveries is minimum possible. Help him find this minimum sum!
Note that each delivery starts exactly at $(x_i, y_i)$ and ends at $(x'_i, y'_i)$, i.e., we don't count the time taken to travel from $(x'_{i-1}, y'_{i-1})$ to $(x_i, y_i)$ in our answer.
-----Input:-----
The first line contains 3 integers, $N$, $M$ and $K$ ($1 \le N, M, K \le 10^5$).
The next $K$ lines describe deliveries. Each line contains 4 space-separated integers $x_i$, $y_i$, $x'_i$, $y'_i$ ($1 \le x_i, x'_i \le N$, $1 \le y_i, y'_i \le M$), describing the $i$-th delivery.
-----Output:-----
Print one integer -- the minimum sum of durations possible.
-----Subtasks-----
- Subtask 1 [17 points]: $y_i = y_{i-1}$ for all $i>0$.
- Subtask 2 [34 points]: $K \le 10$.
- Subtask 3 [49 points]: No additional constraints.
-----Sample Input 1:-----
5 4 3
2 3 4 1
1 4 5 2
3 3 5 3
-----Sample Output 1:-----
16
-----Explanation:-----
Salmon can turn the 3rd horizontal road into a highway.
- For the first delivery, we can go 2 units to the right taking 2 units of time, and 2 units down taking 4 units of time. The time taken is $2 + 4 = 6$.
- For the second delivery, we can go 1 unit down taking 2 units of time, 4 units right taking 4 units of time, and 1 unit down taking 2 units of time. The time taken is $2 + 4 + 2 = 8$.
- For the third delivery, we can go 2 units right taking 2 units of time.
Therefore, the total time taken is $6 + 8 + 2 = 16$.
-----Sample Input 2:-----
10 2 3
1 2 10 2
2 1 9 1
4 1 7 1
-----Sample Output 2:-----
23
-----Explanation:-----
Salmon can turn the 1st horizontal road into a highway.
- For the first delivery, we can go 1 unit down taking 2 units of time, 9 units right taking 9 units of time, and 1 unit up taking 2 units of time. The time taken is $2 + 9 + 2 = 13$.
- For the second delivery, we can go 7 units right taking 7 units of time.
- For the third delivery, we can go 3 units to the right taking 3 units of time.
Therefore, the total time taken is $13 + 7 + 3 = 23$.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
n,m,k=map(int, input().split())
a = []
check = [0]*m
while k!= 0:
x1,y1,x2,y2 =map(int,input().split())
a.append([x1,y1,x2,y2])
check[y1-1] += 1
check[y2-1] += 1
k-= 1
maxi = check.index(max(check))+1
sum = 0
k = 0
for i in range(len(a)):
x1,y1,x2,y2 = a[i]
if (y1 > maxi and y2 > maxi) or (y1<maxi and y2 < maxi):
sum+= abs(y2-y1)*2
sum += abs(x2-x1)*2
else:
if y1 != maxi:
k = abs(y1-maxi)
sum+= k*2
if x1 != x2:
k = abs(x2-x1)
sum += k
if y2 != maxi:
k = abs(y2-maxi)
sum+= k*2
print(sum)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
You like tracking airplane flights a lot. Specifically, you maintain history of an airplaneβs flight at several instants and record them in your notebook. Today, you have recorded N such records h1, h2, ..., hN, denoting the heights of some airplane at several instants. These records mean that airplane was first flying on height h1, then started changing its height to h2, then from h2 to h3 and so on. The airplanes are usually on cruise control while descending or ascending, so
you can assume that plane will smoothly increase/decrease its height from hi to hi + 1 with a constant speed. You can see that during this period, the airplane will cover all possible heights in the range [min(hi, hi+1), max(hi, hi+1)] (both inclusive). It is easy to see that the plane will be at all possible heights in the range exactly a single instant of time during this ascend/descend.
You are interested in finding the maximum integer K such that the plane was at some height exactly K times during the flight.
-----Input-----
There is a single test case.
First line of the input contains an integer N denoting the number of records of heights of the plane.
Second line contains N space separated integers denoting h1, h2, ..., hN.
-----Output-----
Output a single maximum integer K in one line, such that the plane was at some height exactly K times during the flight.
-----Constraints-----
- hi β hi+1
-----Subtasks-----
Subtask #1: (30 points)
- 1 β€ N β€ 1000
- 1 β€ hi β€ 1000
Subtask #2: (70 points)
- 1 β€ N β€ 105
- 1 β€ hi β€ 109
-----Example-----
Input:
5
1 2 3 2 3
Output:
3
-----Explanation-----
The flight can be draw as:
3 /\/
2 /
1
There are infinitely many heights at which the plane was 3 times during the flight, for example 2.5, 2.1. Notice that the plane was only 2 times at height 2. Moreover, there are no height at which the plane was more than 3 times, so the answer is 3.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
def f(n):
s = list(map(int, input().split()))
low = []
high = []
for i in range(n - 1):
low.append(min(s[i], s[i+1]))
high.append(max(s[i], s[i+1]))
low.sort()
high.sort()
curr = mx = 0
i = j = 0
n -= 1
while i < n and j < n:
if low[i] < high[j]:
i += 1
curr += 1
else:
j += 1
curr -= 1
mx = max(mx, curr)
return mx
n = int(input())
print(f(n))
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
There are $n$ lamps on a line, numbered from $1$ to $n$. Each one has an initial state off ($0$) or on ($1$).
You're given $k$ subsets $A_1, \ldots, A_k$ of $\{1, 2, \dots, n\}$, such that the intersection of any three subsets is empty. In other words, for all $1 \le i_1 < i_2 < i_3 \le k$, $A_{i_1} \cap A_{i_2} \cap A_{i_3} = \varnothing$.
In one operation, you can choose one of these $k$ subsets and switch the state of all lamps in it. It is guaranteed that, with the given subsets, it's possible to make all lamps be simultaneously on using this type of operation.
Let $m_i$ be the minimum number of operations you have to do in order to make the $i$ first lamps be simultaneously on. Note that there is no condition upon the state of other lamps (between $i+1$ and $n$), they can be either off or on.
You have to compute $m_i$ for all $1 \le i \le n$.
-----Input-----
The first line contains two integers $n$ and $k$ ($1 \le n, k \le 3 \cdot 10^5$).
The second line contains a binary string of length $n$, representing the initial state of each lamp (the lamp $i$ is off if $s_i = 0$, on if $s_i = 1$).
The description of each one of the $k$ subsets follows, in the following format:
The first line of the description contains a single integer $c$ ($1 \le c \le n$) Β β the number of elements in the subset.
The second line of the description contains $c$ distinct integers $x_1, \ldots, x_c$ ($1 \le x_i \le n$) Β β the elements of the subset.
It is guaranteed that: The intersection of any three subsets is empty; It's possible to make all lamps be simultaneously on using some operations.
-----Output-----
You must output $n$ lines. The $i$-th line should contain a single integer $m_i$ Β β the minimum number of operations required to make the lamps $1$ to $i$ be simultaneously on.
-----Examples-----
Input
7 3
0011100
3
1 4 6
3
3 4 7
2
2 3
Output
1
2
3
3
3
3
3
Input
8 6
00110011
3
1 3 8
5
1 2 5 6 7
2
6 8
2
3 5
2
4 7
1
2
Output
1
1
1
1
1
1
4
4
Input
5 3
00011
3
1 2 3
1
4
3
3 4 5
Output
1
1
1
1
1
Input
19 5
1001001001100000110
2
2 3
2
5 6
2
8 9
5
12 13 14 15 16
1
19
Output
0
1
1
1
2
2
2
3
3
3
3
4
4
4
4
4
4
4
5
-----Note-----
In the first example: For $i = 1$, we can just apply one operation on $A_1$, the final states will be $1010110$; For $i = 2$, we can apply operations on $A_1$ and $A_3$, the final states will be $1100110$; For $i \ge 3$, we can apply operations on $A_1$, $A_2$ and $A_3$, the final states will be $1111111$.
In the second example: For $i \le 6$, we can just apply one operation on $A_2$, the final states will be $11111101$; For $i \ge 7$, we can apply operations on $A_1, A_3, A_4, A_6$, the final states will be $11111111$.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
import sys
readline = sys.stdin.readline
class UF():
def __init__(self, num):
self.par = [-1]*num
self.weight = [0]*num
def find(self, x):
if self.par[x] < 0:
return x
else:
stack = []
while self.par[x] >= 0:
stack.append(x)
x = self.par[x]
for xi in stack:
self.par[xi] = x
return x
def union(self, x, y):
rx = self.find(x)
ry = self.find(y)
if rx != ry:
if self.par[rx] > self.par[ry]:
rx, ry = ry, rx
self.par[rx] += self.par[ry]
self.par[ry] = rx
self.weight[rx] += self.weight[ry]
return rx
N, K = list(map(int, readline().split()))
S = list(map(int, readline().strip()))
A = [[] for _ in range(N)]
for k in range(K):
BL = int(readline())
B = list(map(int, readline().split()))
for b in B:
A[b-1].append(k)
cnt = 0
T = UF(2*K)
used = set()
Ans = [None]*N
inf = 10**9+7
for i in range(N):
if not len(A[i]):
Ans[i] = cnt
continue
kk = 0
if len(A[i]) == 2:
x, y = A[i]
if S[i]:
rx = T.find(x)
ry = T.find(y)
if rx != ry:
rx2 = T.find(x+K)
ry2 = T.find(y+K)
sp = min(T.weight[rx], T.weight[rx2]) + min(T.weight[ry], T.weight[ry2])
if x not in used:
used.add(x)
T.weight[rx] += 1
if y not in used:
used.add(y)
T.weight[ry] += 1
rz = T.union(rx, ry)
rz2 = T.union(rx2, ry2)
sf = min(T.weight[rz], T.weight[rz2])
kk = sf - sp
else:
rx = T.find(x)
ry2 = T.find(y+K)
sp = 0
if rx != ry2:
ry = T.find(y)
rx2 = T.find(x+K)
sp = min(T.weight[rx], T.weight[rx2]) + min(T.weight[ry], T.weight[ry2])
if x not in used:
used.add(x)
T.weight[rx] += 1
if y not in used:
used.add(y)
T.weight[ry] += 1
rz = T.union(rx, ry2)
rz2 = T.union(rx2, ry)
sf = min(T.weight[rz], T.weight[rz2])
kk = sf - sp
else:
if S[i]:
x = A[i][0]
rx = T.find(x)
rx2 = T.find(x+K)
sp = min(T.weight[rx], T.weight[rx2])
T.weight[rx] += inf
sf = min(T.weight[rx], T.weight[rx2])
kk = sf - sp
else:
x = A[i][0]
rx = T.find(x)
rx2 = T.find(x+K)
sp = min(T.weight[rx], T.weight[rx2])
T.weight[rx2] += inf
if x not in used:
used.add(x)
T.weight[rx] += 1
sf = min(T.weight[rx], T.weight[rx2])
kk = sf-sp
Ans[i] = cnt + kk
cnt = Ans[i]
print('\n'.join(map(str, Ans)))
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Ganesh lives in Gopalmath. He is looking for Jojo. So he decides to collect Aadhar Card Information of all the citizens of India from UIDAI.
Someone told Ganesh that the sum of all the digits of Jojoβs Aadhar number is divisible by 10 and it is greater than zero. After finding all Aadhar numbers which are divisible by 10, Jojoβs Aadhar number is $N$th smallest Aadhar number. Hence, Ganesh wants to find Jojoβs Aadhar number which satisfies all of the above conditions. (In this chaotic world, Aadhar numbers can be any natural number.)
However, Guruji refused Ganesh to carry out this task, because he is weak in Maths. Therefore, Ganesh assigns this task to Paritoshbhai who possesses excellent Mathematical skills. Since Paritoshbhai is busy in his jewellery business, help him in this task.
-----Input:-----
- The first line of the input contains a single integer T denoting the number of test cases. The description of T test cases follows.
- The first and only line of each test case contains a single integer N.
-----Output:-----
For each test case, print a single line containing Aadhar number of Jojo.
-----Constraints-----
- $1 \leq T \leq 1000$
- $1 \leq N \leq 10^{100,000}$
-----Sample Input:-----
1
3
-----Sample Output:-----
37
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
for _ in range(int(input())):
N = input()
num = list(N)
s=0
for n in num:
if n.isnumeric():
s+=int(n)
#print(s)
x=(10-s%10)%10
print(int(N)*10+int(x))
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
You are given a string S consisting of lowercase English letters.
Determine whether we can turn S into a palindrome by repeating the operation of swapping two adjacent characters. If it is possible, find the minimum required number of operations.
-----Constraints-----
- 1 \leq |S| \leq 2 Γ 10^5
- S consists of lowercase English letters.
-----Input-----
Input is given from Standard Input in the following format:
S
-----Output-----
If we cannot turn S into a palindrome, print -1. Otherwise, print the minimum required number of operations.
-----Sample Input-----
eel
-----Sample Output-----
1
We can turn S into a palindrome by the following operation:
- Swap the 2-nd and 3-rd characters. S is now ele.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
import collections
class Bit():
def __init__(self, l):
self.size = l
self.bit = [0] * (self.size+1)
def sum(self, i):
s = 0
while i > 0:
s += self.bit[i]
i -= i & -i
return s
def add(self, i, x):
while i <= self.size:
self.bit[i] += x
i += i & -i
def __str__(self):
return str(self.bit)
S = str(input())
N = len(S)
index = collections.defaultdict(list)
for i, c in enumerate(S):
index[c].append(i)
ctr = N // 2
B = [0] * N
flag = 0
P = []
for c, k in list(index.items()):
cnt = len(k)
if cnt % 2:
if flag == 1:
print((-1))
return
flag = 1
B[k[cnt // 2]] = ctr + 1
for i in range(cnt // 2):
l, r = k[i], k[-(i+1)]
P.append((l, r))
P.sort()
for i, (l, r) in enumerate(P):
B[l], B[r] = i + 1, N - i
ans = 0
bit = Bit(N)
for i, b in enumerate(B):
ans += i - bit.sum(b)
bit.add(b, 1)
print(ans)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
A Little Elephant from the Zoo of Lviv likes lucky strings, i.e., the strings that consist only of the lucky digits 4 and 7.
The Little Elephant calls some string T of the length M balanced if there exists at least one integer X (1 β€ X β€ M) such that the number of digits 4 in the substring T[1, X - 1] is equal to the number of digits 7 in the substring T[X, M]. For example, the string S = 7477447 is balanced since S[1, 4] = 7477 has 1 digit 4 and S[5, 7] = 447 has 1 digit 7. On the other hand, one can verify that the string S = 7 is not balanced.
The Little Elephant has the string S of the length N. He wants to know the number of such pairs of integers (L; R) that 1 β€ L β€ R β€ N and the substring S[L, R] is balanced. Help him to find this number.
Notes.
Let S be some lucky string. Then
- |S| denotes the length of the string S;
- S[i] (1 β€ i β€ |S|) denotes the ith character of S (the numeration of characters starts from 1);
- S[L, R] (1 β€ L β€ R β€ |S|) denotes the string with the following sequence of characters: S[L], S[L + 1], ..., S[R], and is called a substring of S. For L > R we mean by S[L, R] an empty string.
-----Input-----
The first line of the input file contains a single integer T, the number of test cases. Each of the following T lines contains one string, the string S for the corresponding test case. The input file does not contain any whitespaces.
-----Output-----
For each test case output a single line containing the answer for this test case.
-----Constraints-----
1 β€ T β€ 10
1 β€ |S| β€ 100000
S consists only of the lucky digits 4 and 7.
-----Example-----
Input:
4
47
74
477
4747477
Output:
2
2
3
23
-----Explanation-----
In the first test case balance substrings are S[1, 1] = 4 and S[1, 2] = 47.
In the second test case balance substrings are S[2, 2] = 4 and S[1, 2] = 74.
Unfortunately, we can't provide you with the explanations of the third and the fourth test cases. You should figure it out by yourself. Please, don't ask about this in comments.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
x=eval(input())
for x in range(0,x):
ans=0
d=input()
a=0
cont=0
for i in range(0,len(d)):
a+=len(d)-i
if d[i]=='7':
ans+=1+cont
cont+=1
else:
cont=0
ans=a-ans
print(ans)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Chef's new hobby is painting, but he learned the fact that it's not easy to paint 2D pictures in a hard way, after wasting a lot of canvas paper, paint and of course time. From now on, he decided to paint 1D pictures only.
Chef's canvas is N millimeters long and is initially all white. For simplicity, colors will be represented by an integer between 0 and 105. 0 indicates white. The picture he is envisioning is also N millimeters long and the ith millimeter consists purely of the color Ci. Unfortunately, his brush isn't fine enough to paint every millimeter one by one. The brush is 3 millimeters wide and so it can only paint three millimeters at a time with the same color. Painting over the same place completely replaces the color by the new one. Also, Chef has lots of bottles of paints of each color, so he will never run out of paint of any color.
Chef also doesn't want to ruin the edges of the canvas, so he doesn't want to paint any part beyond the painting. This means, for example, Chef cannot paint just the first millimeter of the canvas, or just the last two millimeters, etc.
Help Chef by telling him whether he can finish the painting or not with these restrictions.
-----Input-----
The first line of the input contains an integer T denoting the number of test cases. The description of T test cases follows.
The first line of each test case contains a single integer N. The second line contains N space-separated integers C1, C2, ..., CN denoting the colors of Chef's painting.
-----Output-----
For each test case, output a single line containing either βYesβ or βNoβ (without quotes), denoting whether Chef can finish the painting or not.
-----Constraints-----
- 1 β€ T β€ 105
- 3 β€ N β€ 105
- The sum of the Ns over all the test cases in a single test file is β€ 5Γ105
- 1 β€ Ci β€ 105
-----Example-----
Input:3
4
1 5 5 5
4
1 1 1 5
3
5 5 2
Output:Yes
Yes
No
-----Explanation-----
Example case 1. Chef's canvas initially contains the colors [0,0,0,0]. Chef can finish the painting by first painting the first three millimeters with color 1, so the colors become [1,1,1,0], and then the last three millimeters with color 5 so that it becomes [1,5,5,5].
Example case 2. Chef's canvas initially contains the colors [0,0,0,0]. Chef can finish the painting by first painting the last three millimeters by color 5 so the colors become [0,5,5,5], and then the first three millimeters by color 1 so it becomes [1,1,1,5].
Example case 3. In this test case, Chef can only paint the painting as a whole, so all parts must have the same color, and the task is impossible.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
# cook your dish here
import sys
import math
def main(arr):
for i in range(1,len(arr)-1):
if arr[i]==arr[i-1] and arr[i]==arr[i+1]:
return "Yes"
return "No"
test=int(input())
for _ in range(test):
b=int(input())
arr=list(map(int,input().split()))
print(main(arr))
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Alexander is learning how to convert numbers from the decimal system to any other, however, he doesn't know English letters, so he writes any number only as a decimal number, it means that instead of the letter A he will write the number 10. Thus, by converting the number 475 from decimal to hexadecimal system, he gets 11311 (475 = 1Β·16^2 + 13Β·16^1 + 11Β·16^0). Alexander lived calmly until he tried to convert the number back to the decimal number system.
Alexander remembers that he worked with little numbers so he asks to find the minimum decimal number so that by converting it to the system with the base n he will get the number k.
-----Input-----
The first line contains the integer n (2 β€ n β€ 10^9). The second line contains the integer k (0 β€ k < 10^60), it is guaranteed that the number k contains no more than 60 symbols. All digits in the second line are strictly less than n.
Alexander guarantees that the answer exists and does not exceed 10^18.
The number k doesn't contain leading zeros.
-----Output-----
Print the number x (0 β€ x β€ 10^18)Β β the answer to the problem.
-----Examples-----
Input
13
12
Output
12
Input
16
11311
Output
475
Input
20
999
Output
3789
Input
17
2016
Output
594
-----Note-----
In the first example 12 could be obtained by converting two numbers to the system with base 13: 12 = 12Β·13^0 or 15 = 1Β·13^1 + 2Β·13^0.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
n=int(input())
s=input()
pw=[1]
last=1
for i in range(70):
if (last>1e19):
break
pw.append(last*n)
last=last*n
dp=[1e19]*100
for i in range(100):
dp[i]=[1e19]*100
dp[len(s)][0]=0
for i in range(len(s),-1,-1):
for power in range(0,len(pw)):
cur=''
for j in range(i-1,-1,-1):
cur=s[j]+cur
if (int(cur)>n or int(cur)*pw[power]>1e19):
break;
if ((cur[0]!='0' or len(cur)==1) and int(cur)<n):
dp[j][power+1]=min(dp[j][power+1],dp[i][power]+int(cur)*pw[power])
print(min(dp[0]))
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
You are given a sequence $A_1, A_2, \ldots, A_N$. Calculate the number of ways to remove a non-empty contiguous subsequence from it such that the resulting sequence is non-empty and strictly increasing.
-----Input-----
- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
- The first line of each test case contains a single integer $N$.
- The second line contains $N$ space-separated integers $A_1, A_2, \ldots, A_N$.
-----Output-----
For each test case, print a single line containing one integer β the number of ways.
-----Constraints-----
- $1 \le T \le 10$
- $1 \le N \le 10^5$
- $|A_i| \le 10^9$ for each valid $i$
-----Subtasks-----
Subtask #1 (40 points): $N \le 1,000$
Subtask #2 (60 points): original constraints
-----Example Input-----
2
3
1 1 2
4
2 4 3 5
-----Example Output-----
4
7
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
import bisect
def pre(a):
for p in range(n-1):
if(a[p]>=a[p+1]):
return p
return n-1
def suf(a):
for s in range(1,n):
if(a[n-s]<=a[n-s-1]):
return n-s
return 0
t=int(input())
for _ in range(t):
n=int(input())
a=list(map(int,input().split()))
p=pre(a)
s=suf(a)
b=a[s:n]
count=0
for i in range(p+1):
k=bisect.bisect(b,a[i])
k+=s
count+=n-k+1
if(s==0):
print((n*(n+1))//2-1)
else:
print(count+n-s)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
The chef is trying to solve some pattern problems, Chef wants your help to code it. Chef has one number K to form a new pattern. Help the chef to code this pattern problem.
-----Input:-----
- First-line will contain $T$, the number of test cases. Then the test cases follow.
- Each test case contains a single line of input, one integer $K$.
-----Output:-----
For each test case, output as the pattern.
-----Constraints-----
- $1 \leq T \leq 100$
- $1 \leq K \leq 100$
-----Sample Input:-----
2
2
4
-----Sample Output:-----
2
21
210
21
2
4
43
432
4321
43210
4321
432
43
4
-----EXPLANATION:-----
No need, else pattern can be decode easily.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
# cook your dish here
t=int(input())
for _ in range(t):
n = int(input())
for i in range(n+1):
b = n
for space in range(n-i):
print(" ",end="")
for j in range(i+1):
print(b,end="")
b-=1
print()
for l in range(n):
a = n
for j1 in range(0,l+1):
print(" ",end="")
for k in range(n-l):
print(a,end="")
a-=1
print()
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
You are given three strings $a$, $b$ and $c$ of the same length $n$. The strings consist of lowercase English letters only. The $i$-th letter of $a$ is $a_i$, the $i$-th letter of $b$ is $b_i$, the $i$-th letter of $c$ is $c_i$.
For every $i$ ($1 \leq i \leq n$) you must swap (i.e. exchange) $c_i$ with either $a_i$ or $b_i$. So in total you'll perform exactly $n$ swap operations, each of them either $c_i \leftrightarrow a_i$ or $c_i \leftrightarrow b_i$ ($i$ iterates over all integers between $1$ and $n$, inclusive).
For example, if $a$ is "code", $b$ is "true", and $c$ is "help", you can make $c$ equal to "crue" taking the $1$-st and the $4$-th letters from $a$ and the others from $b$. In this way $a$ becomes "hodp" and $b$ becomes "tele".
Is it possible that after these swaps the string $a$ becomes exactly the same as the string $b$?
-----Input-----
The input consists of multiple test cases. The first line contains a single integer $t$ ($1 \leq t \leq 100$) Β β the number of test cases. The description of the test cases follows.
The first line of each test case contains a string of lowercase English letters $a$.
The second line of each test case contains a string of lowercase English letters $b$.
The third line of each test case contains a string of lowercase English letters $c$.
It is guaranteed that in each test case these three strings are non-empty and have the same length, which is not exceeding $100$.
-----Output-----
Print $t$ lines with answers for all test cases. For each test case:
If it is possible to make string $a$ equal to string $b$ print "YES" (without quotes), otherwise print "NO" (without quotes).
You can print either lowercase or uppercase letters in the answers.
-----Example-----
Input
4
aaa
bbb
ccc
abc
bca
bca
aabb
bbaa
baba
imi
mii
iim
Output
NO
YES
YES
NO
-----Note-----
In the first test case, it is impossible to do the swaps so that string $a$ becomes exactly the same as string $b$.
In the second test case, you should swap $c_i$ with $a_i$ for all possible $i$. After the swaps $a$ becomes "bca", $b$ becomes "bca" and $c$ becomes "abc". Here the strings $a$ and $b$ are equal.
In the third test case, you should swap $c_1$ with $a_1$, $c_2$ with $b_2$, $c_3$ with $b_3$ and $c_4$ with $a_4$. Then string $a$ becomes "baba", string $b$ becomes "baba" and string $c$ becomes "abab". Here the strings $a$ and $b$ are equal.
In the fourth test case, it is impossible to do the swaps so that string $a$ becomes exactly the same as string $b$.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
for _ in range(int(input())):
a, b, c = input(), input(), input()
n = len(a)
ok = True
for i in range(n):
if c[i] not in [a[i], b[i]]:
ok = False
print('YES' if ok else 'NO')
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
You will be given m strings. For each of those strings, you need to count the total number of appearances of that string as substrings in all possible strings of length n containing only lower case English letters.
A string may appear in a string multiple times. Also, these appearances may overlap. All these must be counted separately. For example, aa appears thrice in the string aaacaa: aaacaa, aaacaa and aaacaa.
-----Input-----
- The first line contains one integer, T, the number of test cases. The description of each test case follows:
- The first line of each test case will contain two integers n and m.
- The ith of the next m lines will have one string in each line. All the strings will consist only of lower case English letters.
-----Output-----
- For each test case, print "Case x:" (without quotes. x is the test case number, 1-indexed) in the first line.
- Then print m lines. The ith line should contain the number of appearances of the ith string in all possible strings of length n. As the numbers can be very large, print the answers modulo 109+7.
-----Constraints-----
- 1 β€ T β€ 100
- 1 β€ n β€ 100000
- 1 β€ m β€ 1000
- 1 β€ Length of every string in input
- 1 β€ Total length of all strings in one test case β€ 5 * 105
- 1 β€ Total length of all strings in one test file β€ 5 * 106
-----Example-----
Input:
3
2 1
aa
2 1
d
12 3
cdmn
qweewef
qs
Output:
Case 1:
1
Case 2:
52
Case 3:
443568031
71288256
41317270
-----Explanation:-----
Testcase 1: aa is the only string of length 2 which contains aa as a substring. And it occurs only once. Hence the answer is 1.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
for _ in range(int(input())):
n,m=map(int,input().split())
print("Case "+str(_+1)+":")
for i in range(m):
s=input()
ls=len(s)
if ls>n:
print("0")
else:
k=(n-ls+1)
print((k*pow(26,n-ls,1000000007))%1000000007)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
You have a tree consisting of n vertices. You want to color each vertex of the tree in one of the k colors such that for any pair of vertices having same color, all the vertices belonging to the path joining them should also have same color. In other words, for any two vertices u, v with same color, all the vertices in the path joining them should also have color same as that of the u (or same as v, as u and v have same color).
Find out possible number of ways in which you can color the tree satisfying the above property. As the answer could be large, print your answer modulo 109 + 7.
-----Input-----
The first line of the input contains an integer T denoting the number of test cases. The description of T test cases follows.
For each test case, first line contains two space separated integers n, k denoting number of vertices in the tree and total number of colors, respectively
Each of the next n - 1 lines contain two space separated integers ui, vi, denoting that there is an edge between vertices ui and vi in the tree.
-----Output-----
For each test case, output a single line corresponding to number of ways of coloring the tree.
-----Constraints-----
- 1 β€ T β€ 50
- 1 β€ n, k β€ 50
- 1 β€ ui, vi β€ n
- ui β vi
-----Example-----
Input
3
3 2
1 2
2 3
3 1
1 2
2 3
4 3
1 2
2 3
2 4
Output:
6
1
39
-----Explanation-----
In the first example, You can color the vertices in the following 6 ways - {1, 1, 1}, {2, 2, 2}, {1, 2, 2}, {1, 1, 2}, {2, 1, 1}, {2, 2, 1}. Note that you can't color the tree in {1, 2, 1} as the vertices in the path connecting vertex 1 and 3, (i.e. 1, 2, 3) don't have same color. You can see that the color of 2nd vertex is not same as that of 1st and 3rd.
In the second example, Only possible coloring you can do is to color all the vertices with color 1.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
A = [0] * 100001
M = 1000000007
def nCk(n, k):
if k ==0 or k ==n:
return 1
r = (A[n-k]*A[k])%M
x = (A[n]*pow(r, M-2, M))%M
return x
for _ in range(int(input())):
n, k = list(map(int, input().split()))
for i in range(n-1):
u,v = input().split()
summ = 0
A[0] = 1
for i in range(1, len(A)):
A[i] = (i*A[i-1])%M
for i in range(min(n, k)):
b = nCk(k,i+1)
c = (nCk(n-1,i)*b)%M
c *= A[i+1]
summ += (c%M)
summ %= M
print(summ)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Farmer John has just given the cows a program to play with! The program contains two integer variables, x and y, and performs the following operations on a sequence a_1, a_2, ..., a_{n} of positive integers: Initially, x = 1 and y = 0. If, after any step, x β€ 0 or x > n, the program immediately terminates. The program increases both x and y by a value equal to a_{x} simultaneously. The program now increases y by a_{x} while decreasing x by a_{x}. The program executes steps 2 and 3 (first step 2, then step 3) repeatedly until it terminates (it may never terminate). So, the sequence of executed steps may start with: step 2, step 3, step 2, step 3, step 2 and so on.
The cows are not very good at arithmetic though, and they want to see how the program works. Please help them!
You are given the sequence a_2, a_3, ..., a_{n}. Suppose for each i (1 β€ i β€ n - 1) we run the program on the sequence i, a_2, a_3, ..., a_{n}. For each such run output the final value of y if the program terminates or -1 if it does not terminate.
-----Input-----
The first line contains a single integer, n (2 β€ n β€ 2Β·10^5). The next line contains n - 1 space separated integers, a_2, a_3, ..., a_{n} (1 β€ a_{i} β€ 10^9).
-----Output-----
Output n - 1 lines. On the i-th line, print the requested value when the program is run on the sequence i, a_2, a_3, ...a_{n}.
Please do not use the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use the cin, cout streams or the %I64d specifier.
-----Examples-----
Input
4
2 4 1
Output
3
6
8
Input
3
1 2
Output
-1
-1
-----Note-----
In the first sample For i = 1, x becomes $1 \rightarrow 2 \rightarrow 0$ and y becomes 1 + 2 = 3. For i = 2, x becomes $1 \rightarrow 3 \rightarrow - 1$ and y becomes 2 + 4 = 6. For i = 3, x becomes $1 \rightarrow 4 \rightarrow 3 \rightarrow 7$ and y becomes 3 + 1 + 4 = 8.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
n = int(input())
t = [0, 0] + list(map(int, input().split()))
a, b = [0] * (n + 1), [0] * (n + 1)
a[1] = b[1] = -1
def f(s, a, b, l):
nonlocal t
l.reverse()
j, n = 0, len(l)
while True:
s += t[l[j]]
a[l[j]] = s
j += 1
if j == n: return
s += t[l[j]]
b[l[j]] = s
j += 1
if j == n: return
def g(i, k):
nonlocal a, b
l = []
if k:
a[i] = -1
l.append(i)
i += t[i]
while True:
if i > n: return f(0, a, b, l)
if b[i] > 0: return f(b[i], a, b, l)
if b[i] == -1: return
b[i] = -1
l.append(i)
i -= t[i]
if i < 1: return f(0, b, a, l)
if a[i] > 0: return f(a[i], b, a, l)
if a[i] == -1: return
a[i] = -1
l.append(i)
i += t[i]
for i in range(2, n + 1):
if a[i] == 0: g(i, True)
if b[i] == 0: g(i, False)
for i in range(1, n):
if b[i + 1] > 0: t[i] = i + b[i + 1]
else: t[i] = -1
print('\n'.join(map(str, t[1: n])))
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Chef has $N$ axis-parallel rectangles in a 2D Cartesian coordinate system. These rectangles may intersect, but it is guaranteed that all their $4N$ vertices are pairwise distinct.
Unfortunately, Chef lost one vertex, and up until now, none of his fixes have worked (although putting an image of a point on a milk carton might not have been the greatest idea after allβ¦). Therefore, he gave you the task of finding it! You are given the remaining $4N-1$ points and you should find the missing one.
-----Input-----
- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
- The first line of each test case contains a single integer $N$.
- Then, $4N-1$ lines follow. Each of these lines contains two space-separated integers $x$ and $y$ denoting a vertex $(x, y)$ of some rectangle.
-----Output-----
For each test case, print a single line containing two space-separated integers $X$ and $Y$ β the coordinates of the missing point. It can be proved that the missing point can be determined uniquely.
-----Constraints-----
- $T \le 100$
- $1 \le N \le 2 \cdot 10^5$
- $|x|, |y| \le 10^9$
- the sum of $N$ over all test cases does not exceed $2 \cdot 10^5$
-----Subtasks-----
Subtask #1 (20 points):
- $T = 5$
- $N \le 20$
Subtask #2 (30 points): $|x|, |y| \le 10^5$
Subtask #3 (50 points): original constraints
-----Example Input-----
1
2
1 1
1 2
4 6
2 1
9 6
9 3
4 3
-----Example Output-----
2 2
-----Explanation-----
The original set of points are:
Upon adding the missing point $(2, 2)$, $N = 2$ rectangles can be formed:
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
for _ in range(int(input())):
n=int(input())
a=[]
b=[]
for i in range(4*n-1):
c,d=list(map(int,input().split()))
a.append(c)
b.append(d)
c1=0
c2=0
for i in a:
c1^=i
for i in b:
c2^=i
print(c1,c2)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Doubleville, a small town in Texas, was attacked by the aliens. They have abducted some of the residents and taken them to the a spaceship orbiting around earth. After some (quite unpleasant) human experiments, the aliens cloned the victims, and released multiple copies of them back in Doubleville. So now it might happen that there are 6 identical person named Hugh F. Bumblebee: the original person and its 5 copies. The Federal Bureau of Unauthorized Cloning (FBUC) charged you with the task of determining how many copies were made from each person. To help you in your task, FBUC have collected a DNA sample from each person. All copies of the same person have the same DNA sequence, and different people have different sequences (we know that there are no identical twins in the town, this is not an issue).
-----Input-----
The input contains several blocks of test cases. Each case begins with a line containing two integers: the number 1 <= n <= 20000 people, and the length 1 <= m <= 20 of the DNA sequences. The next n lines contain the DNA sequences: each line contains a sequence of m characters, where each character is either 'A', 'C', 'G' or 'T'.
The input is terminated by a block with n = m = 0 .
-----Output-----
For each test case, you have to output n lines, each line containing a single integer. The first line contains the number of different people that were not copied. The second line contains the number of people that were copied only once (i.e., there are two identical copies for each such person.) The third line contains the number of people that are present in three identical copies, and so on: the i -th line contains the number of persons that are present in i identical copies. For example, if there are 11 samples, one of them is from John Smith, and all the others are from copies of Joe Foobar, then you have to print '1' in the first and the tenth lines, and '0' in all the other lines.
-----Example-----
Input:
9 6
AAAAAA
ACACAC
GTTTTG
ACACAC
GTTTTG
ACACAC
ACACAC
TCCCCC
TCCCCC
0 0
Output:
1
2
0
1
0
0
0
0
0
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
def main():
while True:
[n, m] = [int(i) for i in input().split()]
if n == m and n == 0:
break
cache = {}
for i in range(n):
dna = input().rstrip('\n')
if dna in cache:
cache[dna] = 1 + cache[dna]
else:
cache[dna] = 1
c = [0 for i in range(n + 1)]
for dna in cache:
c[cache[dna]] = 1 + c[cache[dna]]
for i in range(1, n + 1):
print(c[i])
def __starting_point():
main()
__starting_point()
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
When Misha hits his favorite gym, he comes across an interesting problem with the barbell. In the gym, someone always leaves the weight plates in the strangest places you can imagine and sometime it's difficult to equip the barbell the way you want. Let's imagine that you have N weight plates placed in any order (remember that any gym has no more than K different types of weight plates and all weights are square-free). As a preliminary step towards solving this problem, Misha wants to simulate a simple gym, and for this purpose you have to deal with some queries:
- [1 I X] Set the weight of the ith weight plate to value X.
- [2 L R] Reverse the sequence of weight plates in the interval from L to R, where 1 β€ L β€ R β€ N.
- [3 L R W] Check the interval from L to R to find out if you can make the weight W using only weight plates on this interval. (Note: this type of query will appear no more than P times)
Please help Misha in solving this problem.
-----Input-----
First line of input contains the number of weight plates N, and number of queries Q. Next line contains N integers w1, w2, ..., wN, where wi is the weight of the ith weight plate. Next Q lines contain some queries described above.
-----Output-----
For all queries of the third type: print "Yes" if your check returns a positive outcome, and "No" otherwise.
-----Constraints-----
- 1 β€ N, W, Q β€ 105
- K β€ 10
- P β€ 1000
- All numbers in the input are positive integers and β€ 105.
- All the weights are square-free.
-----Subtasks-----
- Subtask 1: 1 β€ N β€ 103, 1 β€ W β€ 103, Q = 1 - 10 pts.
- Subtask 2: 1 β€ N β€ 103, 1 β€ W β€ 103, 1 β€ Q β€ 103, P β€ 100 - 15 pts
- Subtask 3: 1 β€ N β€ 104, 1 β€ W β€ 104, 1 β€ Q β€ 104, P β€ 300 - 25 pts.
- Subtask 4: 1 β€ N β€ 105, 1 β€ W β€ 105, 1 β€ Q β€ 105, K β€ 2 - 20 pts.
- Subtask 5: Original constraints - 30 pts.
-----Example-----First
Input:5 10
1 2 3 5 6
3 2 3 3
3 2 3 4
3 2 3 5
2 2 5
3 2 4 8
1 2 1
3 2 4 8
2 1 4
3 2 4 3
3 1 5 7
Output:Yes
No
Yes
Yes
Yes
No
YesSecond
Input:3 4
2013 2015 2017
3 1 3 4030
1 1 111
3 1 3 4030
3 1 2 111
Output:Yes
No
Yes
-----Explanation:-----First test explanation (step by step)
1 2 3 5 6
3 2 3 3 ([2, 3] 3=3 => Yes)
3 2 3 4 ([2, 3] can't make 4 => No)
3 2 3 5 ([2, 3] 2+3=5 => Yes)
2 2 5 (Reverse: [1, 6, 5, 3, 2])
3 2 4 8 ([6, 5, 3] 5+3=8 => Yes)
1 2 1 (Set: [1, 1, 5, 3, 2])
3 2 4 8 ([1, 5, 3] 5+3=8 => Yes)
2 1 4 (Reverse: [3, 5, 1, 1, 2])
3 2 4 3 ([5, 1, 1] can't make 3 => No)
3 1 5 7 ([3, 5, 1, 1, 2] 2+1+1+3=7 => Yes)
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
def fx(s,n,xsum):
sub=[[None for x in range(n+2)]for y in range(xsum+2)]
for i in range(n+1):
sub[0][i]=True
for i in range(1,xsum+1):
sub[i][0]=False
for i in range(1,xsum+1):
for j in range(1,n+1):
sub[i][j]=sub[i][j-1]
if i>=s[j-1]:
sub[i][j]=sub[i][j] or sub[i-s[j-1]][j-1]
if sub[xsum][n]:
print('Yes')
else:
print('No')
n,t=list(map(int,input().split()))
a=list(map(int,input().split()))
for _ in range(t):
q=list(map(int,input().split()))
if q[0]==1:
a[q[1]-1]=q[2]
continue
if q[0]==2:
w=a[q[1]-1:q[2]]
a[q[1]-1:q[2]]=w[::-1]
continue
if q[0]==3:
e=a[q[1]-1:q[2]]
if q[3]<min(e) or q[3]>sum(e):
print('No')
continue
if q[3] in e:
print('Yes')
continue
fx(e,len(e),q[3])
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Katya studies in a fifth grade. Recently her class studied right triangles and the Pythagorean theorem. It appeared, that there are triples of positive integers such that you can construct a right triangle with segments of lengths corresponding to triple. Such triples are called Pythagorean triples.
For example, triples (3, 4, 5), (5, 12, 13) and (6, 8, 10) are Pythagorean triples.
Here Katya wondered if she can specify the length of some side of right triangle and find any Pythagorean triple corresponding to such length? Note that the side which length is specified can be a cathetus as well as hypotenuse.
Katya had no problems with completing this task. Will you do the same?
-----Input-----
The only line of the input contains single integer n (1 β€ n β€ 10^9)Β β the length of some side of a right triangle.
-----Output-----
Print two integers m and k (1 β€ m, k β€ 10^18), such that n, m and k form a Pythagorean triple, in the only line.
In case if there is no any Pythagorean triple containing integer n, print - 1 in the only line. If there are many answers, print any of them.
-----Examples-----
Input
3
Output
4 5
Input
6
Output
8 10
Input
1
Output
-1
Input
17
Output
144 145
Input
67
Output
2244 2245
-----Note-----[Image]
Illustration for the first sample.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
n = int(input())
if n % 4 == 0:
temp = n // 4
m = temp * 3
k = temp * 5
elif n % 2 == 0:
n //= 2
m = n**2 // 2
k = m + 1
m *= 2
k *= 2
else:
m = n**2 // 2
k = m + 1
if 3 > n:
print("-1")
else:
print(m,k)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Writing light novels is the most important thing in Linova's life. Last night, Linova dreamed about a fantastic kingdom. She began to write a light novel for the kingdom as soon as she woke up, and of course, she is the queen of it.
[Image]Β
There are $n$ cities and $n-1$ two-way roads connecting pairs of cities in the kingdom. From any city, you can reach any other city by walking through some roads. The cities are numbered from $1$ to $n$, and the city $1$ is the capital of the kingdom. So, the kingdom has a tree structure.
As the queen, Linova plans to choose exactly $k$ cities developing industry, while the other cities will develop tourism. The capital also can be either industrial or tourism city.
A meeting is held in the capital once a year. To attend the meeting, each industry city sends an envoy. All envoys will follow the shortest path from the departure city to the capital (which is unique).
Traveling in tourism cities is pleasant. For each envoy, his happiness is equal to the number of tourism cities on his path.
In order to be a queen loved by people, Linova wants to choose $k$ cities which can maximize the sum of happinesses of all envoys. Can you calculate the maximum sum for her?
-----Input-----
The first line contains two integers $n$ and $k$ ($2\le n\le 2 \cdot 10^5$, $1\le k< n$) Β β the number of cities and industry cities respectively.
Each of the next $n-1$ lines contains two integers $u$ and $v$ ($1\le u,v\le n$), denoting there is a road connecting city $u$ and city $v$.
It is guaranteed that from any city, you can reach any other city by the roads.
-----Output-----
Print the only line containing a single integer Β β the maximum possible sum of happinesses of all envoys.
-----Examples-----
Input
7 4
1 2
1 3
1 4
3 5
3 6
4 7
Output
7
Input
4 1
1 2
1 3
2 4
Output
2
Input
8 5
7 5
1 7
6 1
3 7
8 3
2 1
4 5
Output
9
-----Note-----
[Image]
In the first example, Linova can choose cities $2$, $5$, $6$, $7$ to develop industry, then the happiness of the envoy from city $2$ is $1$, the happiness of envoys from cities $5$, $6$, $7$ is $2$. The sum of happinesses is $7$, and it can be proved to be the maximum one.
[Image]
In the second example, choosing cities $3$, $4$ developing industry can reach a sum of $3$, but remember that Linova plans to choose exactly $k$ cities developing industry, then the maximum sum is $2$.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
import sys
input = sys.stdin.readline
n, k = list(map(int, input().split()))
begin = [-1] * n
end = [-1] * n
hurt = [-1] * n
adj = [[] for i in range(n)]
for _ in range(n-1):
u ,v = list(map(int, input().split()))
adj[u-1].append(v-1)
adj[v-1].append(u-1)
hurt[0] = 1
begin[0] = 0
stack = [0]
curr = 1
while stack:
nex = stack[-1]
if adj[nex]:
v = adj[nex].pop()
if begin[v] == -1:
begin[v] = curr
curr += 1
stack.append(v)
hurt[v] = len(stack)
else:
end[nex] = curr
stack.pop()
desc = [end[i] - begin[i]-hurt[i] for i in range(n)]
desc.sort(reverse = True)
out = 0
for i in range(n - k):
out += desc[i]
print(out)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Problem description.
This problem is simple and will introduce you to the Dynamic Programming.
You will be given an array and a key value.
You will have to find out the occurrences of the key value depending upon the query using Brute Force and Top Down Dynamic Programming.
-----Brute-Force: -----
You will check the query, and calculate the occurrences.
-----DP: -----
You will check the query; check whether the memoized solution is already available.
If the memoized solution is available, no need to calculate the number of occurrences again.
If the memoized solution is not available, then calculate the number of occurrences and memoize it for future use.
-----Pseudo Code for DP:-----
countOccurences(key,from):
if (from = size of array) then
return 0
endif
if dp[from] is availabe then
return dp[from]
endif
if( array[from] == key) then
dp[from] = 1+countOccurences(key,from+1)
else
dp[from] = countOccurences(key,from+1)
endif
return dp[from]
-----Input:-----
The first line of input is the number of test cases (t).
The first line of each test case is the number of array elements (n).
The next will contain n space separated integers.
The next line will have the key element (k).
The next will have number of queries (q).
The next q lines will contain an integer A such that 0<=A < n.
You have to find out the number of occurrences from a to end of the array using both brute force and DP.
Everything will fit into the range of int.
-----Output:-----
For each test case, the output will have q lines with 3 space separated integers.
The first will be the number of occurrences, other will be the loop count/function calls,
using brute force and the last will be the number of loop count/function calls using DP.
-----Sample Input:-----
1
10
1 2 3 1 2 3 1 2 3 1
3
5
2
4
6
8
2
-----Sample output:-----
3 8 9
2 6 1
1 4 1
1 2 1
3 8 1
-----Explanation:-----
For the first query, we have to find the number of occurrences of 3 from index 2.
Using the brute force, the loop will check each element from index 2 to 9. Thus the loop count is 8.
Using DP, the method countOccurences(key,from) will be called like this :
countOccurences(3,2)->countOccurences(3,3)->countOccurences(3,4)->countOccurences(3,5)
->countOccurences(3,6)->countOccurences(3,7)->countOccurences(3,8)
->countOccurences(3,9)->countOccurences(3,10).
When the countOccurences(3,10) is called, it will return 0. Total 9 function calls.
For the second query, the brute force will do the same as above.
But the DP will check whether solution for countOccurences(3,4) is available or not.
As it was calculated while solving the first query, it wonβt solve it again and will directly give the answer.
Total 1 function calls.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
for __ in range(eval(input())):
x = eval(input())
a = list(map(int,input().split()))
key = eval(input())
query = eval(input())
maxvisited = x #maximum visted value
j = x-1
ans = []
val = 0
while j>=0:
if a[j]==key:
ans.append(val+1)
val = val +1
else: ans.append(val)
j-=1
ans.reverse()
#print ans
for ii in range(query):
W = eval(input())
print(ans[W], end=' ')
print(x-W, end=' ')
#print maxvisited, W
if maxvisited>W:
print(maxvisited-W+1)
maxvisited = W
else: print('1')
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
So the Chef has become health conscious and is now lifting weights at the gym. But its his first time so the trainer gives him a simple job to do.
He has been given a weight lifting rod and N heavy weights, each weighing 20, 21, .... , 2n-1. He has to stick each of the "N" weights on the rod, one after another, in such a way that the right side is never heavier than the left side. At each step he chooses one of the weights that has not yet been fixed on the rod, and fix it on either the left side of the rod or the right, until all of the weights have been placed.
Now help the chef and find out, in how many ways the chef can accomplish this?
-----Input-----
First line of input contains an integer T, the number of test cases. Then T test cases follow. Each line of test case contains one integer, N denoting the number of weights
-----Output-----
The output contains T lines, each containing an integer denoting all possible combinations
-----Example-----
Input:
3
2
5
18
Output:
3
945
221643095476699771875
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
t = int(input())
while(t>0):
n=int(input())
if(n<=0):
print(0)
fact=1
start=1
for i in range(1,n+1):
fact*=start
start+=2
print(fact)
t=t-1
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Coach Khaled is a swag teacher in HIT (Hag Institute of Technology). However, he has some obsession problems.
Recently, coach Khaled was teaching a course in building 8G networks using TV antennas and programming them with assembly. There are $N$ students (numbered $1$ through $N$) in his class; for some reason, this number is always a multiple of $4$. The final exam has finished and Khaled has all the scores of his $N$ students. For each valid $i$, the score of the $i$-th student is $A_i$; each score is an integer between $0$ and $100$. Currently, the score-grade distribution is as follows:
- grade D for score smaller than $60$
- grade C for score greater or equal to $60$, but smaller than $75$
- grade B for score greater or equal to $75$, but smaller than $90$
- grade A for score greater or equal to $90$
However, coach Khaled is not satisfied with this. He wants exactly $N/4$ students to receive each grade (A, B, C and D), so that the grades are perfectly balanced. The scores cannot be changed, but the boundaries between grades can. Therefore, he wants to choose three integers $x$, $y$ and $z$ and change the grade distribution to the following (note that initially, $x = 60$, $y = 75$ and $z = 90$):
- grade D for score smaller than $x$
- grade C for score greater or equal to $x$, but smaller than $y$
- grade B for score greater or equal to $y$, but smaller than $z$
- grade A for score greater or equal to $z$
Your task is to find thresholds $x$, $y$ and $z$ that result in a perfect balance of grades. If there are multiple solutions, choose the one with the maximum value of $x+y+z$ (because coach Khaled wants seem smarter than his students); it can be proved that there is at most one such solution. Sometimes, there is no way to choose the thresholds and coach Khaled would resign because his exam questions were low-quality.
-----Input-----
- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
- The first line of each test case contains a single integer $N$.
- The second line contains $N$ space-separated integers $A_1, A_2, \ldots, A_N$.
-----Output-----
For each test case, if there is no solution, print a single line containing the integer $-1$; otherwise, print a single line containing three space-separated integers $x$, $y$ and $z$.
-----Constraints-----
- $1 \le T \le 1,000$
- $4 \le N \le 100$
- $N$ is divisible by $4$
- $0 \le A_i \le 100$ for each valid $i$
- the sum of $N$ over all test cases does not exceed $5,000$
-----Subtasks-----
Subtask #1 (100 points): original constraints
-----Example Input-----
6
4
90 25 60 75
8
27 29 92 92 67 67 85 92
4
0 1 2 3
4
100 100 100 100
4
30 30 40 50
4
30 40 40 50
-----Example Output-----
60 75 90
-1
1 2 3
-1
-1
-1
-----Explanation-----
Example case 1: The default distribution is the correct one.
Example case 4: All students have the same score and grade, so there is no way to choose the thresholds and coach Khaled must resign.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
# cook your dish here
for _ in range(int(input())):
n = int(input())
k = n//4
# a,b,c = map(int,input().split())
a = sorted(map(int,input().split()))
a60 = (a[k-1],a[k])
a75 = (a[2*k-1],a[2*k])
a90 = (a[3*k-1],a[3*k])
if a60[0]==a60[1] or a75[0]==a75[1] or a90[0]==a90[1] :
print(-1)
else :
print(a60[1],a75[1],a90[1])
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Not everyone probably knows that Chef has younder brother Jeff. Currently Jeff learns to read.
He knows some subset of the letter of Latin alphabet. In order to help Jeff to study, Chef gave him a book with the text consisting of N words. Jeff can read a word iff it consists only of the letters he knows.
Now Chef is curious about which words his brother will be able to read, and which are not. Please help him!
-----Input-----
The first line of the input contains a lowercase Latin letter string S, consisting of the letters Jeff can read. Every letter will appear in S no more than once.
The second line of the input contains an integer N denoting the number of words in the book.
Each of the following N lines contains a single lowecase Latin letter string Wi, denoting the ith word in the book.
-----Output-----
For each of the words, output "Yes" (without quotes) in case Jeff can read it, and "No" (without quotes) otherwise.
-----Constraints-----
- 1 β€ |S| β€ 26
- 1 β€ N β€ 1000
- 1 β€ |Wi| β€ 12
- Each letter will appear in S no more than once.
- S, Wi consist only of lowercase Latin letters.
-----Subtasks-----
- Subtask #1 (31 point): |S| = 1, i.e. Jeff knows only one letter.
- Subtask #2 (69 point) : no additional constraints
-----Example-----
Input:act
2
cat
dog
Output:Yes
No
-----Explanation-----
The first word can be read.
The second word contains the letters d, o and g that aren't known by Jeff.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
knows=input()
n=eval(input())
while n!=0:
n=n-1
word=input()
for x in word:
ctr=0
for y in knows:
if x==y:ctr=ctr+1;break
if ctr==0:print('No');break
else: print('Yes')
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Pied Piper is a startup company trying to build a new Internet called Pipernet. Currently, they have $A$ users and they gain $X$ users everyday. There is also another company called Hooli, which has currently $B$ users and gains $Y$ users everyday.
Whichever company reaches $Z$ users first takes over Pipernet. In case both companies reach $Z$ users on the same day, Hooli takes over.
Hooli is a very evil company (like E-Corp in Mr. Robot or Innovative Online Industries in Ready Player One). Therefore, many people are trying to help Pied Piper gain some users.
Pied Piper has $N$ supporters with contribution values $C_1, C_2, \ldots, C_N$. For each valid $i$, when the $i$-th supporter contributes, Pied Piper gains $C_i$ users instantly. After contributing, the contribution value of the supporter is halved, i.e. $C_i$ changes to $\left\lfloor C_i / 2 \right\rfloor$. Each supporter may contribute any number of times, including zero. Supporters may contribute at any time until one of the companies takes over Pipernet, even during the current day.
Find the minimum number of times supporters must contribute (the minimum total number of contributions) so that Pied Piper gains control of Pipernet.
-----Input-----
- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
- The first line of each test case contains six space-separated integers $N$, $A$, $B$, $X$, $Y$ and $Z$.
- The second line contains $N$ space-separated integers $C_1, C_2, \ldots, C_N$ β the initial contribution values.
-----Output-----
For each test case, if Hooli will always gain control of Pipernet, print a single line containing the string "RIP" (without quotes). Otherwise, print a single line containing one integer β the minimum number of times supporters must contribute.
-----Constraints-----
- $1 \le T \le 10$
- $1 \le N \le 10^5$
- $1 \le A, B, X, Y, Z \le 10^9$
- $A, B < Z$
- $0 \le C_i \le 10^9$ for each valid $i$
-----Example Input-----
3
3 10 15 5 10 100
12 15 18
3 10 15 5 10 100
5 5 10
4 40 80 30 30 100
100 100 100 100
-----Example Output-----
4
RIP
1
-----Explanation-----
Example case 1: After $8$ days, Pied Piper will have $50$ users and Hooli will have $95$ users. Then, if each supporter contributes once, Pied Piper will also have $95$ users. After that, they still need $5$ more users, so supporter $3$ can contribute again, with $18/2 = 9$ more users. So the answer will be $4$.
Example case 2: There is no way to beat Hooli.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
# cook your dish here
import heapq as hq
from math import floor
for _ in range(int(input())):
n,a,b,x,y,z=map(int,input().split())
arr=[-int(i) for i in input().split()]
days=((z-b-1)//y)
ans=0
hq.heapify(arr)
curr=a+days*x
while curr<z :
u=hq.heappop(arr)
u=-u
if u==0 :
break
else:
curr+=u
ans+=1
hq.heappush(arr,-(u//2))
if curr>=z:
print(ans)
else:
print("RIP")
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
You are given integer $n$. You have to arrange numbers from $1$ to $2n$, using each of them exactly once, on the circle, so that the following condition would be satisfied:
For every $n$ consecutive numbers on the circle write their sum on the blackboard. Then any two of written on the blackboard $2n$ numbers differ not more than by $1$.
For example, choose $n = 3$. On the left you can see an example of a valid arrangement: $1 + 4 + 5 = 10$, $4 + 5 + 2 = 11$, $5 + 2 + 3 = 10$, $2 + 3 + 6 = 11$, $3 + 6 + 1 = 10$, $6 + 1 + 4 = 11$, any two numbers differ by at most $1$. On the right you can see an invalid arrangement: for example, $5 + 1 + 6 = 12$, and $3 + 2 + 4 = 9$, $9$ and $12$ differ more than by $1$.
[Image]
-----Input-----
The first and the only line contain one integer $n$ ($1 \le n \le 10^5$).
-----Output-----
If there is no solution, output "NO" in the first line.
If there is a solution, output "YES" in the first line. In the second line output $2n$ numbersΒ β numbers from $1$ to $2n$ in the order they will stay in the circle. Each number should appear only once. If there are several solutions, you can output any of them.
-----Examples-----
Input
3
Output
YES
1 4 5 2 3 6
Input
4
Output
NO
-----Note-----
Example from the statement is shown for the first example.
It can be proved that there is no solution in the second example.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
def main():
n = int(input())
ans = [0] * (2 * n)
for i in range(n):
a = 2 * i + 1
b = 2 * i + 2
if i & 1:
ans[i] = a
ans[i + n] = b
else:
ans[i] = b
ans[i + n] = a
ans *= 2
curr = sum(ans[:n])
mi = curr
ma = curr
for i in range(n, 4 * n):
curr -= ans[i - n]
curr += ans[i]
mi = min(mi, curr)
ma = max(ma, curr)
if ma - mi > 1:
print("NO")
else:
print("YES")
print(*ans[:2*n])
return 0
main()
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
You and your $n - 1$ friends have found an array of integers $a_1, a_2, \dots, a_n$. You have decided to share it in the following way: All $n$ of you stand in a line in a particular order. Each minute, the person at the front of the line chooses either the first or the last element of the array, removes it, and keeps it for himself. He then gets out of line, and the next person in line continues the process.
You are standing in the $m$-th position in the line. Before the process starts, you may choose up to $k$ different people in the line, and persuade them to always take either the first or the last element in the array on their turn (for each person his own choice, not necessarily equal for all people), no matter what the elements themselves are. Once the process starts, you cannot persuade any more people, and you cannot change the choices for the people you already persuaded.
Suppose that you're doing your choices optimally. What is the greatest integer $x$ such that, no matter what are the choices of the friends you didn't choose to control, the element you will take from the array will be greater than or equal to $x$?
Please note that the friends you don't control may do their choice arbitrarily, and they will not necessarily take the biggest element available.
-----Input-----
The input consists of multiple test cases. The first line contains a single integer $t$ ($1 \le t \le 1000$) Β β the number of test cases. The description of the test cases follows.
The first line of each test case contains three space-separated integers $n$, $m$ and $k$ ($1 \le m \le n \le 3500$, $0 \le k \le n - 1$) Β β the number of elements in the array, your position in line and the number of people whose choices you can fix.
The second line of each test case contains $n$ positive integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 10^9$) Β β elements of the array.
It is guaranteed that the sum of $n$ over all test cases does not exceed $3500$.
-----Output-----
For each test case, print the largest integer $x$ such that you can guarantee to obtain at least $x$.
-----Example-----
Input
4
6 4 2
2 9 2 3 8 5
4 4 1
2 13 60 4
4 1 3
1 2 2 1
2 2 0
1 2
Output
8
4
1
1
-----Note-----
In the first test case, an optimal strategy is to force the first person to take the last element and the second person to take the first element. the first person will take the last element ($5$) because he or she was forced by you to take the last element. After this turn the remaining array will be $[2, 9, 2, 3, 8]$; the second person will take the first element ($2$) because he or she was forced by you to take the first element. After this turn the remaining array will be $[9, 2, 3, 8]$; if the third person will choose to take the first element ($9$), at your turn the remaining array will be $[2, 3, 8]$ and you will take $8$ (the last element); if the third person will choose to take the last element ($8$), at your turn the remaining array will be $[9, 2, 3]$ and you will take $9$ (the first element).
Thus, this strategy guarantees to end up with at least $8$. We can prove that there is no strategy that guarantees to end up with at least $9$. Hence, the answer is $8$.
In the second test case, an optimal strategy is to force the first person to take the first element. Then, in the worst case, both the second and the third person will take the first element: you will end up with $4$.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
import sys
readline = sys.stdin.readline
class Segtree:
def __init__(self, A, intv, initialize = True, segf = max):
self.N = len(A)
self.N0 = 2**(self.N-1).bit_length()
self.intv = intv
self.segf = segf
if initialize:
self.data = [intv]*self.N0 + A + [intv]*(self.N0 - self.N)
for i in range(self.N0-1, 0, -1):
self.data[i] = self.segf(self.data[2*i], self.data[2*i+1])
else:
self.data = [intv]*(2*self.N0)
def update(self, k, x):
k += self.N0
self.data[k] = x
while k > 0 :
k = k >> 1
self.data[k] = self.segf(self.data[2*k], self.data[2*k+1])
def query(self, l, r):
L, R = l+self.N0, r+self.N0
s = self.intv
while L < R:
if R & 1:
R -= 1
s = self.segf(s, self.data[R])
if L & 1:
s = self.segf(s, self.data[L])
L += 1
L >>= 1
R >>= 1
return s
def binsearch(self, l, r, check, reverse = False):
L, R = l+self.N0, r+self.N0
SL, SR = [], []
while L < R:
if R & 1:
R -= 1
SR.append(R)
if L & 1:
SL.append(L)
L += 1
L >>= 1
R >>= 1
if reverse:
for idx in (SR + SL[::-1]):
if check(self.data[idx]):
break
else:
return -1
while idx < self.N0:
if check(self.data[2*idx+1]):
idx = 2*idx + 1
else:
idx = 2*idx
return idx - self.N0
else:
for idx in (SL + SR[::-1]):
if check(self.data[idx]):
break
else:
return -1
while idx < self.N0:
if check(self.data[2*idx]):
idx = 2*idx
else:
idx = 2*idx + 1
return idx - self.N0
Tc = int(readline())
Ans = [None]*Tc
for qu in range(Tc):
N, M, K = list(map(int, readline().split()))
A = list(map(int, readline().split()))
Ai = A[::-1]
table = [None]*M
for i in range(M):
j = (M-1)-i
table[i] = max(A[i], Ai[j])
inf = 10**9+7
T = Segtree(table, inf, initialize = True, segf = min)
ans = min(table)
K = min(K, M-1)
R = M-1-K
for ki in range(K+1):
ans = max(ans, T.query(ki, ki+R+1))
Ans[qu] = ans
print('\n'.join(map(str, Ans)))
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
This is another problem about Indraneel's library. His library has one long shelf. His books are numbered and he identifies the books by their number. Each book has a distinct number.
He has lost many books, since many of his friends borrow his books and never bother to return them. He does not want to lose any more books and has decided to keep a record of all books that he lends to his friends. To make the task of borrowing a book a little difficult, he has given the following instructions to his friends: when they borrow a book, they must record in a register its position from the left among the books currently on the shelf.
Suppose there are $5$ books in the library and they are arranged as follows:
261421532614215326 \quad 1 \quad 42 \quad 15 \quad 3
If someone walks in and borrows the book $42$, then he will record $3$ in the register because this book is the third from the left on the shelf. Now the shelf looks like this:
26115326115326 \quad 1 \quad 15 \quad 3
If the next person borrow the book $3$, he writes down $4$ in the register since this is currently the fourth book from the left on the shelf, and so on.
Indraneel knows the initial arrangement of the books in his library at the time that he introduced the register system. After a while he examines his register and would like to know which books have been borrowed. Your task is to write a program to help Indraneel solve this problem.
-----Input:-----
The first line of the input contains a single integer $M$ indicating the number of books in Indraneel's library. The next line contains $M$ distinct positive integers describing the sequence in which the books are arranged on the library shelf. The third line of input contains a single integer $N$ indicating the number of entries in the register. This, in turn, is followed by $N$ lines (lines $4$ to $N+3$), each containing one positive integer. The integer on line $3+i$ indicates the position from left of the book ith book borrowed. (You may assume that the number on line $3+i$ is at most $M-i+1$.)
-----Output:-----
$N$ lines with one positive integer on each line. The number on line $i$ is the book borrowed by the ith borrower.
-----Constraints:-----
- $1 \leq M \leq 1000000$.
- $1 \leq N \leq 4000$.
-----Sample Input-----
5
26 1 42 15 3
2
3
4
-----Sample Output-----
42
3
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
def bookList():
numBooks=int(input())
bookNum=[int(x) for x in input().split()]
takenBooks=int(input())
for i in range(takenBooks):
takenBookPos=(int(input()))
a=bookNum[takenBookPos-1]
print(a)
bookNum.remove(a)
bookList()
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Mysterious Chefland⦠Recently, Chef realised that Discuss, the educational system of Chefland, is out of date. Therefore, he is trying to find ways to update the infrastructure in the country. One possible way is to move all materials from Discuss to Discourse.
Chef will have access to Discourse if his knowledge and power become exactly equal to $N$ and $M$ respectively. Initially, he has power $1$ and knowledge $1$.
Chef can perform actions of the following types to improve his skills:
- solve a problem β increase his knowledge by $X$
- do a push-up β increase his power by $Y$
- install ShareChat to keep in touch with friends β increase both knowledge and power by $1$
Chef can only install ShareChat at most once. The remaining actions may be performed any number of times and the actions may be performed in any order.
Help Chef find out whether it is possible to move from Discuss to Discourse.
-----Input-----
- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
- The first and only line of each test case contains four space-separated integers $N$, $M$, $X$ and $Y$.
-----Output-----
For each test case, print a single line containing the string "Chefirnemo" if it is possible to reach the required knowledge and power or "Pofik" if it is impossible.
-----Constraints-----
- $1 \le T \le 1,000$
- $1 \le N, M, X, Y \le 10^9$
-----Subtasks-----
Subtask #1 (30 points): $1 \le N, M, X, Y \le 100$
Subtask #2 (70 points): original constraints
-----Example Input-----
5
2 2 1 2
11 10 5 9
11 11 5 9
12 11 5 9
1 2 1 100
-----Example Output-----
Chefirnemo
Chefirnemo
Pofik
Chefirnemo
Pofik
-----Explanation-----
Example case 2: We add $Y=9$ once to the power to get power $10$. We add $X=5$ twice to the knowledge to get knowledge $11$.
Example case 3: We can see that it is impossible to reach power $M=11$ no matter which or how many operations we do. Note that the ShareChat operation will increase both knowledge and power by $1$, and hence it will still be impossible to attain the given values of knowledge and power at the same time.
Example case 4: We can reach knowledge $11$ and power $10$ like in example case 2, the only difference is that we also use the ShareChat operation to increase both by $1$.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
t = input()
t = int(t)
for _ in range(t):
n, m, x, y = input().split()
n = int(n)
m = int(m)
x = int(x)
y = int(y)
n -= 1
m -= 1
flag = 0
if n % x == 0 and m % y == 0:
flag = 1
n -= 1
m -= 1
if n >= 0 and m >= 0:
if n % x == 0 and m % y == 0:
flag = 1
if flag == 1:
print("Chefirnemo")
else:
print("Pofik")
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
As we all know, Max is the best video game player among her friends. Her friends were so jealous of hers, that they created an actual game just to prove that she's not the best at games. The game is played on a directed acyclic graph (a DAG) with n vertices and m edges. There's a character written on each edge, a lowercase English letter.
[Image]
Max and Lucas are playing the game. Max goes first, then Lucas, then Max again and so on. Each player has a marble, initially located at some vertex. Each player in his/her turn should move his/her marble along some edge (a player can move the marble from vertex v to vertex u if there's an outgoing edge from v to u). If the player moves his/her marble from vertex v to vertex u, the "character" of that round is the character written on the edge from v to u. There's one additional rule; the ASCII code of character of round i should be greater than or equal to the ASCII code of character of round i - 1 (for i > 1). The rounds are numbered for both players together, i.Β e. Max goes in odd numbers, Lucas goes in even numbers. The player that can't make a move loses the game. The marbles may be at the same vertex at the same time.
Since the game could take a while and Lucas and Max have to focus on finding Dart, they don't have time to play. So they asked you, if they both play optimally, who wins the game?
You have to determine the winner of the game for all initial positions of the marbles.
-----Input-----
The first line of input contains two integers n and m (2 β€ n β€ 100, $1 \leq m \leq \frac{n(n - 1)}{2}$).
The next m lines contain the edges. Each line contains two integers v, u and a lowercase English letter c, meaning there's an edge from v to u written c on it (1 β€ v, u β€ n, v β u). There's at most one edge between any pair of vertices. It is guaranteed that the graph is acyclic.
-----Output-----
Print n lines, a string of length n in each one. The j-th character in i-th line should be 'A' if Max will win the game in case her marble is initially at vertex i and Lucas's marble is initially at vertex j, and 'B' otherwise.
-----Examples-----
Input
4 4
1 2 b
1 3 a
2 4 c
3 4 b
Output
BAAA
ABAA
BBBA
BBBB
Input
5 8
5 3 h
1 2 c
3 1 c
3 2 r
5 1 r
4 3 z
5 4 r
5 2 h
Output
BABBB
BBBBB
AABBB
AAABA
AAAAB
-----Note-----
Here's the graph in the first sample test case:
[Image]
Here's the graph in the second sample test case:
[Image]
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
def mat(shape, inital_val=None):
if len(shape) > 1:
return [mat(shape[1:], inital_val) for _ in range(shape[0])]
else:
return [inital_val] * shape[0]
def main():
n, m = [int(x) for x in input().split()]
graph = [{} for _ in range(n)]
for _ in range(m):
v, u, c = input().split()
graph[int(v) - 1][int(u) - 1] = c
winner_table = mat([n, n, 26])
def get_winner(u, v, char_to_beat):
"""
Args:
u: The position of current turn's player.
v: The position of next turn's player.
char_to_beat: The character played in the previous round.
Returns:
'A' if current turn's player wins, 'B' otherwise.
"""
char_idx = ord(char_to_beat) - ord('a')
if not winner_table[u][v][char_idx]:
winner = 'B'
for w, c in list(graph[u].items()):
if c >= char_to_beat and get_winner(v, w, c) == 'B':
winner = 'A'
break
winner_table[u][v][char_idx] = winner
return winner_table[u][v][char_idx]
for i in range(n):
print(''.join(get_winner(i, j, 'a') for j in range(n)))
def __starting_point():
main()
__starting_point()
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
You are given two matrices $A$ and $B$. Each matrix contains exactly $n$ rows and $m$ columns. Each element of $A$ is either $0$ or $1$; each element of $B$ is initially $0$.
You may perform some operations with matrix $B$. During each operation, you choose any submatrix of $B$ having size $2 \times 2$, and replace every element in the chosen submatrix with $1$. In other words, you choose two integers $x$ and $y$ such that $1 \le x < n$ and $1 \le y < m$, and then set $B_{x, y}$, $B_{x, y + 1}$, $B_{x + 1, y}$ and $B_{x + 1, y + 1}$ to $1$.
Your goal is to make matrix $B$ equal to matrix $A$. Two matrices $A$ and $B$ are equal if and only if every element of matrix $A$ is equal to the corresponding element of matrix $B$.
Is it possible to make these matrices equal? If it is, you have to come up with a sequence of operations that makes $B$ equal to $A$. Note that you don't have to minimize the number of operations.
-----Input-----
The first line contains two integers $n$ and $m$ ($2 \le n, m \le 50$).
Then $n$ lines follow, each containing $m$ integers. The $j$-th integer in the $i$-th line is $A_{i, j}$. Each integer is either $0$ or $1$.
-----Output-----
If it is impossible to make $B$ equal to $A$, print one integer $-1$.
Otherwise, print any sequence of operations that transforms $B$ into $A$ in the following format: the first line should contain one integer $k$ β the number of operations, and then $k$ lines should follow, each line containing two integers $x$ and $y$ for the corresponding operation (set $B_{x, y}$, $B_{x, y + 1}$, $B_{x + 1, y}$ and $B_{x + 1, y + 1}$ to $1$). The condition $0 \le k \le 2500$ should hold.
-----Examples-----
Input
3 3
1 1 1
1 1 1
0 1 1
Output
3
1 1
1 2
2 2
Input
3 3
1 0 1
1 0 1
0 0 0
Output
-1
Input
3 2
0 0
0 0
0 0
Output
0
-----Note-----
The sequence of operations in the first example: $\begin{matrix} 0 & 0 & 0 & & 1 & 1 & 0 & & 1 & 1 & 1 & & 1 & 1 & 1 \\ 0 & 0 & 0 & \rightarrow & 1 & 1 & 0 & \rightarrow & 1 & 1 & 1 & \rightarrow & 1 & 1 & 1 \\ 0 & 0 & 0 & & 0 & 0 & 0 & & 0 & 0 & 0 & & 0 & 1 & 1 \end{matrix}$
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
n, m = map(int, input().split())
A = [list(map(int, input().split())) for _ in range(n)]
B = [[0] * m for _ in range(n)]
ans = []
for i in range(n - 1):
for j in range(m - 1):
if A[i][j] == 1 and A[i + 1][j] == 1 and A[i][j + 1] == 1 and A[i + 1][j + 1] == 1:
B[i][j] = 1
B[i + 1][j] = 1
B[i][j + 1] = 1
B[i + 1][j + 1] = 1
ans.append([i + 1, j + 1])
if A == B:
print(len(ans))
for a, b in ans:
print(a, b)
else:
print(-1)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
You are given a sequence $A_1, A_2, \ldots, A_N$. For each valid $i$, the star value of the element $A_i$ is the number of valid indices $j < i$ such that $A_j$ is divisible by $A_i$.
Chef is a curious person, so he wants to know the maximum star value in the given sequence. Help him find it.
-----Input-----
- The first line of the input contains a single integer $T$ which denotes the number of test cases.
- The first line of each test case contains a single integer $N$ .
- The second line of each test case contains $N$ space-separated integers $A_1, A_2, \ldots, A_N$.
-----Output-----
For each test case, print a single line containing one integer β the maximum star value.
-----Constraints-----
- $1 \le T \le 10$
- $1 \le N \le 10^5$
- $1 \le A_i \le 10^6$ for each valid $i$
- Sum of $N$ over all test cases does not exceed $100,000$.
-----Subtasks-----
Subtask #1 (20 points): sum of $N$ over all test cases does not exceed $5,000$
Subtask #2 (80 points): original constraints
-----Example Input-----
1
7
8 1 28 4 2 6 7
-----Example Output-----
3
-----Explanation-----
$A_5 = 2$ divides $4$, $28$ and $8$, so its star value is $3$. There is no element with a higher star value.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
T = int(input())
for _ in range(T):
n = int(input())
arr = list(map(int, input().split()))
a = [0 for _ in range(max(arr)+1)]
star_val = []
for i in range(len(arr)):
j = 1
val = 0
while j*arr[i] <= len(a):
val += a[j*arr[i]-1]
j += 1
star_val.append(val)
a[arr[i]-1] += 1
print(max(star_val))
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Chef has a cubic die with 6 faces kept on an infinite plane. Each face has a distinct integer in the range [1,6] written on it, but the exact arrangement of the numbers on the faces of the die is unknown to Chef. Curiosity gets the better of Chef and he wants to find out o(1), o(2), ..., o(6), where o(i) is the number written opposite to the number i.
Chef performs the following N-1 steps to learn the exact arrangement of the numbers on the die. In the i-th step, Chef pushes the die in some direction (there are 4 possible directions), and the die rolls 90o in this direction. The picture below demonstrates a die and the result that it produced after rolling in each of the 4 directions respectively. For this die, we have o(1)=4, o(2)=5, o(3)=6, o(4)=1, o(5)=2, o(6)=3.
Chef records N numbers A1, A2, ..., AN, where Ai is the number written on the top of the die before the i-th step. However, the information on the direction in which he pushes the die each time are lost. Can you help him determine the arrangement of 1-6? You need to output o(1), o(2), ..., o(6). If there are multiple solutions, output any one of them.
-----
Input-----
- The first line of input contains a single integer T, the number of test cases.
- Each test case consists of two lines.
- The first line contains an integer N, and the second line contains N space-separated integers A1, A2, ..., AN.
-----
Output-----
For each test case, output one line. If a possible solution exists, then output 6 space-separated integers o(1), o(2), ..., o(6); otherwise, output -1.
-----
Constraints-----
- 1 β€ T, N β€ 500
- 1 β€ Ai β€ 6
Subtask #1 (17 points):
- N β€ 2
Subtask #2 (83 points):
- original constraints
-----
Example-----
Input:
4
9
1 3 4 6 1 3 4 6 1
10
1 2 1 3 1 4 1 5 1 6
6
1 2 3 4 5 6
4
1 3 3 1
Output:
2 1 6 5 4 3
-1
4 5 6 1 2 3
-1
-----
Explanation-----
Example case 1: See below.
Example case 2: You can prove that there's no solution.
Example case 3: The solution is not unique. 3 5 1 6 2 4 is another valid solution.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
from itertools import permutations
def solve(n,a):
ans=[]
for des in desire:
check=1
for i in range(n-1):
if (a[i]==a[i+1]):
return [-1]
if a[i+1]==des[a[i]-1]:
check=0
break
if check:
ans=des
break
if ans:
return ans
return [-1]
per=permutations([1,2,3,4,5,6])
desire=[]
for p in per:
check=1
for i in range(1,7):
if p[i-1]==i:
check=0
break
if check:
doublecheck=1
for i in range(6):
if p[p[i]-1]!=i+1:
doublecheck=0
break
if doublecheck:
desire.append(p)
#print(desire)
for _ in range(int(input())):
n=int(input())
a=list(map(int,input().split( )))
print(*solve(n,a))
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Given a string consisting of only lowercase English alphabets, your task is to find the smallest palindromic substring.
In case there are multiple palindromic substrings of the same length present, print the lexicographically smallest substring.
Formally, a substring is a contiguous sequence of characters within a string. So in a string "abcdef", "abc" is a substring whereas "adf" is not a substring.
A palindrome is a word, phrase, or sequence that reads the same backwards as forwards, e.g. madam or mom.
-----Input:-----
- First-line will contain $T$, the number of test cases. Then the test cases follow.
- Each test case contains of two lines of input, two integers.
- First, we have a single integer $N$ which signifies the length of the substring.
- Next, we have a string of length $N$ that only has lowercase English alphabets.
-----Output:-----
For each testcase, output in a single line the shortest palindromic substring.
-----Constraints-----
- $1 \leq T \leq 100$
- $2 \leq N \leq 10^5$
-----Sample Input:-----
2
2
zy
1
cd
-----Sample Output:-----
y
c
-----EXPLANATION:-----
There are only two possibilities. "z" and "y". Since both of them have the same length. We print the lexicographically smaller substring which is y.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
# cook your dish here
T = int(input())
for t in range(T):
N = int(input())
s = sorted(list(str(input())))
print(s[0])
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Little Elephant is playing a game with arrays. He is given an array A0, A1, ..., ANβ1 of N integers. And then Q queries are given, each containing an integer K. He has to tell how many subarrays satisfy the condition: the function foo returns K when it is applied to the subarray.
In this problem, a subarray is defined as a sequence of continuous elements Ai, Ai+1, ..., Aj where 0 β€ i β€ j β€ Nβ1. The function foo, when applied to an array, returns the minimum of all the elements in the array.
For example, foo returns 5 when it is applied to the array [7, 5, 10, 7, 5, 8]. Please note that the subarrays Ai, Ai+1, ..., Aj and Ak, Ak+1, ..., Al are different if and only if i β k or j β l in this problem.
-----Input-----
The first line of input contains N, denoting the size of the array. The next line contains N space separated integers A0, A1, ..., ANβ1, denoting the array. Then the next line contains Q, denoting the number of queries. Each query consists of one integer per line, denoting K.
-----Output-----
For each query, print the required number of subarrays.
-----Constraints-----
- 1 β€ N β€ 50
- 1 β€ Ai β€ 1000000 (106)
- 1 β€ Q β€ 10
- 1 β€ K β€ 1000000 (106)
-----Example-----
Input:
5
4 1 2 3 4
4
3
4
6
1
Output:
2
2
0
8
-----Explanation-----
Query 1. Only the two subarrays [3, 4] and [3] satisfy.
Query 2. Again only the two subarrays [4] and [4] satisfy. Please note that these subarrays (A0 and A4) are considered different.
Query 3. No subarray satisfies.
Query 4. The eight subarrays [4, 1], [4, 1, 2], [4, 1, 2, 3], [4, 1, 2, 3, 4], [1], [1, 2], [1, 2, 3] and [1, 2, 3, 4] satisfy.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
import sys
import math
def main(arr,k):
ans=0
for i in range(len(arr)):
curr_min=float('inf')
for j in range(i,len(arr)):
curr_min=min(curr_min,arr[j])
if curr_min==k:
ans+=1
return ans
n=int(input())
arr=list(map(int,input().split()))
for i in range(int(input())):
print(main(arr,int(input())))
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Write a program to find the remainder when an integer A is divided by an integer B.
-----Input-----
The first line contains an integer T, the total number of test cases. Then T lines follow, each line contains two Integers A and B.
-----Output-----
For each test case, find the remainder when A is divided by B, and display it in a new line.
-----Constraints-----
- 1 β€ T β€ 1000
- 1 β€ A,B β€ 10000
-----Example-----
Input
3
1 2
100 200
40 15
Output
1
100
10
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
number = int(input())
for i in range(number):
x = list(map(int, input().split(' ')))
print(x[0]%x[1])
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
"Humankind cannot gain anything without first giving something in return. To obtain, something of equal value must be lost. That is alchemy's first law of Equivalent Exchange. In those days, we really believed that to be the world's one, and only truth."
-- Alphonse Elric
Now, here we have an equivalent exchange law for triangles which states that two right-angled isosceles triangles of the same color can be made into a square of the same color using Alchemy.
You are given N$N$ right-angled isosceles colored triangles numbered from 1$1$ to N$N$. For each triangle, the two equal sides have a length of 1$1$ unit. The Color of i$i$-th triangle is given by Ci$C_i$.
To create a tower, we choose some consecutive (2Γk)+1$2 \times k)+1$ triangles for any kβ₯0$k \geq 0$. We then pick some 2Γk$2 \times k$ of them (these need not be consecutive), and form k$k$ pairs of triangles such that both triangles in pair have the same color. Also, each of the 2Γk$2 \times k$ should be in exactly one pair. Then the two triangles in each pair are joined using Alchemy (following the law of equivalent exchange for triangles) to form squares and these k$k$ squares are placed one upon other. The one remaining triangle is placed as a roof to the tower. This results in a tower of the height of k$k$.
Find the maximum height of the tower that can be formed.
In other words, you should select the largest consecutive segment of triangles, such that you can form a tower using every single one of those triangles. In particular, you leave out one triangle, which will form the roof, and the other triangles should all be paired up such that both triangles in a pair have the same colour.
-----Input:-----
- The first line contains T$T$, the number of test cases. Then the test cases follow.
- For every test case, the first line contains N$N$ denoting the number of triangles.
- For every test case, the second line contains N$N$ space-separated integers Ci$C_{i}$ denoting the color of the triangles. ( 1β€iβ€N$1 \leq i \leq N$).
-----Output:-----
For every test case, output a single integer denoting the maximum height of the tower that can be formed.
-----Constraints-----
- 1β€Tβ€100$1 \leq T \leq 100$
- 1β€Nβ€105$1 \leq N \leq 10^{5}$
- 1β€Ciβ€30$1 \leq C_{i} \leq 30$
- Sum of N$N$ over all test cases doesn't exceed 5Γ105$5\times 10^{5}$
-----Sample Input:-----
4
14
5 4 2 2 3 2 1 3 2 7 4 9 9 9
3
1 2 1
3
1 1 1
5
1 2 3 4 1
-----Sample Output:-----
3
1
1
0
-----EXPLANATION:-----
- #1$1$: The subarray [2,2,3,2,1,3,2]$[2, 2, 3, 2, 1, 3, 2]$ results in a tower of height 3$3$.
- #2$2$: The subarray [1,2,1]$[ 1, 2, 1 ]$ results in a tower of height 1$1$.
- #3$3$: The subarray [1,1,1]$[ 1, 1, 1 ]$ results in a tower of height 1$1$.
- #4$4$: The subarrays [1]$[ 1 ]$, [2]$[ 2 ]$ , [3]$[ 3 ]$, [4]$[ 4 ]$ and [1]$[ 1 ]$ all results in a tower of height 0$0$.
The above tower is possible by subarray [2,2,3,2,1,3,2]$[2, 2, 3, 2, 1, 3, 2]$ resulting in a height of 3$3$ in test case 1$1$.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
for i in range(int(input())):
n = int(input())
c = list(map(int, input().split()))
d = {}
d[0] = -1
parity = 0
ans = 0
for i in range(n):
parity ^= 1 << (c[i]-1)
for t in range(30):
x = parity^(1<<t)
if(x in d.keys()):
ans = max(ans, i - d[x])
if parity not in d.keys():
d[parity] = i
print(ans//2)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Chef has a number N, Cheffina challenges the chef to check the divisibility of all the permutation of N by 3. If any of the permutations is divisible by 3 then print 1 else print 0.
-----Input:-----
- First-line will contain $T$, the number of test cases. Then the test cases follow.
- Each test case contains a single line of input, two integers $N$.
-----Output:-----
For each test case, output in a single line answer 1 or 0.
-----Constraints-----
- $1 \leq T \leq 10^6$
- $1 \leq N \leq 10^6$
-----Sample Input:-----
2
18
308
-----Sample Output:-----
1
0
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
from sys import *
input=stdin.readline
for u in range(int(input())):
s=int(input())
if(s%3==0):
print(1)
else:
print(0)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
In this problem you are given a sequence of $N$ positive integers $S[1],S[2],\dots,S[N]$. In addition you are given an integer $T$, and your aim is to find the number of quadruples $(i,j,k,l)$, such that $1 \le i < j < k < l \le N$, and $S[i] + S[j] + S[k] + S[l] = T$. That is, the number of ways of picking four numbers from the sequence summing up to $T$.
-----Constraints:-----
For all test cases,
- $1 \le N \le 5000$
- $1 \le T \le 10^6$
- $1 \le S[i] \le 10^9$, for all $i$.
Subtask $1:10\%$
It is guaranteed that $N \le 50$.
Subtask $2:50\%$
It is guaranteed that $N \le 300$.
Subtask $3:40\%$
No additional guarantees.
-----Input Format:-----
There is only one line of input with $N+2$ space separated integers. The first two integers are $N$ and $T$. The next $N$ integers are $S[1],S[2],\dots,S[N]$.
-----Output Format:-----
A single integer which is the number of valid quadruples.
-----Sample Input 1:-----
6 20 3 1 1 2 5 10
-----Sample Output 1:-----
1
-----Explanation 1:-----
The quadruple $(1,4,5,6)$ is valid because $S[1]+S[4]+S[5]+S[6]=3+2+5+10=20$. You can check that no other quadruple is valid and hence the answer is $1$.
-----Sample Input 2:-----
6 13 1 2 3 4 5 4
-----Sample Output 2:-----
3
-----Explanation 2:-----
You can verify that the only quadruples that are valid are $(2,3,4,6),(1,3,4,5)$ and $(1,3,5,6)$. Thus, the answer is $3$.
-----Note:-----
As the answer might be large, please use 64 bit integers (long long int in
C/C++ and long in Java) instead of 32 bit int.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
# cook your dish here
from itertools import combinations
a = list(map(int, input().split()))
n = a[0]
t = a[1]
q = list(combinations(a[2:], 4))
total = 0
for i in q:
if sum(i) == t:
total += 1
print(total)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
You are given an array of $n$ integers: $a_1, a_2, \ldots, a_n$. Your task is to find some non-zero integer $d$ ($-10^3 \leq d \leq 10^3$) such that, after each number in the array is divided by $d$, the number of positive numbers that are presented in the array is greater than or equal to half of the array size (i.e., at least $\lceil\frac{n}{2}\rceil$). Note that those positive numbers do not need to be an integer (e.g., a $2.5$ counts as a positive number). If there are multiple values of $d$ that satisfy the condition, you may print any of them. In case that there is no such $d$, print a single integer $0$.
Recall that $\lceil x \rceil$ represents the smallest integer that is not less than $x$ and that zero ($0$) is neither positive nor negative.
-----Input-----
The first line contains one integer $n$ ($1 \le n \le 100$)Β β the number of elements in the array.
The second line contains $n$ space-separated integers $a_1, a_2, \ldots, a_n$ ($-10^3 \le a_i \le 10^3$).
-----Output-----
Print one integer $d$ ($-10^3 \leq d \leq 10^3$ and $d \neq 0$) that satisfies the given condition. If there are multiple values of $d$ that satisfy the condition, you may print any of them. In case that there is no such $d$, print a single integer $0$.
-----Examples-----
Input
5
10 0 -7 2 6
Output
4
Input
7
0 0 1 -1 0 0 2
Output
0
-----Note-----
In the first sample, $n = 5$, so we need at least $\lceil\frac{5}{2}\rceil = 3$ positive numbers after division. If $d = 4$, the array after division is $[2.5, 0, -1.75, 0.5, 1.5]$, in which there are $3$ positive numbers (namely: $2.5$, $0.5$, and $1.5$).
In the second sample, there is no valid $d$, so $0$ should be printed.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
n=int(input())
ar=list(map(int,input().split()))
pos=0
neg=0
for a in ar:
if(a>0):pos+=1
elif a<0:neg+=1
if(pos*2>=n):
print(1)
elif neg*2>=n:
print(-1)
else:
print(0)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Chef loves triangles. But the chef is poor at maths. Given three random lengths Chef wants to find if the three sides form a right-angled triangle or not. Can you help Chef in this endeavour?
-----Input:-----
- First-line will contain $T$, the number of test cases. Then the test cases follow.
- Each test case contains a single line of input, three Integers $A,B and C$
-----Output:-----
For each test case, output in a single line "YES" if it is possible to form a triangle using the given numbers or "NO" if it is not possible to form a triangle.
-----Constraints-----
- $1 \leq T \leq 1000000$
- $0 \leq A,B,C \leq 100$
-----Sample Input:-----
2
3 4 5
1 3 4
-----Sample Output:-----
YES
NO
-----EXPLANATION:-----
3,4,5 forms a right-angled triangle. 1, 3 and 4 does not form a right-angled triangle.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
# cook your dish here
def check(a,b,c):
if (a==0) or (b==0) or (c==0):
return "NO"
else:
i=3
while(i>0):
if (a*a)==(b*b)+(c*c):
return "YES"
else:
t=a
a=b
b=c
c=t
i-=1
return "NO"
try:
for _ in range(int(input())):
a,b,c=map(int,input().split())
print(check(a,b,c))
except:
print(e)
pass
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Just to remind, girls in Arpa's land are really nice.
Mehrdad wants to invite some Hoses to the palace for a dancing party. Each Hos has some weight w_{i} and some beauty b_{i}. Also each Hos may have some friends. Hoses are divided in some friendship groups. Two Hoses x and y are in the same friendship group if and only if there is a sequence of Hoses a_1, a_2, ..., a_{k} such that a_{i} and a_{i} + 1 are friends for each 1 β€ i < k, and a_1 = x and a_{k} = y.
[Image]
Arpa allowed to use the amphitheater of palace to Mehrdad for this party. Arpa's amphitheater can hold at most w weight on it.
Mehrdad is so greedy that he wants to invite some Hoses such that sum of their weights is not greater than w and sum of their beauties is as large as possible. Along with that, from each friendship group he can either invite all Hoses, or no more than one. Otherwise, some Hoses will be hurt. Find for Mehrdad the maximum possible total beauty of Hoses he can invite so that no one gets hurt and the total weight doesn't exceed w.
-----Input-----
The first line contains integers n, m and w (1 β€ n β€ 1000, $0 \leq m \leq \operatorname{min}(\frac{n \cdot(n - 1)}{2}, 10^{5})$, 1 β€ w β€ 1000)Β β the number of Hoses, the number of pair of friends and the maximum total weight of those who are invited.
The second line contains n integers w_1, w_2, ..., w_{n} (1 β€ w_{i} β€ 1000)Β β the weights of the Hoses.
The third line contains n integers b_1, b_2, ..., b_{n} (1 β€ b_{i} β€ 10^6)Β β the beauties of the Hoses.
The next m lines contain pairs of friends, the i-th of them contains two integers x_{i} and y_{i} (1 β€ x_{i}, y_{i} β€ n, x_{i} β y_{i}), meaning that Hoses x_{i} and y_{i} are friends. Note that friendship is bidirectional. All pairs (x_{i}, y_{i}) are distinct.
-----Output-----
Print the maximum possible total beauty of Hoses Mehrdad can invite so that no one gets hurt and the total weight doesn't exceed w.
-----Examples-----
Input
3 1 5
3 2 5
2 4 2
1 2
Output
6
Input
4 2 11
2 4 6 6
6 4 2 1
1 2
2 3
Output
7
-----Note-----
In the first sample there are two friendship groups: Hoses {1, 2} and Hos {3}. The best way is to choose all of Hoses in the first group, sum of their weights is equal to 5 and sum of their beauty is 6.
In the second sample there are two friendship groups: Hoses {1, 2, 3} and Hos {4}. Mehrdad can't invite all the Hoses from the first group because their total weight is 12 > 11, thus the best way is to choose the first Hos from the first group and the only one from the second group. The total weight will be 8, and the total beauty will be 7.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
f = lambda: map(int, input().split())
n, m, w = f()
wb = [(0, 0)] + list(zip(f(), f()))
t = list(range(n + 1))
def g(x):
if x == t[x]: return x
t[x] = g(t[x])
return t[x]
for i in range(m):
x, y = f()
x, y = g(x), g(y)
if x != y: t[y] = x
p = [[] for j in range(n + 1)]
for i in range(1, n + 1): p[g(i)].append(i)
d = [1] + [0] * w
for q in p:
if len(q) > 1:
WB = [wb[i] for i in q]
SW = sum(q[0] for q in WB)
SB = sum(q[1] for q in WB)
for D in range(w, -1, -1):
if d[D]:
if D + SW <= w: d[D + SW] = max(d[D + SW], d[D] + SB)
for W, B in WB:
if D + W <= w: d[D + W] = max(d[D + W], d[D] + B)
elif len(q) == 1:
W, B = wb[q[0]]
for D in range(w - W, -1, -1):
if d[D]: d[D + W] = max(d[D + W], d[D] + B)
print(max(d) - 1)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Chef has an array A consisting of N elements. He wants to find number of pairs of non-intersecting segments [a, b] and [c, d] (1 β€ a β€ b < c β€ d β€ N) such there is no number that occurs in the subarray {Aa, Aa+1, ... , Ab} and {Ac, Ac+1, ... , Ad} simultaneously.
Help Chef to find this number.
-----Input-----
- The first line of the input contains an integer T denoting the number of test cases. The description of T test cases follows.
- The first line of each test case contains a single integer N denoting the number of elements in the array.
- The second line contains N space-separated integers A1, A2, ..., AN.
-----Output-----
- For each test case, output a single line containing one integer - number of pairs of non-intersecting segments.
-----Constraints-----
- 1 β€ T β€ 5
- 1 β€ N β€ 1000
- 1 β€ Ai β€ 109
-----Subtasks-----Subtask 1 (7 points)
- 1 β€ N β€ 20Subtask 2 (34 points)
- 1 β€ N β€ 300Subtask 3 (59 points)
- Original constraints
-----Example-----
Input:
2
3
1 2 3
4
1 2 1 2
Output:
5
4
-----Explanation-----
Example case 1.
All possible variants are correct: {[1, 1], [2, 2]}, {[1, 1], [2, 3]}, {[1, 2], [3, 3]}, {[2, 2], [3, 3]}, {[1,1], [3, 3]}.
Example case 2.
Correct segments: {[1, 1], [2, 2]}, {[1, 1], [4, 4]}, {[2, 2], [3, 3]}, {[3, 3], [4, 4]}.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
t=int(input())
for q in range(t):
n=int(input())
x=list(map(int,input().split()))
dic={}
dic2={}
for i in range(n):
dic2[x[i]]=1
#print dic2
if len(dic2)==n:
n+=2
print((n*(n-1)*(n-2)*(n-3))/24)
continue
counter=0
for i in range(n-1):
if x[i] in dic:
dic[x[i]]+=1
else:
dic[x[i]]=1
for j in range(i,n-1):
if x[j] in dic:
dic[x[j]]+=1
else:
dic[x[j]]=1
for p in range(j+1,n):
if x[p] in dic:
continue;
for q in range(p,n):
if x[q] in dic:
break
counter+=1
#print i,j,p,q
dic.clear()
print(counter)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
One day n friends gathered together to play "Mafia". During each round of the game some player must be the supervisor and other n - 1 people take part in the game. For each person we know in how many rounds he wants to be a player, not the supervisor: the i-th person wants to play a_{i} rounds. What is the minimum number of rounds of the "Mafia" game they need to play to let each person play at least as many rounds as they want?
-----Input-----
The first line contains integer n (3 β€ n β€ 10^5). The second line contains n space-separated integers a_1, a_2, ..., a_{n} (1 β€ a_{i} β€ 10^9) β the i-th number in the list is the number of rounds the i-th person wants to play.
-----Output-----
In a single line print a single integer β the minimum number of game rounds the friends need to let the i-th person play at least a_{i} rounds.
Please, do not use the %lld specifier to read or write 64-bit integers in Π‘++. It is preferred to use the cin, cout streams or the %I64d specifier.
-----Examples-----
Input
3
3 2 2
Output
4
Input
4
2 2 2 2
Output
3
-----Note-----
You don't need to know the rules of "Mafia" to solve this problem. If you're curious, it's a game Russia got from the Soviet times: http://en.wikipedia.org/wiki/Mafia_(party_game).
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
n = int(input())
a = list(map(int, input().split()))
r = n-2
for d in a:
r += d
print(max(max(a), r//(n-1)))
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Let's consider a rectangular table R consisting of N rows and M columns. Rows are enumerated from 1 to N from top to bottom. Columns are enumerated from 1 to M from left to right. Each element of R is a non-negative integer. R is called steady if the sum of elements in the ith row is not less then the sum of elements in the (i-1)th row for each i where 2 β€ i β€ N and the sum of elements in the Nth row is less than or equal to M. Your task is to find the number of different steady tables of size N x M modulo 1 000 000 000.
-----Input-----
The first line of input contains a single integer T denoting number of test cases. First and the only line of each test case contains two space separated integers N and M denoting the number of rows and columns respectively.
-----Output-----
For each test case, print a single integer corresponding to the answer.
-----Constraints-----
- 1 β€ T β€ 10
- 1 β€ N, M β€ 2000
-----Subtasks-----
- Subtask 1 : 1 β€ T β€ 10 , 1 β€ N,M β€ 50 : ( 23 pts )
- Subtask 2 : 1 β€ T β€ 10 , 1 β€ N,M β€ 500 : ( 29 pts )
- Subtask 3 : 1 β€ T β€ 10 , 1 β€ N,M β€ 2000 : ( 48 pts )
-----Example-----
Input:
3
1 1
2 2
2 3
Output:
2
25
273
-----Explanation-----
Test case 1 : There are only 2 such grids possible 0 and 1.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
# This is not my code, it's Snehasish Karmakar's. Refer to http://www.codechefΒ Β Β Β .com/viewsolution/7153774
# for original version.
# Submitting it to try and work out if it can be sped up.
def compute_nCr(n,r) :
C[0][0]=1
for i in range(1,n+1) :
# print "i",i
C[i][0]=1
for j in range(1,min(i,r)+1) :
if i!=j :
C[i][j]=(C[i-1][j-1]+C[i-1][j])%MOD
else :
C[i][j]=1
def solve(n,m) :
store=[C[m+i-1][i] for i in range(m+1)]
for i in range(1,n+1) :
s=1
for j in range(1,m+1) :
s=(s+store[j])%MOD
store[j]=(s*C[m+j-1][j])%MOD
# print "a[%d][%d]=%d"%(i,j,s)
return s
MOD=1000000000
LIMIT=2000
C=[[0] * (LIMIT + 1) for _ in range(2*LIMIT+1)]
compute_nCr(2*LIMIT,LIMIT)
t=int(input())
while t :
n,m=list(map(int,input().split()))
print(solve(n,m))
t-=1
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Given a triplet of integers (X , Y , Z), such that X β€ Y and Y β₯ Z, we define f(X , Y , Z) to be (X + Y) * (Y + Z). If either X > Y or Y < Z, or both, then f(X , Y , Z) is defined to be 0.
You are provided three arrays A , B and C of any length (their lengths may or may not be equal).
Your task is to find the sum of f(X , Y , Z) over all triplets (X, Y , Z) where X, Y and Z belong to A, B and C respectively.
Output your sum for each test case modulo 1000000007.
-----Input-----
- The first line contains a single integer, T, which is the number of test cases. The description of each testcase follows:
- The first line of each testcase contains 3 integers: p, q and r. These denote the lengths of A,B and C respectively.
- The second line contains p integers, which are the elements of A
- The third line contains q integers, which are the elements of B
- The fourth line contains r integers, which are the elements of C
-----Output-----
Output the required sum modulo 1000000007 for each test case in a new line.
-----Constraints-----
- 1 β€ T β€ 10
- 1 β€ p, q, r β€ 100000
- 1 β€ every array element β€ 1000000000
-----Subtasks -----
- Subtask #1 (30 points): 1 β€ p,q,r β€ 100
- Subtask #2 (70 points): 1 β€ p,q,r β€ 100000
-----Example : -----
Input:
1
3 1 3
1 2 3
5
4 5 6
Output:
399
-----Explanation: -----
As there is only one choice for Y which equals to 5, to get a non-zero function value,we can choose any element for X from the set { 1 , 2 , 3 } and for Z from the set { 4 , 5 }
So triplets which give non-zero function values are:
{ 1 , 5 , 4 } : ( 1 + 5 ) * ( 5 + 4 ) = 54
{ 1 , 5 , 5 } : ( 1 + 5 ) * ( 5 + 5 ) = 60
{ 2 , 5 , 4 } : ( 2 + 5 ) * ( 5 + 4 ) = 63
{ 2 , 5 , 5 } : ( 2 + 5 ) * ( 5 + 5 ) = 70
{ 3 , 5 , 4 } : ( 3 + 5 ) * ( 5 + 4 ) = 72
{ 3 , 5 , 5 } : ( 3 + 5 ) * ( 5 + 5 ) = 80
Final answer : 54 + 60 + 63 + 70 + 72 + 80 = 399
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
T=int(input()) # cook your dish here
for i in range(T):
n=list(map(int,input().split()))
a=n[0]
b=n[1]
c=n[2]
l=[]
A=list(map(int,input().split()))
B=list(map(int,input().split()))
C=list(map(int,input().split()))
for i in range(b):
for j in range(a):
for k in range(c):
if(A[j]<=B[i] and B[i]>=C[k]):
sum=((A[j]+B[i])*(B[i]+C[k]))
l.append(int(sum))
sum=0
for i in range(len(l)):
sum+=int(l[i])
print(sum%1000000007)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
The new Formula 1 season is about to begin and Chef has got the chance to work with the Formula 1 technical team.
Recently, the pre-season testing ended and the technical team found out that their timing system for qualifying was a little bit buggy. So, they asked Chef to fix it before the season begins.
His task is to write a program to find the starting lineup of the race by taking the timings of the drivers in qualifying.
(If you donβt know the rules that make the starting grid in Formula 1, consider that the driver with the least time will start at the front).
Note:
- Two or more drivers can have the same name.
- Every driver will have a distinct time.
-----Input:-----
- The first line of the input consists of a single integer $T$ denoting the number of test cases.
- First line of each test case consists of a single integer $N$ denoting the number of drivers to set a time.
- The following $2*N$ lines consists of the driverβs name $S$ in one line and its timing details $X$ (in milliseconds) in the next line.
-----Output:-----
- For each test case output the starting lineup of the race i.e., name of each driver in the order they will start the race. Print each name in a new line.
-----Constraints-----
- 1 <= $T$ <= 10
- 1 <= $N$ <= 105
- 1 <= $|S|$ <= 20
- 1 <= $X$ <= 109
-----Subtasks-----
Subtask #1 (20 points):
- 1 <= $N$ <= 100
Subtask #2 (80 points):
- Original Constraints
-----Sample Input:-----
2
3
Hamilton
75000
Vettel
76000
Bottas
75500
2
Leclerc
666666
Verstappen
666777
-----Sample Output:-----
Hamilton
Bottas
Vettel
Leclerc
Verstappen
-----EXPLANATION:-----
The drivers with the least time are ahead in the lineup.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
# cook your dish here
t=int(input())
for i in range(t):
n=int(input())
if n<101:
l1=[]
l2=[]
d=dict()
for i in range(1,2*n+1):
if i%2==0:
l1.append(int(input()))
else:
l2.append(str(input()))
r1=[]
for i in l1:
r1.append(i)
l1.sort()
ind=[]
for i in l1:
a=r1.index(i)
ind.append(a)
for i in ind:
print(l2[i])
else:
print(0)
break
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Mr. Funt now lives in a country with a very specific tax laws. The total income of mr. Funt during this year is equal to n (n β₯ 2) burles and the amount of tax he has to pay is calculated as the maximum divisor of n (not equal to n, of course). For example, if n = 6 then Funt has to pay 3 burles, while for n = 25 he needs to pay 5 and if n = 2 he pays only 1 burle.
As mr. Funt is a very opportunistic person he wants to cheat a bit. In particular, he wants to split the initial n in several parts n_1 + n_2 + ... + n_{k} = n (here k is arbitrary, even k = 1 is allowed) and pay the taxes for each part separately. He can't make some part equal to 1 because it will reveal him. So, the condition n_{i} β₯ 2 should hold for all i from 1 to k.
Ostap Bender wonders, how many money Funt has to pay (i.e. minimal) if he chooses and optimal way to split n in parts.
-----Input-----
The first line of the input contains a single integer n (2 β€ n β€ 2Β·10^9)Β β the total year income of mr. Funt.
-----Output-----
Print one integerΒ β minimum possible number of burles that mr. Funt has to pay as a tax.
-----Examples-----
Input
4
Output
2
Input
27
Output
3
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
def is_izi(k):
i = 2
while (i * i <= k):
if (k % i == 0):
return 0
i += 1
return 1
n = int(input())
if (is_izi(n)):
print(1)
elif n % 2 == 0:
print(2)
elif n % 2 == 1:
if (is_izi(n - 2)):
print(2)
else:
print(3)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
At first, let's define function $f(x)$ as follows: $$ \begin{matrix} f(x) & = & \left\{ \begin{matrix} \frac{x}{2} & \mbox{if } x \text{ is even} \\ x - 1 & \mbox{otherwise } \end{matrix} \right. \end{matrix} $$
We can see that if we choose some value $v$ and will apply function $f$ to it, then apply $f$ to $f(v)$, and so on, we'll eventually get $1$. Let's write down all values we get in this process in a list and denote this list as $path(v)$. For example, $path(1) = [1]$, $path(15) = [15, 14, 7, 6, 3, 2, 1]$, $path(32) = [32, 16, 8, 4, 2, 1]$.
Let's write all lists $path(x)$ for every $x$ from $1$ to $n$. The question is next: what is the maximum value $y$ such that $y$ is contained in at least $k$ different lists $path(x)$?
Formally speaking, you need to find maximum $y$ such that $\left| \{ x ~|~ 1 \le x \le n, y \in path(x) \} \right| \ge k$.
-----Input-----
The first line contains two integers $n$ and $k$ ($1 \le k \le n \le 10^{18}$).
-----Output-----
Print the only integer β the maximum value that is contained in at least $k$ paths.
-----Examples-----
Input
11 3
Output
5
Input
11 6
Output
4
Input
20 20
Output
1
Input
14 5
Output
6
Input
1000000 100
Output
31248
-----Note-----
In the first example, the answer is $5$, since $5$ occurs in $path(5)$, $path(10)$ and $path(11)$.
In the second example, the answer is $4$, since $4$ occurs in $path(4)$, $path(5)$, $path(8)$, $path(9)$, $path(10)$ and $path(11)$.
In the third example $n = k$, so the answer is $1$, since $1$ is the only number occuring in all paths for integers from $1$ to $20$.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
def gg(n,lol):
ans = 0
cur = 1
lol2 = lol
while(2*lol+1<=n):
cur *= 2
ans += cur
lol = 2*lol+1
lol2 *= 2
if lol2*2 <= n:
ans += n-lol2*2+1
return ans
n,k = list(map(int,input().split()))
low = 1
high = n//2
res = 1
while low <= high:
mid = (low+high)//2
if gg(n,mid) >= k:
res = mid
low = mid+1
else:
high = mid-1
if n == k:
print(1)
elif(gg(n,res)-1-gg(n,res*2) >= k):
print(res*2+1)
else:
print(res*2)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Note : This question carries $100$ $points$
CodeLand is celebrating a festival by baking cakes! In order to avoid wastage, families follow a unique way of distributing cakes.
For $T$ families in the locality, $i$-th family (1 <= $i$ <= $T$) has $N$ members. They baked $S$ slices of cakes. The smallest member of the family gets $K$ slices of cakes. Each family has a lucky number of $R$ and they agree to distribute the slices such that the member gets $R$ times more slices than the member just smaller than them. Since the family is busy in festival preparations, find out if the number of slices would be sufficient for the family or not. Also, find how many extra slices they have or how many slices are they short of.
Also, the locality is kind and believes in sharing. So, you also need to determine if each family would have sufficient slices if families shared their cakes among each other!
-----Input :-----
- First line of input will have a single integer $T$ i.e. the number of families in the locality
- For next $T$ lines, each line will describe one family through 4 integers i.e. $S$, $N$, $K$, $R$ separated by spaces
-----Output-----
- First $T$ lines of output will show if slices are enough for the family or not, followed by extra or required slices. For example, if slices are sufficient, the output would be $POSSIBLE$ $10$ which implies 10 slices are extra. If slices are insufficient, the output would be $IMPOSSIBLE$ $15$ which implies 15 slices are required to fulfill the requirement.
- Last line of output would be $IMPOSSIBLE$ or $POSSIBLE$ depending on whether each family would get enough slices after sharing.
-----Constraints:-----
- 1 β€ $T$ β€ 50
- 1 β€ $N$ β€ 15
- 1 β€ $S$ β€ 10^9
- 1 β€ $K$ β€ 5
- 1 β€ $R$ β€ 5
-----Sample Input:-----
5
100 4 2 2
100 4 3 2
100 4 3 3
200 4 4 2
10 3 2 2
-----Sample Output:-----
POSSIBLE 70
POSSIBLE 55
IMPOSSIBLE 20
POSSIBLE 140
IMPOSSIBLE 4
POSSIBLE
-----Explanation-----
For the first home, the youngest member has got 2 slices, the one older than them gets 2 times more slices, and so forth. So, first home needs 2 + 4 + 8 + 16 = 30 slices. But since they made 100, they have 70 extra, hence we print 'POSSIBLE 70'.
Doing the same for other houses, we find 20 + 4 = 24 slices extra are required so that all families have enough slices. In this case we have 70 + 55 + 140 = 265 extra slices which is > 24, so we print 'POSSIBLE' in last line.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
# cook your dish here
extra, less = 0,0
for _ in range(int(input())):
sli,mem,sma,luc = list(map(int, input().split()))
total = sma
t = sma
while mem > 1:
t *= luc
total += t
mem -= 1
if total <= sli:
extra += sli-total
print('POSSIBLE',sli-total)
else:
less += total-sli
print('IMPOSSIBLE',total-sli)
if extra >= less:
print('POSSIBLE')
else:
print('IMPOSSIBLE')
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Koa the Koala and her best friend want to play a game.
The game starts with an array $a$ of length $n$ consisting of non-negative integers. Koa and her best friend move in turns and each have initially a score equal to $0$. Koa starts.
Let's describe a move in the game: During his move, a player chooses any element of the array and removes it from this array, xor-ing it with the current score of the player.
More formally: if the current score of the player is $x$ and the chosen element is $y$, his new score will be $x \oplus y$. Here $\oplus$ denotes bitwise XOR operation.
Note that after a move element $y$ is removed from $a$.
The game ends when the array is empty.
At the end of the game the winner is the player with the maximum score. If both players have the same score then it's a draw.
If both players play optimally find out whether Koa will win, lose or draw the game.
-----Input-----
Each test contains multiple test cases. The first line contains $t$ ($1 \le t \le 10^4$)Β β the number of test cases. Description of the test cases follows.
The first line of each test case contains the integer $n$ ($1 \le n \le 10^5$)Β β the length of $a$.
The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ($0 \le a_i \le 10^9$)Β β elements of $a$.
It is guaranteed that the sum of $n$ over all test cases does not exceed $10^5$.
-----Output-----
For each test case print: WIN if Koa will win the game. LOSE if Koa will lose the game. DRAW if the game ends in a draw.
-----Examples-----
Input
3
3
1 2 2
3
2 2 3
5
0 0 0 2 2
Output
WIN
LOSE
DRAW
Input
4
5
4 1 5 1 3
4
1 0 1 6
1
0
2
5 4
Output
WIN
WIN
DRAW
WIN
-----Note-----
In testcase $1$ of the first sample we have:
$a = [1, 2, 2]$. Here Koa chooses $1$, other player has to choose $2$, Koa chooses another $2$. Score for Koa is $1 \oplus 2 = 3$ and score for other player is $2$ so Koa wins.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
import sys
input = lambda: sys.stdin.readline().rstrip()
T = int(input())
for _ in range(T):
N = int(input())
A = [int(a) for a in input().split()]
X = [0] * 30
for a in A:
for i in range(30):
if a & (1 << i):
X[i] += 1
for i in range(30)[::-1]:
if X[i] % 2:
if X[i] == 1:
print("WIN")
elif N % 2 == 0:
print("WIN")
elif X[i] % 4 == 1:
print("WIN")
else:
print("LOSE")
break
else:
print("DRAW")
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
You are given an array $a$ consisting of $n$ integers. You have to find the length of the smallest (shortest) prefix of elements you need to erase from $a$ to make it a good array. Recall that the prefix of the array $a=[a_1, a_2, \dots, a_n]$ is a subarray consisting several first elements: the prefix of the array $a$ of length $k$ is the array $[a_1, a_2, \dots, a_k]$ ($0 \le k \le n$).
The array $b$ of length $m$ is called good, if you can obtain a non-decreasing array $c$ ($c_1 \le c_2 \le \dots \le c_{m}$) from it, repeating the following operation $m$ times (initially, $c$ is empty): select either the first or the last element of $b$, remove it from $b$, and append it to the end of the array $c$.
For example, if we do $4$ operations: take $b_1$, then $b_{m}$, then $b_{m-1}$ and at last $b_2$, then $b$ becomes $[b_3, b_4, \dots, b_{m-3}]$ and $c =[b_1, b_{m}, b_{m-1}, b_2]$.
Consider the following example: $b = [1, 2, 3, 4, 4, 2, 1]$. This array is good because we can obtain non-decreasing array $c$ from it by the following sequence of operations: take the first element of $b$, so $b = [2, 3, 4, 4, 2, 1]$, $c = [1]$; take the last element of $b$, so $b = [2, 3, 4, 4, 2]$, $c = [1, 1]$; take the last element of $b$, so $b = [2, 3, 4, 4]$, $c = [1, 1, 2]$; take the first element of $b$, so $b = [3, 4, 4]$, $c = [1, 1, 2, 2]$; take the first element of $b$, so $b = [4, 4]$, $c = [1, 1, 2, 2, 3]$; take the last element of $b$, so $b = [4]$, $c = [1, 1, 2, 2, 3, 4]$; take the only element of $b$, so $b = []$, $c = [1, 1, 2, 2, 3, 4, 4]$Β β $c$ is non-decreasing.
Note that the array consisting of one element is good.
Print the length of the shortest prefix of $a$ to delete (erase), to make $a$ to be a good array. Note that the required length can be $0$.
You have to answer $t$ independent test cases.
-----Input-----
The first line of the input contains one integer $t$ ($1 \le t \le 2 \cdot 10^4$) β the number of test cases. Then $t$ test cases follow.
The first line of the test case contains one integer $n$ ($1 \le n \le 2 \cdot 10^5$) β the length of $a$. The second line of the test case contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 2 \cdot 10^5$), where $a_i$ is the $i$-th element of $a$.
It is guaranteed that the sum of $n$ does not exceed $2 \cdot 10^5$ ($\sum n \le 2 \cdot 10^5$).
-----Output-----
For each test case, print the answer: the length of the shortest prefix of elements you need to erase from $a$ to make it a good array.
-----Example-----
Input
5
4
1 2 3 4
7
4 3 3 8 4 5 2
3
1 1 1
7
1 3 1 4 5 3 2
5
5 4 3 2 3
Output
0
4
0
2
3
-----Note-----
In the first test case of the example, the array $a$ is already good, so we don't need to erase any prefix.
In the second test case of the example, the initial array $a$ is not good. Let's erase first $4$ elements of $a$, the result is $[4, 5, 2]$. The resulting array is good. You can prove that if you erase fewer number of first elements, the result will not be good.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
for __ in range(int(input())):
n = int(input())
ar = list(map(int, input().split()))
ar.reverse()
ans = n - 1
flag = False
for i in range(1, n):
if ar[i] < ar[i - 1]:
flag = True
if flag:
if ar[i] > ar[i - 1]:
break
ans -= 1
print(ans)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Zonal Computing Olympiad 2012, 26 Nov 2011
We consider sequences of opening and closing brackets with two types of brackets, () and []. A bracket sequence is well-bracketed if we can pair up each opening bracket with a matching closing bracket in the usual sense. For instance, the sequences (), [] ([]) and []([]) are well-bracketed, while (, ()], (], )( and [(]) are not well-bracketed. In the last case, each opening bracket has a matching closing bracket and vice versa, but the intervals spanned by the different types of brackets intersect each other instead of being contained one within the other.
The alternating depth of a well-bracketed sequence tells us the maximum number of times we switch between the two types of brackets when we have inner matched brackets enclosed within outer matched brackets. For instance, the alternating depth of (), [[[]]] and ()[][] is 1, the alternating depth of [()] and ()([]) is 2, the alternating depth of ([()]) and [()][(([]))] is 3, and so on.
Given a well-bracketed sequence, we are interested in computing three quantities.
- The alternating depth of the sequence.
- The maximum number of symbols between any pair of matched brackets of the type ( and ), including both the outer brackets.
- The maximum number of symbols between any pair of matched brackets of the type [ and ], including both the outer brackets.
For instance, the alternating depth of (([]))[[[()]]] is 2, the maximum number of symbols between a matched pair () is 6 and the maximum number of symbols between a matched pair [] is 8.
-----Input format-----
The input consists of two lines. The first line is a single integer N, the length of the bracket sequence. Positions in the sequence are numbered 1,2,β¦,N. The second line is a sequence of N space-separated integers that encode the bracket expression as follows: 1 denotes an opening bracket (, 2 denotes a closing bracket ), 3 denotes an opening bracket [ and 4 denotes a closing bracket ]. Nothing other than 1, 2, 3 or 4 appears in the second line of input and the corresponding expression is guaranteed to be well-bracketed.
-----Output format-----
Your program should print 3 space-separated integers in a line, denoting the three quantities asked for in the following order: alternating depth, length of the maximum sequence between matching () brackets and length of the maximum sequence between matching [] brackets.
-----Testdata-----
You may assume that 2 β€ N β€ 105. In 30% of the test cases, 2 β€ N β€ 103.
- Subtask 1 (30 marks)
- Subtask 2 (70 marks)
-----Sample Input-----
14
1 1 3 4 2 2 3 3 3 1 2 4 4 4
-----Sample Output-----
2 6 8
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
# cook your dish here
n=int(input())
stringa=list(map(int,input().split()))
counter=0
counter1=0
counter3=0
somma1=0
somma2=0
massimo=0
massimo1=0
massimo3=0
stack=[]
for par in stringa:
if par==1 or par==3:
if counter1==0 and par==1:
counter1=1
somma1=1
massimo1=max(massimo1, 1)
elif counter1>0:
counter1+=1
somma1+=1
massimo1=max(massimo1, somma1)
if counter3==0 and par==3:
counter3=1
somma3=1
massimo3=max(massimo3, 1)
elif counter3>0:
counter3+=1
somma3+=1
massimo3=max(massimo3, somma3)
if counter==0:
counter=1
massimo=max(massimo,1)
if len(stack)>0 and par!=stack[-1]:
counter+=1
massimo=max(massimo,counter)
stack.append(par)
else:
if counter1>0:
counter1-=1
somma1+=1
massimo1=max(massimo1, somma1)
if counter3>0:
counter3-=1
somma3+=1
massimo3=max(massimo3, somma3)
appo=stack.pop()
if len(stack)>0 and appo==stack[-1]:
pass
else:
counter-=1
print(massimo, massimo1, massimo3)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Chef bought a huge (effectively infinite) planar island and built $N$ restaurants (numbered $1$ through $N$) on it. For each valid $i$, the Cartesian coordinates of restaurant $i$ are $(X_i, Y_i)$.
Now, Chef wants to build $N-1$ straight narrow roads (line segments) on the island. The roads may have arbitrary lengths; restaurants do not have to lie on the roads. The slope of each road must be $1$ or $-1$, i.e. for any two points $(x_1, y_1)$ and $(x_2, y_2)$ on the same road, $|x_1-x_2| = |y_1-y_2|$ must hold.
Let's denote the minimum distance Chef has to walk from restaurant $i$ to reach a road by $D_i$. Then, let's denote $a = \mathrm{max}\,(D_1, D_2, \ldots, D_N)$; Chef wants this distance to be minimum possible.
Chef is a busy person, so he decided to give you the job of building the roads. You should find a way to build them that minimises $a$ and compute $a \cdot \sqrt{2}$.
-----Input-----
- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
- The first line of each test case contains a single integer $N$.
- $N$ lines follow. For each valid $i$, the $i$-th of these lines contains two space-separated integers $X_i$ and $Y_i$.
-----Output-----
For each test case, print a single line containing one real number β the minimum distance $a$ multiplied by $\sqrt{2}$. Your answer will be considered correct if its absolute or relative error does not exceed $10^{-6}$.
-----Constraints-----
- $1 \le T \le 100$
- $2 \le N \le 10^4$
- $|X_i|, |Y_i| \le 10^9$ for each valid $i$
-----Subtasks-----
Subtask #1 (10 points):
- $1 \le T \le 10$
- $2 \le N \le 5$
- $|X_i|, |Y_i| \le 10$ for each valid $i$
- $a \cdot \sqrt{2}$ is an integer
Subtask #2 (90 points): original constraints
-----Example Input-----
2
3
0 0
0 1
0 -1
3
0 1
1 0
-1 0
-----Example Output-----
0.5
0
-----Explanation-----
Example case 1: We should build roads described by equations $y-x+0.5 = 0$ and $y-x-0.5 = 0$.
Example case 2: We should build roads described by equations $y-x-1 = 0$ and $y+x-1 = 0$.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
import sys
def input(): return sys.stdin.readline().strip()
def iinput(): return int(input())
def rinput(): return list(map(int, sys.stdin.readline().strip().split()))
def get_list(): return list(map(int, sys.stdin.readline().strip().split()))
t=iinput()
for _ in range(t):
n=iinput()
p=[]
mi=[]
for i in range(n):
x,y=rinput()
p.append(x+y)
mi.append(x-y)
p.sort()
mi.sort()
m=float('inf')
for i in range(1,n):
if(p[i]-p[i-1]<m):
m=p[i]-p[i-1]
if(mi[i]-mi[i-1]<m):
m=mi[i]-mi[i-1]
if m%2==0:
print(m//2)
else:
print(m/2)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
You are provided with the marks of entire class in Data structures exam out of 100. You need to calculate the number of students having backlog (passing marks is >=31) and the average of the class. But this average is not a normal average, for this average marks of students having backlog are not considered but they will be considered in number of students. Also print the index of topperβs marks and print the difference of everyoneβs marks with respect to the topper.
In first line print the number of students having backlog and average of the class. In second line print indices of all the toppers(in case of more than 1 topper print index of all toppers in reverse order). Next N lines print the difference of everyoneβs marks with respect to topper(s).
Note- if all students have backlog than average will be 0.
INPUT
The first line of the input contains an integer T denoting the number of test cases.
Next line contains N denoting the no of students in the class.
The line contains N space seprated integers A1,A2,A3β¦.AN denoting the marks of each student in exam.
OUTPUT
First line contains the number of students having backlog and the special average of marks as described above. Average must have 2 decimal places.
Next line contains the indices of all the toppers in given array in reverse order.
Next N lines contain the difference of every studentβs marks with respect to toppers.
Constraints
1<= T <= 100
1<= N <= 30
0<= Ai<= 100
Example
Input
1
9
56 42 94 25 74 99 27 52 83
Output
2 55.55
5
43
57
5
74
25
0
72
47
16
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
for j in range(int(input())):
input()
a = list(map(int,input().split()))
marks = 0
backlok = 0
top_marks = max(a)
topper = []
for i in range(len(a)):
if(a[i] >= 31):
marks+=a[i]
if(a[i]<31):
backlok+=1
if(a[i] == top_marks):
topper.append(i)
print(backlok, "{:0.2f}".format(marks/len(a),2))
topper.sort(reverse=True)
for i in topper:
print(i," ")
for i in a:
print(top_marks-i)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Leha is a usual student at 'The Usual University for Usual Students'. Sometimes he studies hard; at other times he plays truant and gets busy with other things besides academics. He has already studied at the university for N months. For the ith month (1 β€ i β€ N), he has received some non-negative integer grade A[i].
Now he wants to analyse his progress for some periods of his university education. An arbitrary period, defined by two positive integers L and R, begins at Leha's Lth month at the university and ends at the Rth. The analysis is performed via the following steps.
1. Write down all the grades for each month from L to R and sort them. Let's call the sorted list S.
2. Calculate the sum of squared differences of consecutive elements in S, that is, (S[2] - S[1])2 + (S[3] - S[2])2 + ... + (S[R-L+1] - S[R-L])2.
-----Input-----
The first line contains one integer N β the number of months Leha has already studied at the university.
The second line contains N integers β list A of Leha's grades.
The third line contains one integer M β the number of periods Leha is interested in analyzing.
Each of the following M lines contain two integers L and R describing each period.
-----Output-----
For each query, output one integer β the result of the progress analysis for the corresponding period.
-----Constraints-----
- 1 β€ N, M β€ 5*104
- 0 β€ A[i] β€ 106
-----Subtasks-----
- Subtask 1 (19 points) 1 β€ N, M β€ 200, time limit = 2 sec
- Subtask 2 (31 points) 1 β€ N, M β€ 10 000, time limit = 2 sec
- Subtask 3 (26 points) 0 β€ A[i] β€ 100, time limit = 5 sec
- Subtask 4 (24 points) no additional constraints, , time limit = 5 sec
-----Example-----
Input:5
1 3 2 4 5
5
1 5
1 4
2 4
3 3
3 5
Output:4
3
2
0
5
Explanation
The first query: sorted array looks like (1, 2, 3, 4, 5) and the answer is calculated as (2-1)2 + (3-2)2 + (4-3)2 + (5-4)2 = 4
The second query: sorted array looks like (1, 2, 3, 4) and the answer is calculated as (2-1)2 + (3-2)2 + (4-3)2 = 3
The last query: sorted array looks like (2, 4, 5) and the answer is calculated as (4-2)2 + (5-4)2 = 5
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
n=eval(input())
grades=list(map(int,input().split()))
m=eval(input())
for df in range(m):
x,y=list(map(int,input().split()))
arr=[]
arr=grades[x-1:y]
arr.sort()
sum=0
#arr.append(1000000)
for nh in range(0,len(arr)-1,1):
sum=sum+(arr[nh+1]-arr[nh])**2
#print sum,len(arr),nh+1,nh
print(sum)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Chef has been working in a restaurant which has N floors. He wants to minimize the time it takes him to go from the N-th floor to ground floor. He can either take the elevator or the stairs.
The stairs are at an angle of 45 degrees and Chef's velocity is V1 m/s when taking the stairs down. The elevator on the other hand moves with a velocity V2 m/s. Whenever an elevator is called, it always starts from ground floor and goes to N-th floor where it collects Chef (collecting takes no time), it then makes its way down to the ground floor with Chef in it.
The elevator cross a total distance equal to N meters when going from N-th floor to ground floor or vice versa, while the length of the stairs is sqrt(2) * N because the stairs is at angle 45 degrees.
Chef has enlisted your help to decide whether he should use stairs or the elevator to minimize his travel time. Can you help him out?
-----Input-----
The first line contains a single integer T, the number of test cases. Each test case is described by a single line containing three space-separated integers N, V1, V2.
-----Output-----
For each test case, output a single line with string Elevator or Stairs, denoting the answer to the problem.
-----Constraints-----
- 1 β€ T β€ 1000
- 1 β€ N, V1, V2 β€ 100
-----Example-----
Input:
3
5 10 15
2 10 14
7 14 10
Output:
Elevator
Stairs
Stairs
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
n=int(input())
l=[]
for i in range(0,n):
a,b,c=map(int,input().split())
n1=(2**0.5)*(a/b)
n2=2*(a/c)
if n1>n2:
l.append("Elevator")
else:
l.append("Stairs")
for i in l:
print(i)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
A binary string is called a self-destructing string if it can reduced to an empty string by performing the following operation some number of times (possibly zero): Choose a valid integer $i$ such that the $i$-th character of the current string is different from the $i+1$-th character, and remove these two characters from the string.
You are given a binary string $s$. Your task is to convert $s$ to a self-destructing string. To do that, you may perform the following operation any number of times (possibly zero): Choose an integer $i$ ($1 \le i \le |s|-1$) such that the $i$-th character of $s$ is different from the $i+1$-th character, and invert one of these characters (inverting a character means changing '0' to '1' or '1' to '0', e.g. the string "01" can be changed to "00").
Find the smallest number of operations required to convert $s$ to a self-destructing string or determine that it is impossible.
-----Input-----
- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
- The first and only line of each test case contains a single string $s$.
-----Output-----
For each test case, print a single line containing one integer β the smallest required number of operations or $-1$ if it is impossible to convert $s$ to a self-destructing string.
-----Constraints-----
- $1 \le T \le 1,000$
- $1 \le |s| \le 10^6$
- $s$ contains only characters '0' and '1'
- the sum of $|s|$ over all test cases does not exceed $10^6$
-----Example Input-----
3
001101
1101
110
-----Example Output-----
0
1
-1
-----Explanation-----
Example case 1: We already have a self-destructing string because "001101" can be converted to "0101", to "01" and finally to an empty string.
Example case 2: We can choose $i=3$ (since $s_3 \neq s_4$) and then invert $s_4$ to obtain "1100", which is a self-destructing string.
Example case 3: It can be shown that "110" cannot be converted to a self-destructing string.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
t=int(input())
for i in range(t):
s=input()
zeroes=s.count('0')
ones=s.count('1')
if (len(s)%2==1 or zeroes==0 or ones==0):
ans= -1
else:
ans=abs(zeroes-ones)//2
print(ans)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Consider a currency system in which there are notes of six denominations, namely, Rs. 1, Rs. 2, Rs. 5, Rs. 10, Rs. 50, Rs. 100.
If the sum of Rs. N is input, write a program to computer smallest number of notes that will combine to give Rs. N.
-----Input-----
The first line contains an integer T, total number of testcases. Then follow T lines, each line contains an integer N.
-----Output-----
For each test case, display the smallest number of notes that will combine to give N, in a new line.
-----Constraints-----
- 1 β€ T β€ 1000
- 1 β€ N β€ 1000000
-----Example-----
Input
3
1200
500
242
Output
12
5
7
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
# cook your dish here
t= int(input())
for i in range(t):
cnt=0
n=int(input())
while(n>=100):
n-=100
cnt+=1
while(n>=50):
n-=50
cnt+=1
while(n>=10):
n-=10
cnt+=1
while(n>=5):
n-=5
cnt+=1
while(n>=2):
n-=2
cnt+=1
while(n>=1):
n-=1
cnt+=1
print(cnt)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Batman is about to face Superman so he decides to prepare for the battle by upgrading his Batmobile. He manufactures multiple duplicates of his standard Batmobile each tweaked in a different way such that the maximum speed of each is never less than that of the standard model.
After carrying out this process, he wishes to know how many of his prototypes are faster than his standard Batmobile?
-----Input-----
- The first line of the input contains an integer T denoting the number of test cases. The description of T test cases follow:
- The first line of each test case contains a single integer N denoting the number of copies of the standard Batmobile.
- The second line contains a sequence of N+1 space-separated integers, S0 to SN, sorted in non-decreasing order separated by space. S0 is the maximum speed of the standard Batmobile. S1 to SN denote the maximum speeds of the prototypes.
-----Output-----
- For each test case, output a single line containing an integer denoting the answer.
-----Constraints-----
- 1 β€ T β€ 1000
- 1 β€ N β€ 1000
- 1 β€ Si β€ 109
-----Example-----
Input:
2
4
1 2 3 4 5
5
1 10 100 1000 10000 100000
Output:
4
5
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
t = int(input())
while(t):
n = int(input())
ar = list(map(int,input().strip().split(" ")))
print(len([x for x in ar[1:len(ar)] if ar[0]<x]))
t-=1
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
After failing to clear his school mathematics examination, infinitepro decided to prepare very hard for his upcoming re-exam, starting with the topic he is weakest at β computational geometry.
Being an artist, infinitepro has C$C$ pencils (numbered 1$1$ through C$C$); each of them draws with one of C$C$ distinct colours. He draws N$N$ lines (numbered 1$1$ through N$N$) in a 2D Cartesian coordinate system; for each valid i$i$, the i$i$-th line is drawn with the ci$c_i$-th pencil and it is described by the equation y=aiβ
x+bi$y = a_i \cdot x + b_i$.
Now, infinitepro calls a triangle truly-geometric if each of its sides is part of some line he drew and all three sides have the same colour. He wants to count these triangles, but there are too many of them! After a lot of consideration, he decided to erase a subset of the N$N$ lines he drew. He wants to do it with his eraser, which has length K$K$.
Whenever erasing a line with a colour i$i$, the length of the eraser decreases by Vi$V_i$. In other words, when the eraser has length k$k$ and we use it to erase a line with a colour i$i$, the length of the eraser decreases to kβVi$k-V_i$; if k<Vi$k < V_i$, it is impossible to erase such a line.
Since infinitepro has to study for the re-exam, he wants to minimise the number of truly-geometric triangles. Can you help him find the minimum possible number of truly-geometric triangles which can be obtained by erasing a subset of the N$N$ lines in an optimal way? He promised a grand treat for you if he passes the examination!
-----Input-----
- The first line of the input contains a single integer T$T$ denoting the number of test cases. The description of T$T$ test cases follows.
- The first line of the input contains three space-separated integers N$N$, C$C$ and K$K$.
- N$N$ lines follow. For each i$i$ (1β€iβ€N$1 \le i \le N$), the i$i$-th of these lines contains three space-separated integers ai$a_i$, bi$b_i$ and ci$c_i$.
- The last line contains C$C$ space-separated integers V1,V2,β¦,VC$V_1, V_2, \ldots, V_C$.
-----Output-----
For each test case, print a single line containing one integer β the smallest possible number of truly-geometric triangles after erasing lines.
-----Constraints-----
- 1β€Tβ€10$1 \le T \le 10$
- 1β€Cβ€Nβ€3,000$1 \le C \le N \le 3,000$
- 0β€Kβ€3,000$0 \le K \le 3,000$
- 0β€ai,biβ€109$0 \le a_i, b_i \le 10^9$ for each valid i$i$
- 1β€ciβ€C$1 \le c_i \le C$ for each valid i$i$
- 0β€Viβ€K$0 \le V_i \le K$ for each valid i$i$
- no two lines coincide, regardless of their colours
- no three lines are concurrent
-----Subtasks-----
Subtask #1 (10 points):
- Nβ€10$N \le 10$
- Kβ€100$K \le 100$
Subtask 2 (15 points):
- V1=V2=β¦=VC$V_1 = V_2 = \ldots = V_C$
- no two lines are parallel
Subtask #3 (25 points): no two lines are parallel
Subtask #4 (50 points): original constraints
-----Example Input-----
2
7 2 13
1 10 1
1 14 2
6 4 1
2 2 1
0 12 2
2 11 2
0 6 1
8 10
6 1 20
1 5 1
2 11 1
4 0 1
6 8 1
0 11 1
3 3 1
9
-----Example Output-----
2
4
-----Explanation-----
Example case 1: We can remove exactly one line. Initially, we have 5$5$ truly geometric triangles (see the image below; red is colour 1$1$ and green is colour 2$2$).
- Removing any line with colour 2$2$ brings the total number of truly-geometric triangles down to 4+0=4$4+0=4$.
- Removing any line with colour 1$1$ brings the total number of truly-geometric triangles down to 1+1=2$1+1=2$.
Thus, the smallest number of truly-geometric triangles we can obtain is 2$2$.
Example case 2: We can remove at most 2$2$ lines and removing any 2$2$ lines gives us a total of 4$4$ truly-geometric triangles.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
from collections import Counter
from math import factorial
def nc3(n):
a=factorial(n)
b=factorial(n-3)
return ((a)/(b*6))
def rem(s,k):
t=-1
x=-1
for i in range(len(s)):
if s[i][0]>2 and s[i][1]<=k:
if s[i][0]>3:
ch=(nc3(s[i][0])-nc3(s[i][0]-1))/s[i][1]
else:
ch=1/s[i][1]
if t<ch:
t=ch
x=i
return x
t=int(input())
for x in range(t):
n,c,k=map(int,input().split())
l={}
for i in range(n):
a,b,e=map(int,input().split())
if e in l:
l[e].append(a)
else:
l[e]=[]
l[e].append(a)
v=list(map(int,input().split()))
s=[]
for i in range(1,c+1):
if i in l:
s+=[[len(l[i]),v[i-1]]]
s.sort(key = lambda x: x[0],reverse=True)
while True:
ma=rem(s,k)
if ma<=-1:
break
else:
s[ma][0]-=1
k=k-s[ma][1]
re=0
for i in s:
if i[0]>2:
re=re+nc3(i[0])
print(int(re))
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
You are given a tree with $N$ vertices (numbered $1$ through $N$) and a bag with $N$ markers. There is an integer written on each marker; each of these integers is $0$, $1$ or $2$. You must assign exactly one marker to each vertex.
Let's define the unattractiveness of the resulting tree as the maximum absolute difference of integers written on the markers in any two vertices which are connected by an edge.
Find the minimum possible unattractiveness of the resulting tree.
-----Input-----
- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
- The first line of each test case contains a single integer $N$.
- The second line contains $N$ space-separated integers denoting the numbers on markers in the bag.
- Each of the next $N-1$ lines contains two space-separated integers $u$ and $v$ denoting an edge between vertices $u$ and $v$.
-----Output-----
For each test case, print a single line containing one integer β the minimum unattractiveness.
-----Constraints-----
- $1 \le T \le 30$
- $1 \le N \le 100$
- $1 \le u, v \le N$
- the graph described on the input is a tree
-----Example Input-----
3
3
0 1 1
1 2
1 3
3
0 1 2
1 2
1 3
4
2 2 2 2
1 2
1 3
3 4
-----Example Output-----
1
1
0
-----Explanation-----
Example case 1:
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
# cook your dish here
import numpy as np
tests = int(input())
for _ in range(tests):
n = int(input())
weights = [int(j) for j in input().split()]
edges = [[0] for _ in range(n-1)]
for i in range(n-1):
edges[i] = [int(j)-1 for j in input().split()]
vertex_set = [[] for _ in range(n)]
for i in range(n-1):
vertex_set[edges[i][0]].append(edges[i][1])
vertex_set[edges[i][1]].append(edges[i][0])
counts = [0 for _ in range(3)]
for i in range(n):
counts[weights[i]] += 1
if counts[1] == 0:
print(2 * (counts[0] != 0 and counts[2] != 0))
elif counts[1] == n:
print(0)
else:
visited = [0]
for i in range(n):
vertex = visited[i]
for v in vertex_set[vertex]:
if v not in visited:
visited.append(v)
vertex_nums = [[0] for _ in range(n)]
for i in range(n-1,-1,-1):
vertex = visited[i]
for v in vertex_set[vertex]:
if v in visited[i:]:
vertex_nums[vertex].append(sum(vertex_nums[v])+1)
for i in range(n):
vertex_nums[i].append(n-1-sum(vertex_nums[i]))
sums = np.zeros(n,dtype=bool)
sums[0] = True
for i in range(n):
new_sums = np.zeros(n,dtype=bool)
new_sums[0] = True
for num in vertex_nums[i]:
new_sums[num:n] = np.logical_or(new_sums[num:n],new_sums[:n-num])
sums = np.logical_or(sums,new_sums)
solved = False
for i in range(n):
if sums[i] and counts[0] <= i and counts[2] <= n - 1 - i:
solved = True
break
if solved or counts[1] > 1:
print(1)
else:
print(2)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
To help Lavanya learn all about binary numbers and binary sequences, her father has bought her a collection of square tiles, each of which has either a 0 or a 1 written on it. Her brother Nikhil has played a rather nasty prank. He has glued together pairs of tiles with 0 written on them. Lavanya now has square tiles with 1 on them and rectangular tiles with two 0's on them, made up of two square tiles with 0 stuck together). Thus, she can no longer make all possible binary sequences using these tiles.
To amuse herself, Lavanya has decided to pick a number $N$ and try and construct as many binary sequences of length $N$ as possible using her collection of tiles. For example if $N$ = 1, she can only make the sequence 1. For $N$=2, she can make 11 and 00. For $N$=4, there are 5 possibilities: 0011, 0000, 1001, 1100 and 1111.
Lavanya would like you to write a program to compute the number of arrangements possible with $N$ tiles so that she can verify that she has generated all of them. Since she cannot count beyond 15746, it is sufficient to report this number modulo 15746.
-----Input:-----
A single line with a single integer $N$.
-----Output:-----
A single integer indicating the number of binary sequences of length $N$, modulo 15746, that Lavanya can make using her tiles.
-----Constraints:-----
You may assume that $N \leq$ 1000000.
-----Sample Input:-----
4
-----Sample Output:-----
5
-----Explanation:-----
This corresponds to the example discussed above.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
n=int(input())
modulo=15746
num=[1,1]
for i in range(2,n+1):
num.append((num[i-1]+num[i-2])%modulo)
print(num[n])
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Chef recently learned about concept of periodicity of strings. A string is said to have a period P, if P divides N and for each i, the i-th of character of the string is same as i-Pth character (provided it exists), e.g. "abab" has a period P = 2, It also has a period of P = 4, but it doesn't have a period of 1 or 3.
Chef wants to construct a string of length N that is a palindrome and has a period P. It's guaranteed that N is divisible by P. This string can only contain character 'a' or 'b'. Chef doesn't like the strings that contain all a's or all b's.
Given the values of N, P, can you construct one such palindromic string that Chef likes? If it's impossible to do so, output "impossible" (without quotes)
-----Input-----
The first line of the input contains an integer T denoting the number of test cases.
The only line of each test case contains two space separated integers N, P.
-----Output-----
For each test case, output a single line containing the answer of the problem, i.e. the valid string if it exists otherwise "impossible" (without quotes). If there are more than possible answers, you can output any.
-----Constraints-----
- 1 β€ T β€ 20
- 1 β€ P, N β€ 105
-----Subtasks-----
- Subtask #1 (25 points) : P = N
- Subtask #2 (75 points) : No additional constraints
-----Example-----
Input
5
3 1
2 2
3 3
4 4
6 3
Output
impossible
impossible
aba
abba
abaaba
-----Explanation-----
Example 1: The only strings possible are either aaa or bbb, which Chef doesn't like. So, the answer is impossible.
Example 2: There are four possible strings, aa, ab, ba, bb. Only aa and bb are palindromic, but Chef doesn't like these strings. Hence, the answer is impossible.
Example 4: The string abba is a palindrome and has a period of 4.
Example 5: The string abaaba is a palindrome and has a period of length 3.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
T=int(input())
for i in range(T):
n,m=list(map(int,input().split()))
if(m<=2):
print("impossible")
else:
l=[0]*m
if(m%2==0):
a=m//2
else:
a=(m//2)+1
for j in range(a):
if(j%2==0):
l[j]="a"
l[m-j-1]="a"
else:
l[j]="b"
l[m-j-1]="b"
r=""
s=n//m
for e in l:
r=r+e
print(r*s)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
This is the easier version of the problem. In this version, $1 \le n \le 10^5$ and $0 \le a_i \le 1$. You can hack this problem only if you solve and lock both problems.
Christmas is coming, and our protagonist, Bob, is preparing a spectacular present for his long-time best friend Alice. This year, he decides to prepare $n$ boxes of chocolate, numbered from $1$ to $n$. Initially, the $i$-th box contains $a_i$ chocolate pieces.
Since Bob is a typical nice guy, he will not send Alice $n$ empty boxes. In other words, at least one of $a_1, a_2, \ldots, a_n$ is positive. Since Alice dislikes coprime sets, she will be happy only if there exists some integer $k > 1$ such that the number of pieces in each box is divisible by $k$. Note that Alice won't mind if there exists some empty boxes.
Charlie, Alice's boyfriend, also is Bob's second best friend, so he decides to help Bob by rearranging the chocolate pieces. In one second, Charlie can pick up a piece in box $i$ and put it into either box $i-1$ or box $i+1$ (if such boxes exist). Of course, he wants to help his friend as quickly as possible. Therefore, he asks you to calculate the minimum number of seconds he would need to make Alice happy.
-----Input-----
The first line contains a single integer $n$ ($1 \le n \le 10^5$)Β β the number of chocolate boxes.
The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ($0 \le a_i \le 1$)Β β the number of chocolate pieces in the $i$-th box.
It is guaranteed that at least one of $a_1, a_2, \ldots, a_n$ is positive.
-----Output-----
If there is no way for Charlie to make Alice happy, print $-1$.
Otherwise, print a single integer $x$Β β the minimum number of seconds for Charlie to help Bob make Alice happy.
-----Examples-----
Input
3
1 0 1
Output
2
Input
1
1
Output
-1
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
# η΄ ε ζ°ε解
def prime_decomposition(n):
i = 2
table = []
while i * i <= n:
while n % i == 0:
n //= i
table.append(i)
i += 1
if n > 1:
table.append(n)
return table
import sys
input = sys.stdin.readline
N = int(input())
A = list(map(int, input().split()))
# γγγγ移εγγγ¦ε
±ιε ζ°γζγ€γγγ«γγ
su = sum(A)
if su == 1:
print(-1)
return
primes = list(set(prime_decomposition(su)))
ans = float("inf")
Idx1 = [i for i, a in enumerate(A) if a]
for p in primes:
an = 0
half = p // 2
for t in zip(*[iter(Idx1)]*p):
idx = t[half]
an += sum(abs(i-idx) for i in t)
ans = min(ans, an)
print(ans)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
You have a string S consisting of N uppercase English letters. You are allowed to perform at most one operation of following kind: Choose any position in the string, remove the character at that position and insert it back to any other place in the string.
Find the lexicographically smallest string you can achieve.
-----Input-----
The first line of the input contains an integer T denoting the number of test cases. The description of T test cases follows.
The first line of each test case contains the single integer N denoting length of string S.
The second line contains the string S.
-----Output-----
For each test case, output a single line containing the answer to the corresponding test case.
-----Constraints-----
- 1 β€ T β€ 50
- 1 β€ N β€ 50
- S will consist of uppercase English letters.
-----Example-----
Input:
2
4
DCBA
7
XYZZYZZ
Output:
ADCB
XYYZZZZ
-----Explanation-----
Example case 1. The optimal solution here is to choose the last character and put it in the beginning of the string. So the answer will be ADCB
Example case 2. The optimal solution here is to choose the 5-th character (1-based index) and put it between the 2-nd and the 3-rd characters. So the answer will be XYYZZZZ
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
for _1 in range(int(input())):
n=int(input())
s=input().strip()
answer=s
for i in range(len(s)):
c=s[i]
string=s[:i]+s[i+1:]
for j in range(len(string)+1):
answer=min(answer, string[:j]+c+string[j:])
print(answer)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Chef likes all arrays equally. But he likes some arrays more equally than others. In particular, he loves Rainbow Arrays.
An array is Rainbow if it has the following structure:
- First a1 elements equal 1.
- Next a2 elements equal 2.
- Next a3 elements equal 3.
- Next a4 elements equal 4.
- Next a5 elements equal 5.
- Next a6 elements equal 6.
- Next a7 elements equal 7.
- Next a6 elements equal 6.
- Next a5 elements equal 5.
- Next a4 elements equal 4.
- Next a3 elements equal 3.
- Next a2 elements equal 2.
- Next a1 elements equal 1.
- ai can be any non-zero positive integer.
- There are no other elements in array.
Help Chef in finding out if the given array is a Rainbow Array or not.
-----Input-----
- The first line of the input contains an integer T denoting the number of test cases.
- The first line of each test case contains an integer N, denoting the number of elements in the given array.
- The second line contains N space-separated integers A1, A2, ..., AN denoting the elements of array.
-----Output-----
- For each test case, output a line containing "yes" or "no" (without quotes) corresponding to the case if the array is rainbow array or not.
-----Constraints-----
- 1 β€ T β€ 100
- 7 β€ N β€ 100
- 1 β€ Ai β€ 10
-----Subtasks-----
- Subtask 1 (100 points) : Original constraints
-----Example-----
Input
3
19
1 2 3 4 4 5 6 6 6 7 6 6 6 5 4 4 3 2 1
14
1 2 3 4 5 6 7 6 5 4 3 2 1 1
13
1 2 3 4 5 6 8 6 5 4 3 2 1
Output
yes
no
no
-----Explanation-----
The first example satisfies all the conditions.
The second example has 1 element of value 1 at the beginning and 2 elements of value 1 at the end.
The third one has no elements with value 7 after elements with value 6.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
t=int(input())
x=[1,2,3,4,5,6,7]
for i in range(t):
N=int(input())
a=list(map(int,input().split()))
rev=a[::-1]
dup=set(a)
if rev== a and list(dup) ==x:
print("yes")
else:
print("no")
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Toad Rash has a binary string $s$. A binary string consists only of zeros and ones.
Let $n$ be the length of $s$.
Rash needs to find the number of such pairs of integers $l$, $r$ that $1 \leq l \leq r \leq n$ and there is at least one pair of integers $x$, $k$ such that $1 \leq x, k \leq n$, $l \leq x < x + 2k \leq r$, and $s_x = s_{x+k} = s_{x+2k}$.
Find this number of pairs for Rash.
-----Input-----
The first line contains the string $s$ ($1 \leq |s| \leq 300\,000$), consisting of zeros and ones.
-----Output-----
Output one integer: the number of such pairs of integers $l$, $r$ that $1 \leq l \leq r \leq n$ and there is at least one pair of integers $x$, $k$ such that $1 \leq x, k \leq n$, $l \leq x < x + 2k \leq r$, and $s_x = s_{x+k} = s_{x+2k}$.
-----Examples-----
Input
010101
Output
3
Input
11001100
Output
0
-----Note-----
In the first example, there are three $l$, $r$ pairs we need to count: $1$, $6$; $2$, $6$; and $1$, $5$.
In the second example, there are no values $x$, $k$ for the initial string, so the answer is $0$.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
X = [[], ['0', '1'], ['00', '01', '10', '11'], ['001', '010', '011', '100', '101', '110'], ['0010', '0011', '0100', '0101', '0110', '1001', '1010', '1011', '1100', '1101'], ['00100', '00101', '00110', '01001', '01011', '01100', '01101', '10010', '10011', '10100', '10110', '11001', '11010', '11011'], ['001001', '001011', '001100', '001101', '010010', '010011', '010110', '011001', '011010', '011011', '100100', '100101', '100110', '101001', '101100', '101101', '110010', '110011', '110100', '110110'], ['0010011', '0011001', '0011010', '0011011', '0100101', '0101100', '0101101', '0110011', '1001100', '1010010', '1010011', '1011010', '1100100', '1100101', '1100110', '1101100'], ['00110011', '01011010', '01100110', '10011001', '10100101', '11001100']]
s = input()
N = len(s)
ans = (N-1)*(N-2)//2
for i in range(N):
for j in range(i+3, min(i+9, N+1)):
if s[i:j] in X[j-i]:
ans -= 1
print(ans)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Tomya is a girl. She loves Chef Ciel very much.
Tomya like a positive integer p, and now she wants to get a receipt of Ciel's restaurant whose total price is exactly p.
The current menus of Ciel's restaurant are shown the following table.
Name of Menupriceeel flavored water1deep-fried eel bones2clear soup made with eel livers4grilled eel livers served with grated radish8savory egg custard with eel16eel fried rice (S)32eel fried rice (L)64grilled eel wrapped in cooked egg128eel curry rice256grilled eel over rice512deluxe grilled eel over rice1024eel full-course2048
Note that the i-th menu has the price 2i-1 (1 β€ i β€ 12).
Since Tomya is a pretty girl, she cannot eat a lot.
So please find the minimum number of menus whose total price is exactly p.
Note that if she orders the same menu twice, then it is considered as two menus are ordered. (See Explanations for details)
-----Input-----
The first line contains an integer T, the number of test cases.
Then T test cases follow.
Each test case contains an integer p.
-----Output-----
For each test case, print the minimum number of menus whose total price is exactly p.
-----Constraints-----
1 β€ T β€ 5
1 β€ p β€ 100000 (105)
There exists combinations of menus whose total price is exactly p.
-----Sample Input-----
4
10
256
255
4096
-----Sample Output-----
2
1
8
2
-----Explanations-----
In the first sample, examples of the menus whose total price is 10 are the following:
1+1+1+1+1+1+1+1+1+1 = 10 (10 menus)
1+1+1+1+1+1+1+1+2 = 10 (9 menus)
2+2+2+2+2 = 10 (5 menus)
2+4+4 = 10 (3 menus)
2+8 = 10 (2 menus)
Here the minimum number of menus is 2.
In the last sample, the optimal way is 2048+2048=4096 (2 menus).
Note that there is no menu whose price is 4096.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
t= int(input())
while(t>0):
n = int(input())
m=0
m=n//(2**11)
n%=(2**11)
while(n>0):
num=n%2
m+=num
n//=2
print(m)
t-=1
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Dr. S. De teaches computer architecture in NIT Patna. Whenever he comes across any good question(with complexity $k$), he gives that question to students within roll number range $i$ and $j$
At the start of semester he assigns score of $10$ to every student in his class if a student submits a question of complexity $k$, his score gets multiplied by $k$
This month he gave $M$ questions and he is wondering what will be mean of maximum scores of all the student. He is busy in improving his finger print attendance module, can you help him?
Input file may be large so try to use fast input output
-----Input:-----
- First line will contain $T$, number of testcases. Then the testcases follow.
- Each testcase contains of a First line of input, two integers $N, M$ i.e. Number of students in the class and number of questions given in this month.
- Next $M$ lines contains 3 integers -$i, j, k$ i.e. starting roll number, end roll number and complexity of the question
-----Output:-----
For each testcase, output in a single line answer - $floor$ value of Mean of maximum possible score for all students.
-----Constraints-----
- $1 \leq T \leq 100$
- $1 \leq N, M \leq 10^5$
- $1 \leq i \leq j \leq N$
- $1 \leq k \leq 100$
-----Subtasks-----
Subtask1
-
$1 \leq T \leq 10$
-
$1 \leq N, M \leq 10^4$
Subtask2
-
Original Constraints
-----Sample Input:-----
1
5 3
1 3 5
2 5 2
3 4 7
-----Sample Output:-----
202
-----EXPLANATION:-----
Initial score of students will be : $[10, 10, 10, 10, 10]$
after solving question 1 scores will be: $[50, 50, 50, 10, 10]$
after solving question 2 scores will be: $[50, 100, 100, 20, 20]$
after solving question 1 scores will be: $[50, 100, 700, 140, 20]$
Hence after all questions mean of maximum scores will $(50+100+700+140+20)/5 = 202$
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
try:
t=int(input())
for a in range(t):
l=input().split()
n=int(l[0])
m=int(l[1])
d={}
s=0
for b in range(m):
l1=input().split()
i=int(l1[0])
j=int(l1[1])
k=int(l1[2])
for c in range(i,j+1):
if c not in d:
d[c]=10
for c in range(i,j+1):
d[c]=d[c]*k
for i in d:
s=s+d[i]
print(s//n)
except:
pass
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
One day, Chef prepared D brand new dishes. He named the i-th dish by a string Si. After the cooking, he decided to categorize each of these D dishes as special or not.
A dish Si is called special if it's name (i.e. the string Si) can be represented in the form of a double string by removing at most one (possibly zero) character from it's name from any position.
A string is called a double string if it can be represented as a concatenation of two identical, non-empty strings.
e.g. "abab" is a double string as it can be represented as "ab" + "ab" where + operation denotes concatenation.
Similarly, "aa", "abcabc" are double strings whereas "a", "abba", "abc" are not.
-----Input-----
- First line of the input contains an integer D denoting the number of dishes prepared by Chef on that day.
- Each of the next D lines will contain description of a dish.
- The i-th line contains the name of i-th dish Si.
-----Output-----
For each of the D dishes, print a single line containing "YES" or "NO" (without quotes) denoting whether the dish can be called as a special or not.
-----Constraints-----
- 1 β€ D β€ 106
- 1 β€ |Si| β€ 106.
- Each character of string Si will be lower case English alphabet (i.e. from 'a' to 'z').
-----Subtasks-----
Subtask #1 : (20 points)
- Sum of |Si| in an input file doesn't exceed 2 * 103
Subtask 2 : (80 points)
- Sum of |Si| in an input file doesn't exceed 2 * 106
-----Example-----
Input:
3
aba
abac
abcd
Output:
YES
NO
NO
-----Explanation-----
Example case 1.
We can remove the character at position 1 (0-based index) to get "aa" which is a double string. Hence, it is a special dish.
Example case 2.
It is not possible to remove the character at any of the position to get the double string. Hence, it is not a special dish.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
# cook your dish here
def check_equal(a,b):
index=0
for i in a:
while index<len(b) and i != b[index]:
index+=1
if(index>=len(b)):
return False
index+=1
return True
def Dob_String(n):
size=len(n)
midpoint=size//2
if(check_equal(n[0:midpoint],n[midpoint:size])):
return("YES")
elif(size%2!=0 and check_equal(n[midpoint+1:size],n[0:midpoint+1])):
return("YES")
else:
return("NO")
T=int(input())
for _ in range(T):
n=input()
if(len(n)>1):
print(Dob_String(n))
else:
print("NO")
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
You like playing chess tournaments online.
In your last tournament you played $n$ games. For the sake of this problem, each chess game is either won or lost (no draws). When you lose a game you get $0$ points. When you win you get $1$ or $2$ points: if you have won also the previous game you get $2$ points, otherwise you get $1$ point. If you win the very first game of the tournament you get $1$ point (since there is not a "previous game").
The outcomes of the $n$ games are represented by a string $s$ of length $n$: the $i$-th character of $s$ is W if you have won the $i$-th game, while it is L if you have lost the $i$-th game.
After the tournament, you notice a bug on the website that allows you to change the outcome of at most $k$ of your games (meaning that at most $k$ times you can change some symbol L to W, or W to L). Since your only goal is to improve your chess rating, you decide to cheat and use the bug.
Compute the maximum score you can get by cheating in the optimal way.
-----Input-----
Each test contains multiple test cases. The first line contains an integer $t$ ($1\le t \le 20,000$) β the number of test cases. The description of the test cases follows.
The first line of each testcase contains two integers $n, k$ ($1\le n\le 100,000$, $0\le k\le n$) β the number of games played and the number of outcomes that you can change.
The second line contains a string $s$ of length $n$ containing only the characters W and L. If you have won the $i$-th game then $s_i=\,$W, if you have lost the $i$-th game then $s_i=\,$L.
It is guaranteed that the sum of $n$ over all testcases does not exceed $200,000$.
-----Output-----
For each testcase, print a single integer β the maximum score you can get by cheating in the optimal way.
-----Example-----
Input
8
5 2
WLWLL
6 5
LLLWWL
7 1
LWLWLWL
15 5
WWWLLLWWWLLLWWW
40 7
LLWLWLWWWLWLLWLWWWLWLLWLLWLLLLWLLWWWLWWL
1 0
L
1 1
L
6 1
WLLWLW
Output
7
11
6
26
46
0
1
6
-----Note-----
Explanation of the first testcase. Before changing any outcome, the score is $2$. Indeed, you won the first game, so you got $1$ point, and you won also the third, so you got another $1$ point (and not $2$ because you lost the second game).
An optimal way to cheat is to change the outcomes of the second and fourth game. Doing so, you end up winning the first four games (the string of the outcomes becomes WWWWL). Hence, the new score is $7=1+2+2+2$: $1$ point for the first game and $2$ points for the second, third and fourth game.
Explanation of the second testcase. Before changing any outcome, the score is $3$. Indeed, you won the fourth game, so you got $1$ point, and you won also the fifth game, so you got $2$ more points (since you won also the previous game).
An optimal way to cheat is to change the outcomes of the first, second, third and sixth game. Doing so, you end up winning all games (the string of the outcomes becomes WWWWWW). Hence, the new score is $11 = 1+2+2+2+2+2$: $1$ point for the first game and $2$ points for all the other games.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
import sys
input = sys.stdin.readline
def main():
n, k = map(int, input().split())
string = input().strip()
if "W" not in string:
ans = min(n, k) * 2 - 1
print(max(ans, 0))
return
L_s = []
cnt = 0
bef = string[0]
ans = 0
for s in string:
if s == bef:
cnt += 1
else:
if bef == "L":
L_s.append(cnt)
else:
ans += cnt * 2 - 1
cnt = 1
bef = s
if bef == "W":
ans += cnt * 2 - 1
cnt = 0
if string[0] == "L" and L_s:
cnt += L_s[0]
L_s = L_s[1:]
L_s.sort()
for l in L_s:
if k >= l:
ans += l * 2 + 1
k -= l
else:
ans += k * 2
k = 0
ans += 2 * min(k, cnt)
print(ans)
for _ in range(int(input())):
main()
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Iroha has a sequence of N strings S_1, S_2, ..., S_N. The length of each string is L.
She will concatenate all of the strings in some order, to produce a long string.
Among all strings that she can produce in this way, find the lexicographically smallest one.
Here, a string s=s_1s_2s_3...s_n is lexicographically smaller than another string t=t_1t_2t_3...t_m if and only if one of the following holds:
- There exists an index i(1β¦iβ¦min(n,m)), such that s_j = t_j for all indices j(1β¦j<i), and s_i<t_i.
- s_i = t_i for all integers i(1β¦iβ¦min(n,m)), and n<m.
-----Constraints-----
- 1 β¦ N, L β¦ 100
- For each i, the length of S_i equals L.
- For each i, S_i consists of lowercase letters.
-----Input-----
The input is given from Standard Input in the following format:
N L
S_1
S_2
:
S_N
-----Output-----
Print the lexicographically smallest string that Iroha can produce.
-----Sample Input-----
3 3
dxx
axx
cxx
-----Sample Output-----
axxcxxdxx
The following order should be used: axx, cxx, dxx.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
n,l = map(int,input().split())
a = []
for i in range(n):
a.append(input())
a.sort()
print("".join(str(i) for i in a))
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Chef is a brilliant university student that does not attend lectures because he believes that they are boring and coding is life! However, his university follows certain rules and regulations, and a student may only take an exam for a course if he has attended at least 75% of lectures for this course.
Since you are Chef's best friend, you want to help him reach the attendance he needs to take exams. Unfortunately, Chef is still focused on his code and refuses to attend more lectures, so the only option is to have some of his friends mark him as present by proxy. This trick is well-known in the university, but only few have the talent to pull it off.
In a certain course, there is exactly one lesson per day over the course of $D$ days (numbered $1$ through $D$). You are given a string $S$ with length $D$ describing the lessons Chef attended β for each valid $i$, the $i$-th character of this string is either 'A' if Chef was absent on day $i$ or 'P' if Chef was actually present on day $i$.
For each day $d$ when Chef is absent, one of Chef's friends can mark him as present by proxy on this day only if he was present (if he was really present, not just marked as present) on at least one of the previous two days, i.e. days $d-1$ and $d-2$, and on at least one of the following two days, i.e. days $d+1$ and $d+2$. However, it is impossible to mark him as present by proxy on the first two days and the last two days.
Find the minimum number of times Chef has to be marked as present by proxy so that his attendance becomes at least 75% ($0.75$). Chef's attendance is number of days when he was marked as present, either by proxy or by actually being present, divided by $D$.
-----Input-----
- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
- The first line of each test case contains a single integer $D$.
- The second line contains a single string $S$ with length $D$.
-----Output-----
For each test case, print a single line containing one integer β the minimum number of times Chef needs to be marked as present by proxy, or $-1$ if it is impossible to make Chef achieve 75% attendance.
-----Constraints-----
- $1 \le T \le 200$
- $1 \le D \le 1,000$
- $S$ contains only characters 'A' and 'P'
-----Subtasks-----
Subtask #1 (100 points): original constraints
-----Example Input-----
1
9
PAAPPAPPP
-----Example Output-----
1
-----Explanation-----
Example case 1: With a proxy on the third day, the attendance string is "PAPPPAPPP". Now, Chef's attendance is at least 75%, so the minimum number of times Chef needs to be marked as present by proxy is $1$.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
# cook your dish here
def ceil(num):
if num%1==0:
return int(num//1)
else:
return int((num//1)+1)
for _ in range(int(input())):
n=int(input())
s=input()
p=0
a=[]
for i in range(n):
if s[i]=="P":
p=p+1
req=ceil(0.75*n)
requirement=req-p
for i in range(2,n-2):
if s[i]=="A":
if (s[i-1]=="P" or s[i-2]=="P") and (s[i+1]=="P" or s[i+2]=="P"):
a.append(i)
if requirement>len(a):
print(-1)
else:
print(max(requirement,0))
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
You are given an undirected unweighted graph consisting of $n$ vertices and $m$ edges (which represents the map of Bertown) and the array of prices $p$ of length $m$. It is guaranteed that there is a path between each pair of vertices (districts).
Mike has planned a trip from the vertex (district) $a$ to the vertex (district) $b$ and then from the vertex (district) $b$ to the vertex (district) $c$. He can visit the same district twice or more. But there is one issue: authorities of the city want to set a price for using the road so if someone goes along the road then he should pay the price corresponding to this road (he pays each time he goes along the road). The list of prices that will be used $p$ is ready and they just want to distribute it between all roads in the town in such a way that each price from the array corresponds to exactly one road.
You are a good friend of Mike (and suddenly a mayor of Bertown) and want to help him to make his trip as cheap as possible. So, your task is to distribute prices between roads in such a way that if Mike chooses the optimal path then the price of the trip is the minimum possible. Note that you cannot rearrange prices after the start of the trip.
You have to answer $t$ independent test cases.
-----Input-----
The first line of the input contains one integer $t$ ($1 \le t \le 10^4$) β the number of test cases. Then $t$ test cases follow.
The first line of the test case contains five integers $n, m, a, b$ and $c$ ($2 \le n \le 2 \cdot 10^5$, $n-1 \le m \le min(\frac{n(n-1)}{2}, 2 \cdot 10^5)$, $1 \le a, b, c \le n$) β the number of vertices, the number of edges and districts in Mike's trip.
The second line of the test case contains $m$ integers $p_1, p_2, \dots, p_m$ ($1 \le p_i \le 10^9$), where $p_i$ is the $i$-th price from the array.
The following $m$ lines of the test case denote edges: edge $i$ is represented by a pair of integers $v_i$, $u_i$ ($1 \le v_i, u_i \le n$, $u_i \ne v_i$), which are the indices of vertices connected by the edge. There are no loops or multiple edges in the given graph, i. e. for each pair ($v_i, u_i$) there are no other pairs ($v_i, u_i$) or ($u_i, v_i$) in the array of edges, and for each pair $(v_i, u_i)$ the condition $v_i \ne u_i$ is satisfied. It is guaranteed that the given graph is connected.
It is guaranteed that the sum of $n$ (as well as the sum of $m$) does not exceed $2 \cdot 10^5$ ($\sum n \le 2 \cdot 10^5$, $\sum m \le 2 \cdot 10^5$).
-----Output-----
For each test case, print the answer β the minimum possible price of Mike's trip if you distribute prices between edges optimally.
-----Example-----
Input
2
4 3 2 3 4
1 2 3
1 2
1 3
1 4
7 9 1 5 7
2 10 4 8 5 6 7 3 3
1 2
1 3
1 4
3 2
3 5
4 2
5 6
1 7
6 7
Output
7
12
-----Note-----
One of the possible solution to the first test case of the example:
[Image]
One of the possible solution to the second test case of the example:
[Image]
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
import sys
from collections import deque
input = sys.stdin.readline
t = int(input())
for _ in range(t):
n, m, a, b, c = list(map(int,input().split()))
p = list(map(int, input().split()))
p.sort()
pref = [0]
curr = 0
for i in range(m):
curr += p[i]
pref.append(curr)
adj = [[] for i in range(n)]
for _ in range(m):
u, v = list(map(int,input().split()))
adj[u - 1].append(v - 1)
adj[v - 1].append(u - 1)
aD = [-1] * n
bD = [-1] * n
cD = [-1] * n
for i in range(3):
q = deque()
q.append(([a,b,c][i]-1,0))
l = [aD,bD,cD][i]
l[q[0][0]] = 0
while q:
v, d = q.popleft()
for nex in adj[v]:
if l[nex] == -1:
l[nex] = d + 1
q.append((nex,d+1))
poss = []
for i in range(n):
if aD[i] + bD[i] + cD[i] <= m:
poss.append(pref[aD[i] + bD[i] + cD[i]] + pref[bD[i]])
print(min(poss))
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
You are given three non-negative integers $X$, $Y$ and $N$. Find the number of integers $Z$ such that $0 \le Z \le N$ and $(X \oplus Z) < (Y \oplus Z)$, where $\oplus$ denotes the bitwise XOR operation.
-----Input-----
- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
- The first and only line of each test case contains three space-separated integers $X$, $Y$ and $N$.
-----Output-----
For each test case, print a single line containing one integer β the number of integers $Z$ which satisfy all conditions.
-----Constraints-----
- $1 \le T \le 1,000$
- $0 \le X, Y, N \le 2^{30} - 1$
-----Subtasks-----
Subtask #1 (5 points): $X, Y, N \le 2^6 - 1$
Subtask #2 (95 points): original constraints
-----Example Input-----
3
1 2 10
2 1 10
0 0 7
-----Example Output-----
6
5
0
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
# cook your dish here
tc=int(input())
for j in range(tc):
ip=list(map(int,input().rstrip().split()))
x=ip[0]
y=ip[1]
n=ip[2]
cnt=0
if(x==y):
print('0')
continue
ln=bin(x).replace("0b", "")
rn=bin(y).replace("0b", "")
ll=len(ln)
rl=len(rn)
#print(ln)
#print(rn)
if(ll==len(rn)):
for i in range(ll):
if(ln[i]!=rn[i]):
ln=ln[i:]
rn=rn[i:]
break
#print(ln)
if(ln[0]=='0'):
ln=ln[1:]
ll-=1
#print(rn)
if(rn[0]=='0'):
rn=rn[1:]
rl-=1
ll=len(ln)
rl=len(rn)
if(ll>rl):
lb=ll
else:
lb=rl
pl=2**lb
hpl=pl//2
amn=((n+1)//pl)*hpl
rm=(n+1)%pl
if((rm*2)<=pl):
amn+=rm
else:
amn+=hpl
#print("amn = ",amn)
aln=(n+1)-amn
#print("aln = ",aln)
if(x<y):
print(amn)
else:
print(aln)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Let x be a string of length at least 1.
We will call x a good string, if for any string y and any integer k (k \geq 2), the string obtained by concatenating k copies of y is different from x.
For example, a, bbc and cdcdc are good strings, while aa, bbbb and cdcdcd are not.
Let w be a string of length at least 1.
For a sequence F=(\,f_1,\,f_2,\,...,\,f_m) consisting of m elements,
we will call F a good representation of w, if the following conditions are both satisfied:
- For any i \, (1 \leq i \leq m), f_i is a good string.
- The string obtained by concatenating f_1,\,f_2,\,...,\,f_m in this order, is w.
For example, when w=aabb, there are five good representations of w:
- (aabb)
- (a,abb)
- (aab,b)
- (a,ab,b)
- (a,a,b,b)
Among the good representations of w, the ones with the smallest number of elements are called the best representations of w.
For example, there are only one best representation of w=aabb: (aabb).
You are given a string w. Find the following:
- the number of elements of a best representation of w
- the number of the best representations of w, modulo 1000000007 \, (=10^9+7)
(It is guaranteed that a good representation of w always exists.)
-----Constraints-----
- 1 \leq |w| \leq 500000 \, (=5 \times 10^5)
- w consists of lowercase letters (a-z).
-----Partial Score-----
- 400 points will be awarded for passing the test set satisfying 1 \leq |w| \leq 4000.
-----Input-----
The input is given from Standard Input in the following format:
w
-----Output-----
Print 2 lines.
- In the first line, print the number of elements of a best representation of w.
- In the second line, print the number of the best representations of w, modulo 1000000007.
-----Sample Input-----
aab
-----Sample Output-----
1
1
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
w=list(input());n=len(w);t=-1
def Z(s):
m=len(s);z=[0]*m;c=0;f=[1]*m;
for i in range(1,m):
if i+z[i-c]<c+z[c]:z[i]=z[i-c]
else:
j=max(0,c+z[c]-i)
while i+j<n and s[j]==s[i+j]:j=j+1
z[i]=j;c=i
for p in range(1,m):
for k in range(2,z[p]//p+2):f[k*p-1]=0
return f
for j in range(1,n//2+1):
if n%j==0 and w[:n-j]==w[j:]:t=j;break;
if t==-1:print ('1\n1')
elif t==1:print (n);print((1))
else:
zl=Z(w)
w.reverse()
zr=Z(w)
cnt=0
for i in range(0,n-1):
if zl[i] and zr[n-2-i]:cnt=cnt+1
print((2));print(cnt);
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
For Diwali, Chef arranges all $K$ laddus in a row in his sweet shop. Whenever a customer comes to buy laddus, chef follows a rule that each customer must buy all laddus on odd position. After the selection of the laddu, a new row is formed, and again out of these only laddus on odd position are selected. This continues until the chef left with the last laddu. Find out the position of that last laddu in the original row.
-----Input:-----
- First line will contain $T$, number of testcases. Then the testcases follow.
- Each testcase contains of a single line of input, one integer $K$.
-----Output:-----
For each testcase, print the position of that laddu who is left, in the original row.
-----Constraints-----
- $1 \leq T \leq 10^5$
- $1 \leq K \leq 10^5$
-----Sample Input:-----
3
1
5
8
-----Sample Output:-----
1
4
8
-----EXPLANATION:-----
For 1) Only one laddu which is last so print 1.
For 2) Customer 1: [1, 3, 5]
New row = [2, 4]
Customer 2: [2]
Last laddu = 4
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
# cook your dish here
t=int(input())
while t>0:
n=int(input())
if n==1:
print(1)
else:
c,num=1,2
while num<n:
num*=2
if num==n:
print(num)
else:
print(num//2)
t-=1
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Indian National Olympiad in Informatics 2012
You are given a table with 2 rows and N columns. Each cell has an integer in it. The score of such a table is defined as follows: for each column, consider the sum of the two numbers in the column; the maximum of the N numbers so obtained is the score. For example, for the table
7162
1234
the score is max(7 + 1, 1 + 2, 6 + 3, 2 + 4) = 9.
The first row of the table is fixed, and given as input. N possible ways to fill the second row are considered:
1,2,...,N
2,3,...,N,1
3,4,...,N,1,2
Β·Β·Β·
N, 1, ... , ,N β 1
For instance, for the example above, we would consider each of the following as possibilities for the second row.
1234
2341
3412
4123
Your task is to find the score for each of the above choices of the second row. In the example above, you would evaluate the following four tables,
7162 7162 7162 7162
1234 2341 3412 4123
and compute scores 9, 10, 10 and 11, respectively.
-----Input format -----
The first line of the input has a single integer, N. The second line of the input has N integers, representing the first row, from left to right.
-----Output format -----
The output should consist of a single line with N integers. For 1 Β² k Β² N, the kth number in the output should be the score when the second row of the table is taken to be k,k+1,...,N,1,...,kβ1.
-----Test Data -----
The testdata is grouped into two subtasks with the following constraints on the inputs.
β’ Subtask 1 [30 points] : 1 β€ N β€ 3000.
β’ Subtask 2 [70 points] : 1 β€ N β€ 200000.
In both the subtasks, all the integers in the first row of the table are between 1 and 100000, inclusive.
-----Example -----
Here is the sample input and output corresponding to the example above.
-----Sample input -----
4
7 1 6 2
-----Sample output-----
9 10 10 11
Note: Your program should not print anything other than what is specified in the output format. Please remove all diagnostic print statements before making your final submission. A program with extraneous output will be treated as incorrect!
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
# cook your dish here
try:
n=int(input())
list_n = list(range(1,n+1))
list_n_flag=[]
fix_arr = list(map(int,input().split()))
k=1
res_list=[]
fin_list=[]
list_n_flag = list_n[k:] + list_n[:k]
res_list = [list_n[i] + fix_arr[i] for i in range(len(fix_arr))]
maxx = max(res_list)
fin_list.append(maxx)
while list_n!=list_n_flag:
res_list = [list_n_flag[i] + fix_arr[i] for i in range(len(fix_arr))]
maxx = max(res_list)
fin_list.append(maxx)
list_n_flag = list_n_flag[k:] + list_n_flag[:k]
print(*fin_list,sep=" ")
except:
pass
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
In this problem the input will consist of a number of lines of English text consisting of the letters of the English alphabet, the punctuation marks ' (apostrophe), . (full stop), , (comma), ; (semicolon), :(colon) and white space characters (blank, newline). Your task is print the words in the text in reverse order without any punctuation marks.
For example consider the following candidate for the input text:
$ $
This is a sample piece of text to illustrate this
problem. If you are smart you will solve this right.
$ $
The corresponding output would read as:
$ $
right this solve will you smart are you If problem
this illustrate to text of piece sample a is This
$ $
That is, the lines are printed in reverse order and in each line the words are printed in reverse order.
-----Input:-----
The first line of input contains a single integer $N$, indicating the number of lines in the input. This is followed by $N$ lines of input text.
-----Output:-----
$N$ lines of output text containing the input lines in reverse order and where each line contains the words in reverse order as illustrated above.
-----Constraints:-----
- $1 \leq N \leq 10000$.
- There are at most $80$ characters in each line
-----Sample input-----
2
This is a sample piece of text to illustrate this
problem. If you are smart you will solve this right.
-----Sample output-----
right this solve will you smart are you If problem
this illustrate to text of piece sample a is This
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
N = int(input())
l = []
for i in range(N):
l.append(input())
for j in range(N-1,-1,-1):
s = '` '+ l[j]
n = len(s)-1
y = s[n]
f = ''
while y != '`':
w = ''
while y != ' ':
if ord(y) in range(97,123) or ord(y) in range(65,91):
w += y
n -= 1
y = s[n]
wf = ''
n -= 1
y = s[n]
x = len(w)
for k in range(x):
wf += w[x-k-1]
f += wf+' '
print(f)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Find sum of all the numbers that are multiples of 10 and are less than or equal to a given number "N". (quotes for clarity and be careful of integer overflow)
-----Input-----
Input will start with an integer T the count of test cases, each case will have an integer N.
-----Output-----
Output each values, on a newline.
-----Constraints-----
- 1 β€ T β€ 10
- 1 β€ N β€1000000000
-----Example-----
Input:
1
10
Output:
10
-----Explanation-----
Example case 1. Only integer that is multiple 10 that is less than or equal to 10 is 10
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
for t in range(eval(input())):
n=eval(input())
n-=n%10
n/=10
print(n*(n+1)/2*10)
```
|
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