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open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Your company was appointed to lay new asphalt on the highway of length $n$. You know that every day you can either repair one unit of the highway (lay new asphalt over one unit of the highway) or skip repairing.
Skipping the repair is necessary because of the climate. The climate in your region is periodical: there are $g$ days when the weather is good and if you lay new asphalt these days it becomes high-quality pavement; after that, the weather during the next $b$ days is bad, and if you lay new asphalt these days it becomes low-quality pavement; again $g$ good days, $b$ bad days and so on.
You can be sure that you start repairing at the start of a good season, in other words, days $1, 2, \dots, g$ are good.
You don't really care about the quality of the highway, you just want to make sure that at least half of the highway will have high-quality pavement. For example, if the $n = 5$ then at least $3$ units of the highway should have high quality; if $n = 4$ then at least $2$ units should have high quality.
What is the minimum number of days is needed to finish the repair of the whole highway?
-----Input-----
The first line contains a single integer $T$ ($1 \le T \le 10^4$) — the number of test cases.
Next $T$ lines contain test cases — one per line. Each line contains three integers $n$, $g$ and $b$ ($1 \le n, g, b \le 10^9$) — the length of the highway and the number of good and bad days respectively.
-----Output-----
Print $T$ integers — one per test case. For each test case, print the minimum number of days required to repair the whole highway if at least half of it should have high quality.
-----Example-----
Input
3
5 1 1
8 10 10
1000000 1 1000000
Output
5
8
499999500000
-----Note-----
In the first test case, you can just lay new asphalt each day, since days $1, 3, 5$ are good.
In the second test case, you can also lay new asphalt each day, since days $1$-$8$ are good.
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,g,b=map(int,input().split())
nn=(n+1)//2
print(max(nn+(nn-1)//g*b,n))
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
There are total N friends went to Chef's Pizza shop. There they bought a pizza. Chef divided the pizza into K equal slices. Now you have to check whether these K pizza slices can be distributed equally among the friends. Also given that every person should get at least one slice. If the above conditions are possible then print "YES" otherwise print "NO".
-----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 integers N.
The second line of each test case contains K.
-----Output:-----
For each test case, print a single line containing "YES" if the given conditions are true else "NO" if the given conditions are false.
-----Constraints-----
1<=T<=10
1<=N<=10^6
1<=K<=10^6
-----Sample Input:-----
2
10
20
12
5
-----Sample Output:-----
YES
NO
-----EXPLANATION:-----
Explanation case 1: since there are 10 friends and 20 pizza slice, so each can get 2 slices, so "YES".
Explanation case 2: Since there are 12 friends and only 5 pizza slice, so there is no way pizza slices can be distributed equally and each friend gets at least one pizza slice, so "NO".
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())
k = int(input())
if k%n==0:
print("YES")
else:
print("NO")
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Polycarp is making a quest for his friends. He has already made n tasks, for each task the boy evaluated how interesting it is as an integer q_{i}, and the time t_{i} in minutes needed to complete the task.
An interesting feature of his quest is: each participant should get the task that is best suited for him, depending on his preferences. The task is chosen based on an interactive quiz that consists of some questions. The player should answer these questions with "yes" or "no". Depending on the answer to the question, the participant either moves to another question or goes to one of the tasks that are in the quest. In other words, the quest is a binary tree, its nodes contain questions and its leaves contain tasks.
We know that answering any of the questions that are asked before getting a task takes exactly one minute from the quest player. Polycarp knows that his friends are busy people and they can't participate in the quest for more than T minutes. Polycarp wants to choose some of the n tasks he made, invent the corresponding set of questions for them and use them to form an interactive quiz as a binary tree so that no matter how the player answers quiz questions, he spends at most T minutes on completing the whole quest (that is, answering all the questions and completing the task). Specifically, the quest can contain zero questions and go straight to the task. Each task can only be used once (i.e., the people who give different answers to questions should get different tasks).
Polycarp wants the total "interest" value of the tasks involved in the quest to be as large as possible. Help him determine the maximum possible total interest value of the task considering that the quest should be completed in T minutes at any variant of answering questions.
-----Input-----
The first line contains two integers n and T (1 ≤ n ≤ 1000, 1 ≤ T ≤ 100) — the number of tasks made by Polycarp and the maximum time a quest player should fit into.
Next n lines contain two integers t_{i}, q_{i} (1 ≤ t_{i} ≤ T, 1 ≤ q_{i} ≤ 1000) each — the time in minutes needed to complete the i-th task and its interest value.
-----Output-----
Print a single integer — the maximum possible total interest value of all the tasks in the quest.
-----Examples-----
Input
5 5
1 1
1 1
2 2
3 3
4 4
Output
11
Input
5 5
4 1
4 2
4 3
4 4
4 5
Output
9
Input
2 2
1 1
2 10
Output
10
-----Note-----
In the first sample test all the five tasks can be complemented with four questions and joined into one quest.
In the second sample test it is impossible to use all the five tasks, but you can take two of them, the most interesting ones.
In the third sample test the optimal strategy is to include only the second task into the quest.
Here is the picture that illustrates the answers to the sample tests. The blue circles represent the questions, the two arrows that go from every circle represent where a person goes depending on his answer to that question. The tasks are the red ovals. [Image]
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 defaultdict
def __starting_point():
n, T = [int(_) for _ in input().split()]
data = defaultdict(list)
for i in range(n):
t, q = [int(_) for _ in input().split()]
data[T - t].append(q)
prev_level = []
for level_id in range(1, T + 1):
level = sorted(data[T - level_id] + prev_level, reverse=True)
if T - level_id <= 10:
max_size = 2 ** (T - level_id)
level = level[:max_size]
if len(level) % 2 == 1:
level.append(0)
prev_level = [
level[i] + level[i + 1]
for i in range(0, len(level), 2)
]
print(prev_level[0])
__starting_point()
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Chef has $N$ points (numbered $1$ through $N$) in a 2D Cartesian coordinate system. For each valid $i$, the $i$-th point is $(x_i, y_i)$. He also has a fixed integer $c$ and he may perform operations of the following type: choose a point $(x_i, y_i)$ and move it to $(x_i + c, y_i + c)$ or $(x_i - c, y_i - c)$.
Now, Chef wants to set up one or more checkpoints (points in the same coordinate system) and perform zero or more operations in such a way that after they are performed, each of his (moved) $N$ points is located at one of the checkpoints.
Chef's primary objective is to minimise the number of checkpoints. Among all options with this minimum number of checkpoints, he wants to choose one which minimises the number of operations he needs to perform.
Can you help Chef find the minimum number of required checkpoints and the minimum number of operations he needs to perform to move all $N$ points to these checkpoints?
-----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 $c$.
- $N$ 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 two integers ― the minimum number of checkpoints and the minimum number of moves.
-----Constraints-----
- $1 \le T \le 5$
- $1 \le N \le 5 \cdot 10^5$
- $|x_i|, |y_i| \le 10^9$ for each valid $i$
- $0 < c \le 10^9$
- the sum of $N$ over all test cases does not exceed $5 \cdot 10^5$
-----Example Input-----
1
3 1
1 1
1 0
3 2
-----Example Output-----
2 2
-----Explanation-----
Example case 1: One optimal solution is to set up checkpoints at coordinates $(1, 1)$ and $(1, 0)$. Since the points $(1, 1)$ and $(1, 0)$ are already located at checkpoints, Chef can just move the point $(3, 2)$ to the checkpoint $(1, 0)$ in two moves: $(3, 2) \rightarrow (2, 1) \rightarrow (1, 0)$.
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, c = list(map(int,input().split()))
pts = {}
moves = 0
for i in range(n):
x, y = list(map(int,input().split()))
if (y-x,x%c) in pts:
pts[(y-x,x%c)].append(x)
else:
pts[(y-x,x%c)] = [x]
for i in pts:
arc = sorted(pts[i])
for j in arc:
moves = moves + abs((j-arc[len(arc)//2]))//c
print(len(pts),moves)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Vasya likes the number $239$. Therefore, he considers a number pretty if its last digit is $2$, $3$ or $9$.
Vasya wants to watch the numbers between $L$ and $R$ (both inclusive), so he asked you to determine how many pretty numbers are in this range. Can you help him?
-----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 two space-separated integers $L$ and $R$.
-----Output-----
For each test case, print a single line containing one integer — the number of pretty numbers between $L$ and $R$.
-----Constraints-----
- $1 \le T \le 100$
- $1 \le L \le R \le 10^5$
-----Subtasks-----
Subtask #1 (100 points): original constraints
-----Example Input-----
2
1 10
11 33
-----Example Output-----
3
8
-----Explanation-----
Example case 1: The pretty numbers between $1$ and $10$ are $2$, $3$ and $9$.
Example case 2: The pretty numbers between $11$ and $33$ are $12$, $13$, $19$, $22$, $23$, $29$, $32$ and $33$.
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,m = map(int,input().split())
count=0
for i in range(n,m+1):
p=str(i)
if p[-1]=='2' or p[-1]=='3' or p[-1]=='9':
count+=1
print(count)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Snakeland is a well organised city. The houses of the city are organised in an orderly rectangular fashion with dimensions 2 * n, i.e. there are total two rows and n columns. The house in the i-th row and j-th column is also said to be the house at coordinates (i, j). Some of the houses are occupied by snakes, while the others are empty. You are given this information through an array s of dimension 2 * n, where, if s[i][j] = '*', it denotes that there is a snake in the house at coordinates (i, j), and if s[i][j] = '.', it denotes that the house is empty.
These snakes are planning a coup against a mongoose who controls their city from outside. So, they are trying their best to meet with other snakes and spread information about the date of the coup. For spreading this information, they can just hiss from their house and usually their hiss is so loud that it will be heard in all the cells except if there is a soundproof fence built that cuts the voice. Note that the external borders of Snakeland are already built of soundproof material. The mongoose got to know about the plan, and he wants to construct sound proof fences along the borders of the houses so that no two people should be able to communicate with each other. The fence can be either vertical or horizontal. Each fence can be of any length, but the mongoose wants to minimize the number of fences to be built. Find out the minimum number of fences that the mongoose should build.
-----Input-----
The first line of the input contains an integer T denoting number of test cases. The descriptions of the T test cases follow.
The first line of each test case contains a single integer, n.
Each of the next two lines contains n characters denoting the first and the second rows of Snakeland respectively.
-----Output-----
For each test case, output a single integer corresponding to the minimum number of fences that the mongoose needs to build.
-----Constraints-----
- 1 ≤ T ≤ 10
- 1 ≤ n ≤ 105
-----Example-----
Input
3
2
**
**
3
***
*..
3
*..
.*.
Output
2
3
1
-----Explanation-----
All the examples are shown in the pictures. The fences built are shown by red colored horizontal or vertical segments. You can see that after putting these borders no snake can talk with any another snake.
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:
n=int(input())
r1=input()
r2=input()
r1count=0
r2count=0
count=0
for i in range(n):
if(r1[i]=="*"):
r1count+=1
if(r2[i]=="*"):
r2count+=1
if(r1count>0) and (r2count>0):
count=1
r1count=0
r2count=0
i=0
while(i<n):
if(r1[i]=="*"):
r1count+=1
if(r2[i]=="*"):
r2count+=1
if(r1count>1) or (r2count>1):
count+=1
r1count=0
r2count=0
i-=1
i+=1
elif(r1count==0 and r2count>0) or (r2count==0 and r1count>0):
count=max(r1count,r2count)-1
else:
count=0
print(count)
t-=1
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Sereja has a bracket sequence s_1, s_2, ..., s_{n}, or, in other words, a string s of length n, consisting of characters "(" and ")".
Sereja needs to answer m queries, each of them is described by two integers l_{i}, r_{i} (1 ≤ l_{i} ≤ r_{i} ≤ n). The answer to the i-th query is the length of the maximum correct bracket subsequence of sequence s_{l}_{i}, s_{l}_{i} + 1, ..., s_{r}_{i}. Help Sereja answer all queries.
You can find the definitions for a subsequence and a correct bracket sequence in the notes.
-----Input-----
The first line contains a sequence of characters s_1, s_2, ..., s_{n} (1 ≤ n ≤ 10^6) without any spaces. Each character is either a "(" or a ")". The second line contains integer m (1 ≤ m ≤ 10^5) — the number of queries. Each of the next m lines contains a pair of integers. The i-th line contains integers l_{i}, r_{i} (1 ≤ l_{i} ≤ r_{i} ≤ n) — the description of the i-th query.
-----Output-----
Print the answer to each question on a single line. Print the answers in the order they go in the input.
-----Examples-----
Input
())(())(())(
7
1 1
2 3
1 2
1 12
8 12
5 11
2 10
Output
0
0
2
10
4
6
6
-----Note-----
A subsequence of length |x| of string s = s_1s_2... s_{|}s| (where |s| is the length of string s) is string x = s_{k}_1s_{k}_2... s_{k}_{|}x| (1 ≤ k_1 < k_2 < ... < k_{|}x| ≤ |s|).
A correct bracket sequence is a bracket sequence that can be transformed into a correct aryphmetic expression by inserting characters "1" and "+" between the characters of the string. For example, bracket sequences "()()", "(())" are correct (the resulting expressions "(1)+(1)", "((1+1)+1)"), and ")(" and "(" are not.
For the third query required sequence will be «()».
For the fourth query required sequence will be «()(())(())».
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
s = input()
M = int(input())
def next_pow_2(n):
p = 1
while p < n:
p <<= 1
return p
def represented_range(node, size):
l = node
r = node
while l < size:
l = 2*l
r = 2*r + 1
return l-size, r-size
class SegTree:
def __init__(self, size):
self.size = next_pow_2(size)
self.answer = [0] * (2*self.size)
self.opened = [0] * (2*self.size)
self.closed = [0] * (2*self.size)
# O(size * (O(func) + O(init))
def build(self, s):
for i in range(self.size):
self.answer[self.size + i] = 0
self.opened[self.size + i] = 1 if i < len(s) and s[i] == '(' else 0
self.closed[self.size + i] = 1 if i < len(s) and s[i] == ')' else 0
for i in range(self.size - 1, 0, -1):
matched = min(self.opened[2*i], self.closed[2*i+1])
self.answer[i] = self.answer[2*i] + self.answer[2*i+1] + matched
self.opened[i] = self.opened[2*i] + self.opened[2*i+1] - matched
self.closed[i] = self.closed[2*i] + self.closed[2*i+1] - matched
# O(log(size)), [l,r]
def query(self, l, r):
l += self.size
r += self.size
eventsR = []
answer = 0
opened = 0
while l <= r:
if l & 1:
matched = min(self.closed[l], opened)
answer += self.answer[l] + matched
opened += self.opened[l] - matched
l += 1
if not (r & 1):
eventsR.append((self.answer[r], self.opened[r], self.closed[r]))
r -= 1
l >>= 1
r >>= 1
for i in range(len(eventsR)-1, -1, -1):
a, o, c = eventsR[i]
matched = min(c, opened)
answer += a + matched
opened += o - matched
return answer
seg = SegTree(len(s))
seg.build(s)
for i in range(M):
l, r = [int(_) for _ in input().split()]
print(2*seg.query(l-1, r-1))
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Anton has the integer x. He is interested what positive integer, which doesn't exceed x, has the maximum sum of digits.
Your task is to help Anton and to find the integer that interests him. If there are several such integers, determine the biggest of them.
-----Input-----
The first line contains the positive integer x (1 ≤ x ≤ 10^18) — the integer which Anton has.
-----Output-----
Print the positive integer which doesn't exceed x and has the maximum sum of digits. If there are several such integers, print the biggest of them. Printed integer must not contain leading zeros.
-----Examples-----
Input
100
Output
99
Input
48
Output
48
Input
521
Output
499
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
num = list(map(int, input()))
best = num[:]
for i in range(-1, -len(num) - 1, -1):
if num[i] == 0:
continue
num[i] -= 1
for j in range(i + 1, 0):
num[j] = 9
if sum(num) > sum(best):
best = num[:]
s = ''.join(map(str, best)).lstrip('0')
print(s)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Chef has a sequence of N$N$ integers A1,A2,...,AN$A_1, A_2, ..., A_N$.
Chef thinks that a triplet of integers (i,j,k)$(i,j,k)$ is good if 1≤i<j<k≤N$1 \leq i < j < k \leq N$ and P$P$ in the following expression contains an odd number of ones in its binary representation:
P=[Ai<<(⌊log2(Aj)⌋+⌊log2(Ak)⌋+2)]+[Aj<<(⌊log2(Ak)⌋+1)]+Ak$P = [ A_i<< ( \lfloor \log_2(A_j) \rfloor + \lfloor \log_2(A_k) \rfloor + 2 ) ] + [A_j << ( \lfloor \log_2(A_k) \rfloor + 1) ] + A_k$
The <<$<<$ operator is called left shift, x<<y$x << y$ is defined as x⋅2y$x \cdot 2^y$.
Help the Chef finding the total number of good triplets modulo 109+7$10^9 + 7$.
-----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 each test case contains a single integer N$N$.
- The second line of each test case contains N$N$ space-separated integers A1,A2,...,AN$A_1, A_2, ..., A_N$.
-----Output:-----
For each test case, print a single line containing one integer, the number of good triplets modulo 109+7$10^9+7$.
-----Constraints:-----
- 1≤T≤103$1 \leq T \leq 10^3$
- 1≤N≤105$1\leq N \leq 10^5$
- 1≤Ai≤109$1 \leq A_i \leq 10^9$
- The sum of N$N$ over all testcases is less than 106$10^6$
-----Sample Input:-----
1
4
1 1 2 3
-----Sample Output:-----
1
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
from math import *
t = int(input())
for _ in range(t):
n = int(input())
a = [int(d) for d in input().split()]
odd,even = 0,0
for i in range(n):
if bin(a[i]).count("1")%2 == 1:
odd += 1
else:
even +=1
total = 0
if odd >= 3 and even >= 2:
total += (odd*(odd-1)*(odd-2))//6
total += odd*(even*(even-1))//2
elif odd >= 3 and even < 2:
total += (odd*(odd-1)*(odd-2))//6
elif 0<odd < 3 and even >= 2:
total += odd*(even*(even-1))//2
print(total%(10**9+7))
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
The only difference between easy and hard versions is constraints.
Now elections are held in Berland and you want to win them. More precisely, you want everyone to vote for you.
There are $n$ voters, and two ways to convince each of them to vote for you. The first way to convince the $i$-th voter is to pay him $p_i$ coins. The second way is to make $m_i$ other voters vote for you, and the $i$-th voter will vote for free.
Moreover, the process of such voting takes place in several steps. For example, if there are five voters with $m_1 = 1$, $m_2 = 2$, $m_3 = 2$, $m_4 = 4$, $m_5 = 5$, then you can buy the vote of the fifth voter, and eventually everyone will vote for you. Set of people voting for you will change as follows: ${5} \rightarrow {1, 5} \rightarrow {1, 2, 3, 5} \rightarrow {1, 2, 3, 4, 5}$.
Calculate the minimum number of coins you have to spend so that everyone votes for you.
-----Input-----
The first line contains one integer $t$ ($1 \le t \le 5000$) — the number of test cases.
The first line of each test case contains one integer $n$ ($1 \le n \le 5000$) — the number of voters.
The next $n$ lines contains the description of voters. $i$-th line contains two integers $m_i$ and $p_i$ ($1 \le p_i \le 10^9, 0 \le m_i < n$).
It is guaranteed that the sum of all $n$ over all test cases does not exceed $5000$.
-----Output-----
For each test case print one integer — the minimum number of coins you have to spend so that everyone votes for you.
-----Example-----
Input
3
3
1 5
2 10
2 8
7
0 1
3 1
1 1
6 1
1 1
4 1
4 1
6
2 6
2 3
2 8
2 7
4 4
5 5
Output
8
0
7
-----Note-----
In the first test case you have to buy vote of the third voter. Then the set of people voting for you will change as follows: ${3} \rightarrow {1, 3} \rightarrow {1, 2, 3}$.
In the second example you don't need to buy votes. The set of people voting for you will change as follows: ${1} \rightarrow {1, 3, 5} \rightarrow {1, 2, 3, 5} \rightarrow {1, 2, 3, 5, 6, 7} \rightarrow {1, 2, 3, 4, 5, 6, 7}$.
In the third test case you have to buy votes of the second and the fifth voters. Then the set of people voting for you will change as follows: ${2, 5} \rightarrow {1, 2, 3, 4, 5} \rightarrow {1, 2, 3, 4, 5, 6}$.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
import heapq
for _ in range(int(input())):
n = int(input())
voters = []
for i in range(n):
m,p = list(map(int, input().split()))
voters.append((m, -p))
voters.sort()
for i in range(n):
voters[i] = (voters[i][0], -voters[i][1])
ans = 0
costs = []
heapq.heapify(costs)
bought = 0
for i in range(n-1, -1, -1):
buysNeeded = voters[i][0] - i - bought
heapq.heappush(costs, voters[i][1])
while buysNeeded > 0 and len(costs) > 0:
ans += heapq.heappop(costs)
bought += 1
buysNeeded -= 1
print(ans)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Chef Tobby is trying to run a code given to him by Bhuvan for an experiment they want to include in the manuscript to be submitted to a conference. The deadline to submit the manuscript is within a couple of hours and Chef Tobby needs to finish the experiments before then.
The code given by Bhuvan is the following which runs given an array of N integers and another integer K :
void recurse ( array a, int n )
{
// n = size of array
define array b currently empty
consider all 2^n subsets of a[]
{
x = bitwise OR of elements in the subsets
add x into "b" if it is not present yet
}
if (sizeof( b ) == 1 << k)
{
printf(“Won”);
return;
}
recurse ( b, sizeof( b ) );
}
Chef Tobby tried to run an experiment with only one integer in the array with value 2 and K = 3. To his horror, he found out that the algorithm is resulting in an infinite loop. He is livid with the possibility that the algorithm can lead to infinite loops for certain cases. On closer inspection he determines that it might be possible to insert additional elements in the initial array to subvert the problem. Since time is very less, Chef Tobby would like to insert the minimum number of elements.
Chef Tobby has to finish writing the paper, so he asks his graduate student Leamas to fix it. Leamas has no idea how to fix the problem so he asks you for help.
-----Input section-----
The first line contains T, the number of test cases.
Each test case consists of 2 lines. The first line contains 2 integers N and K, denoting the number of elements in the array and parameter mentioned in problem statement.
Next line contains N space separated integers, denoting the elements of the array.
-----Output section-----
Output the minimum number of elements that need to be inserted so that inifinite loop can be avoided.
-----Input constraints-----
1 ≤ T ≤ 10
1 ≤ Sum of N over all test cases ≤ 105
1 ≤ K ≤ 20
0 ≤ A[i] ≤ 2K-1, where A[i] denotes the ith element of the array.
-----Sample Input - 1-----
1
2 2
3 1
-----Sample Output - 1-----
1
-----Explanation - 1-----
You can win the game by inserting the element 2 into the array.
-----Sample Input - 2-----
1
7 3
3 7 5 4 6 2 1
-----Sample Output - 2-----
0
-----Explanation - 2-----
The initial array will result will terminate in the first step of algorithm only. Thus there is no need to insert any new element.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
from bisect import *
for x in range(eval(input())):
n,k = list(map(int,input().split()))
arr = list(map(int,input().split()))
arr.sort()
t = 1
result = 0
y = 0
while y < n:
if arr[y]<t:
y += 1
elif arr[y]==t:
t = t*2
y += 1
else:
result += 1
t = t*2
while t < 2**(k):
result += 1
t = t*2
print(result)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
One upon a time there were three best friends Abhinav, Harsh, and Akash decided to form a
team and take part in ICPC from KIIT. Participants are usually offered several problems during
the programming contest. Long before the start, the friends decided that they will implement a
problem if at least two of them are sure about the solution. Otherwise, friends won't write the
problem's solution.
This contest offers $N$ problems to the participants. For each problem we know, which friend is
sure about the solution. Help the KIITians find the number of problems for which they will write a
solution.
Then n lines contain three integers each, each integer is either 0 or 1. If the first number in the
line equals 1, then Abhinav is sure about the problem's solution, otherwise, he isn't sure. The
second number shows Harsh's view on the solution, the third number shows Akash's view. The
numbers on the lines are
-----Input:-----
- A single integer will contain $N$, number of problems.
-----Output:-----
Print a single integer — the number of problems the friends will implement on the contest.
-----Constraints-----
- $1 \leq N \leq 1000$
-----Sample Input:-----
3
1 1 0
1 1 1
1 0 0
-----Sample Output:-----
2
-----EXPLANATION:-----
In the first sample, Abhinav and Harsh are sure that they know how to solve the first problem
and all three of them know how to solve the second problem. That means that they will write
solutions for these problems. Only Abhinav is sure about the solution for the third problem, but
that isn't enough, so the group won't take it.
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())
count = 0
for _ in range(n):
L = list(map(int, input().split()))
if (L.count(1)>=2):
count+=1
print(count)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Note : This question carries $150$ $points$
There is an outcry in Middle Earth, as the greatest war between Orgs of Dark Lord Sauron and Frodo Baggins is about to begin. To end the war, Frodo decides to destroy the ring in the volcano of Mordor. There are many ships that lead Frodo to Mordor, and he is confused about which one he should board. Given two-ship numbers $M$ and $N$, Frodo has to solve a problem to find the ship which he should board.
Find the number of pairs (x, y), such that $1<=x<=M$ and $1<=y<=N$, for which $x*y + x+ y = string(x)+string(y)$ is true.
Also, calculate the number of distinct x satisfying the given condition. The number of pairs and the number of distinct x will help select Frodo the boat he should board. Help Frodo defeat Sauron.
-----Input :-----
- First line contains $T$ as number of test cases
- Each test case contains two integers $M$ and $N$
-----Output :-----
- For each test case, print two integers - the number of such pairs (x,y) and the number of distinct x
-----Constraints :-----
- 1 ≤ T ≤ 5000
- 1 ≤ M, N ≤ 10^9
-----Sample Input :-----
1
1 9
-----Sample Output :-----
1 1
-----Explanation :-----
For test case two M=1 and N=9 Pair (1,9) satisfies the above condition 1*9+1+9= “19” and only x=1 satisfies the equation.
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 math import pow
t = int(input())
for _ in range(t):
m,n = map(int,input().rstrip().split())
cnt = len(str(n))
x = pow(10,cnt)
if n == x-1:
print(m*cnt,m)
else:
print(m*(cnt-1),m)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Given an integer N. Integers A and B are chosen randomly in the range [1..N]. Calculate the probability that the Greatest Common Divisor(GCD) of A and B equals to B.
-----Input-----
The first line of the input contains an integer T denoting the number of test cases. The description of T test cases follows. Each test case consists of a single integer N on a separate line.
-----Output-----
For each test case, output a single line containing probability as an irreducible fraction.
-----Example-----
Input:
3
1
2
3
Output:
1/1
3/4
5/9
-----Constraints-----
1<=T<=103
1<=N<=109
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
import math
for _ in range(int(input())):
n=int(input())
s=int(math.sqrt(n))
ans=0
for i in range(1,s+1):
ans+=(n//i)
ans=ans*2-(s*s)
g=math.gcd(n*n,ans)
print(str(ans//g)+"/"+str(n*n//g))
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
This question is similar to the $"Operation$ $on$ $a$ $Tuple"$ problem in this month's Long Challenge but with a slight variation.
Consider the following operations on a triple of integers. In one operation, you should:
- Choose a positive integer $d>0$ and an arithmetic operation - in this case, it will only be addition.
- Choose a subset of elements of the triple.
- Apply arithmetic operation to each of the chosen elements.
For example, if we have a triple $(3,5,7)$, we may choose to add $3$ to the first and third element, and we get $(6,5,10)$ using one operation.
You are given an initial triple $(p,q,r)$ and a target triple $(a,b,c)$. Find the maximum number of operations needed to transform $(p,q,r)$ into $(a,b,c)$ or say the conversion 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 line of each test case contains three space-separated integers p, q and r.
- The second line contains three space-separated integers a, b and c.Output:
For each test case, print a single line containing one integer ― the maximum required number of operations(if the conversion is possible), or else print "-1"
Constraints:
- $1 \leq T \leq 1,000$
- $2 \leq |p|,|q|,|r|,|a|,|b|,|c| \leq 10^9$Sample Input:
1
2 2 1
3 3 2
Sample Output:
3
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
"""
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 three space-separated integers p, q and r.
The second line contains three space-separated integers a, b and c.
Output:
For each test case, print a single line containing one integer ― the maximum required number of operations(if the conversion is possible), or else print "-1"
"""
T=int(input())
while T>0:
T-=1
p,q,r=list(map(int,input().split()))
a,b,c=list(map(int,input().split()))
#ds=list()
s=0
d1=a-p
if d1>0:
#ds.append(d1)
s+=d1
d2=b-q
if d2>0:
#ds.append(d2)
s+=d2
d3=c-r
if d3>0:
#ds.append(d3)
s+=d3
if(d1==0 and d2==0 and d3==0):
print(0)
elif(d1<0 or d2<0 or d3<0):
print(-1)
else:
print(s)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Chef has a circular plot of land of radius $R$ on which he wants to construct a swimming pool.
He wants the swimming pool to be square in shape with maximum possible area,so that he along
with his friends can enjoy themselves during their summer vacations.
Help Chef to find out the maximum area of the swimming pool that can be constructed in his
circular plot.
-----Input:-----
- First line will contain $T$, number of testcases. Then the testcases follow.
- Each testcase contains of a single line of input, $R$ i.e the radius of the plot.
-----Output:-----
For each testcase, output in a single line answer displaying the maximum possible area of the swimming pool.
-----Constraints-----
- $1 \leq T \leq 1000$
- $1 \leq R \leq 10^8$
-----Sample Input:-----
2
5
10
-----Sample Output:-----
50
200
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())
l=[]
for t in range(T):
R=int(input())
a=2*(R**2)
l.append(a)
for s in l:
print(s)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
You are given a sequence a = \{a_1, ..., a_N\} with all zeros, and a sequence b = \{b_1, ..., b_N\} consisting of 0 and 1. The length of both is N.
You can perform Q kinds of operations. The i-th operation is as follows:
- Replace each of a_{l_i}, a_{l_i + 1}, ..., a_{r_i} with 1.
Minimize the hamming distance between a and b, that is, the number of i such that a_i \neq b_i, by performing some of the Q operations.
-----Constraints-----
- 1 \leq N \leq 200,000
- b consists of 0 and 1.
- 1 \leq Q \leq 200,000
- 1 \leq l_i \leq r_i \leq N
- If i \neq j, either l_i \neq l_j or r_i \neq r_j.
-----Input-----
Input is given from Standard Input in the following format:
N
b_1 b_2 ... b_N
Q
l_1 r_1
l_2 r_2
:
l_Q r_Q
-----Output-----
Print the minimum possible hamming distance.
-----Sample Input-----
3
1 0 1
1
1 3
-----Sample Output-----
1
If you choose to perform the operation, a will become \{1, 1, 1\}, for a hamming distance of 1.
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=int(input())
b=list(map(int,input().split()))
ope=[[] for i in range(n)]
Q=int(input())
for i in range(Q):
l,r=list(map(int,input().split()))
ope[r-1].append(l-1)
res=b.count(0)
Data=[(-1)**((b[i]==1)+1) for i in range(n)]
for i in range(1,n):
Data[i]+=Data[i-1]
Data=[0]+Data
for i in range(n):
ope[i].sort(reverse=True)
# N: 処理する区間の長さ
N=n+1
N0 = 2**(N-1).bit_length()
data = [None]*(2*N0)
INF = (-2**31, -2**31)
# 区間[l, r+1)の値をvに書き換える
# vは(t, value)という値にする (新しい値ほどtは大きくなる)
def update(l, r, v):
L = l + N0; R = r + N0
while L < R:
if R & 1:
R -= 1
if data[R-1]:
data[R-1] = max(v,data[R-1])
else:
data[R-1]=v
if L & 1:
if data[L-1]:
data[L-1] = max(v,data[L-1])
else:
data[L-1]=v
L += 1
L >>= 1; R >>= 1
# a_iの現在の値を取得
def _query(k):
k += N0-1
s = INF
while k >= 0:
if data[k]:
s = max(s, data[k])
k = (k - 1) // 2
return s
# これを呼び出す
def query(k):
return _query(k)[1]
for i in range(n+1):
update(i,i+1,(-Data[i],-Data[i]))
if ope[0]:
update(1,2,(0,0))
for i in range(1,n):
val=query(i)
update(i+1,i+2,(val+Data[i]-Data[i+1],val+Data[i]-Data[i+1]))
for l in ope[i]:
val=query(l)
update(l+1,i+2,(val,val))
print((n-(res+query(n)+Data[n])))
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Chef is playing a game with his childhood friend. He gave his friend a list of N numbers named $a_1, a_2 .... a_N$ (Note: All numbers are unique). Adjust the numbers in the following order:
$(i)$ swap every alternate number with it's succeeding number (If N is odd, do not swap the last number i.e. $a_N$ ).
$(ii)$ add %3 of every number to itself.
$(iii)$ swap the ith number and the (N-i-1) th number.
After this, Chef will give a number to his friend and he has to give the nearest greater and smaller number to it.
If there is no greater or lesser number, put -1.
Help his friend to find the two numbers.
-----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, an integers $N$.
- Next line contains $N$ integers separated by a space.
- Next line contains a number to be found, $M$.
-----Output:-----
For each test case, output in a single line answer given the immediate smaller and greater number separated by a space.
-----Constraints-----
- $1 \leq T \leq 1000$
- $3 \leq N \leq 10^5$
- $1 \leq N_i \leq 10^9$
- $1 \leq M \leq 10^9$
-----Sample Input:-----
1
10
5 15 1 66 55 32 40 22 34 11
38
-----Sample Output:-----
35 41
-----Explaination:-----
Step 1: 15 5 66 1 32 55 22 40 11 34
Step 2: 15 7 66 2 34 56 23 41 13 35
Step 3: 35 13 41 23 56 34 2 66 7 15
35 is the number lesser than 38 and 41 is the number greater than 38 in the given set of numbers.
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=list(map(int,input().split()))
x=int(input())
for _ in range(1,n,2):
a[_],a[_-1]=a[_-1],a[_]
for _ in range(n):
a[_]+=(a[_]%3)
# a=a[::-1]
# a.sort()
# if x>a[-1]:
# print(-1)
# continue
l,h=-1,9999999999
for _ in range(n):
# if a[_]>=x:
# if _==n-1:
# print(-1)
# break
# elif _==0:
# print(-1)
# break
# else:
# print(a[_-1],a[_])
# break
if a[_]>l and a[_]<x :
l=a[_]
if a[_]<h and a[_]>x :
h=a[_]
print(l,end=" ")
if h==9999999999:
print(-1)
else:
print(h)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Chef has come to a 2 dimensional garden in which there are N points. Each point has coordinates (x, y), where x can either be 1 or 2 or 3. Chef will now choose every triplet of these N points and make a triangle from it. You need to tell the sum of areas of all the triangles the Chef makes.
Note that some of the triplets might not form proper triangles, and would end up as a line or a point (ie. degenerate), but that is fine because their area will be zero.
-----Input-----
- The first line contains a single integer T, the number of test cases. The description of each testcase follows.
- The first line of each test case contains an integer N denoting the number of points on the plane.
- The next N lines contain 2 space separated integers x and y denoting the coordinates of the points.
-----Output-----
For each test case, output a single line containing the answer. Your answer will be considered correct if the absolute error is less than or equal to 10-2.
-----Constraints-----
- 1 ≤ T ≤ 20
- 1 ≤ N ≤ 2000
- 1 ≤ x ≤ 3
- 1 ≤ y ≤106
- All (x, y) pairs are distinct
-----Example-----
Input:
2
3
1 1
2 1
3 3
4
1 1
2 2
2 1
3 3
Output:
1.0
2.0
-----Explanation:-----
Test Case 1: There is only one triangle which has non-zero area, and it's area is 1, hence the output.
Test Case 2: Let the points be A(1,1), B(2,2), C(2,1), D(3,3). There are 3 non degenerate triangles possible.
- area ABC = 0.5
- area BCD = 0.5
- area ACD = 1
Total area = 2
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
# Author: Dancing Monkey | Created: 09.DEC.2018
import bisect
for _ in range(int(input())):
n = int(input())
x1 , x2, x3 = [], [], []
for i in range(n):
x, y = list(map(int, input().split()))
if x == 1: x1.append(y)
if x == 2: x2.append(y)
if x == 3: x3.append(y)
x1.sort()
x2.sort()
x3.sort()
y1, y2, y3 = len(x1), len(x2), len(x3)
area = 0
for i in range(y1):
for j in range(i+1, y1):
area += abs(x1[i] - x1[j])*(y2 + (2*y3))
for i in range(y3):
for j in range(i+1, y3):
area += abs(x3[i] - x3[j])*(y2 + (2*y1))
for i in range(y2):
for j in range(i+1, y2):
area += abs(x2[i] - x2[j])*(y1 + y3)
area /= 2
s1 = [0]
for i in range(y2): s1.append(s1[-1] + x2[i])
# print(s1)
s2 = [0]
for i in range(y2):s2.append(s2[-1] + x2[y2 - 1 - i])
# print(s2)
for i in x1:
for j in x3:
p1 = (i + j) / 2
p = bisect.bisect_left(x2, p1)
# print('p', p)
l = p
h = y2 - l
# print(l, h)
area += p1*(l) - s1[l]
# print('dfg', area)
area += s2[h] - p1*(h)
print(format(area, 'f'))
# print()
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
RedDreamer has an array $a$ consisting of $n$ non-negative integers, and an unlucky integer $T$.
Let's denote the misfortune of array $b$ having length $m$ as $f(b)$ — the number of pairs of integers $(i, j)$ such that $1 \le i < j \le m$ and $b_i + b_j = T$. RedDreamer has to paint each element of $a$ into one of two colors, white and black (for each element, the color is chosen independently), and then create two arrays $c$ and $d$ so that all white elements belong to $c$, and all black elements belong to $d$ (it is possible that one of these two arrays becomes empty). RedDreamer wants to paint the elements in such a way that $f(c) + f(d)$ is minimum possible.
For example:
if $n = 6$, $T = 7$ and $a = [1, 2, 3, 4, 5, 6]$, it is possible to paint the $1$-st, the $4$-th and the $5$-th elements white, and all other elements black. So $c = [1, 4, 5]$, $d = [2, 3, 6]$, and $f(c) + f(d) = 0 + 0 = 0$; if $n = 3$, $T = 6$ and $a = [3, 3, 3]$, it is possible to paint the $1$-st element white, and all other elements black. So $c = [3]$, $d = [3, 3]$, and $f(c) + f(d) = 0 + 1 = 1$.
Help RedDreamer to paint the array optimally!
-----Input-----
The first line contains one integer $t$ ($1 \le t \le 1000$) — the number of test cases. Then $t$ test cases follow.
The first line of each test case contains two integers $n$ and $T$ ($1 \le n \le 10^5$, $0 \le T \le 10^9$) — the number of elements in the array and the unlucky integer, respectively.
The second line contains $n$ integers $a_1$, $a_2$, ..., $a_n$ ($0 \le a_i \le 10^9$) — the elements of the array.
The sum of $n$ over all test cases does not exceed $10^5$.
-----Output-----
For each test case print $n$ integers: $p_1$, $p_2$, ..., $p_n$ (each $p_i$ is either $0$ or $1$) denoting the colors. If $p_i$ is $0$, then $a_i$ is white and belongs to the array $c$, otherwise it is black and belongs to the array $d$.
If there are multiple answers that minimize the value of $f(c) + f(d)$, print any of them.
-----Example-----
Input
2
6 7
1 2 3 4 5 6
3 6
3 3 3
Output
1 0 0 1 1 0
1 0 0
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 test in range(T):
n,t = list(map(int,input().split()))
a = list(map(int,input().split()))
res = []
j=0
for i in a:
if(i*2<t):
res+=["0"]
elif(i*2>t):
res+=["1"]
else:
res.append(["0","1"][j])
j = 1-j
print(" ".join(res))
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Vasya is an active Internet user. One day he came across an Internet resource he liked, so he wrote its address in the notebook. We know that the address of the written resource has format: <protocol>://<domain>.ru[/<context>]
where: <protocol> can equal either "http" (without the quotes) or "ftp" (without the quotes), <domain> is a non-empty string, consisting of lowercase English letters, the /<context> part may not be present. If it is present, then <context> is a non-empty string, consisting of lowercase English letters.
If string <context> isn't present in the address, then the additional character "/" isn't written. Thus, the address has either two characters "/" (the ones that go before the domain), or three (an extra one in front of the context).
When the boy came home, he found out that the address he wrote in his notebook had no punctuation marks. Vasya must have been in a lot of hurry and didn't write characters ":", "/", ".".
Help Vasya to restore the possible address of the recorded Internet resource.
-----Input-----
The first line contains a non-empty string that Vasya wrote out in his notebook. This line consists of lowercase English letters only.
It is guaranteed that the given string contains at most 50 letters. It is guaranteed that the given string can be obtained from some correct Internet resource address, described above.
-----Output-----
Print a single line — the address of the Internet resource that Vasya liked. If there are several addresses that meet the problem limitations, you are allowed to print any of them.
-----Examples-----
Input
httpsunrux
Output
http://sun.ru/x
Input
ftphttprururu
Output
ftp://http.ru/ruru
-----Note-----
In the second sample there are two more possible answers: "ftp://httpruru.ru" and "ftp://httpru.ru/ru".
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
s=""
L=[]
s=input()
k=0
r=0
c=0
if s[0]=='h':
L.append('http://')
c=4
s=s[c:]
elif s[0]=='f':
L.append('ftp://')
c=3
s=s[c:]
r=s.find('ru',1)
L.append(s[:r])
L.append('.ru')
k=r+2
if k<len(s):
L.append('/')
L.append(s[k:])
print(''.join(L))
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Vishal Wants to buy 2 gifts for his best friend whose name is Annabelle(her age is 20), So they both went for shopping in a store. But Annabelle gave, Vishal a condition that she will accept this gifts only when the total price of the gifts is the same as her age times 100.
The store contains, a list of items whose prices are also displayed, Now Vishal is asking for your help to buy gifts, as he wants to impress Annabelle this time.
Note: Vishal cannot buy the same item more than once.
-----Input:-----
- The first line of the input contains a single integer $T$. $T$ denoting the number of test cases. The description of $T$ test cases is as follows.
- The next line of the input contains a single integer $N$. $N$ denotes the total number of items in store.
- The next line of the input contains $N$ space-separated integers $A1, A2, A3...An$ where $ith$ number denotes the price of $ith$ element.
-----Output:-----
- For each test-case print "Accepted"(without quotes) if the gifts are accepted by Annabelle, else print "Rejected"(without quotes)
-----Constraints:-----
- $1 \leq T \leq 10^3$
- $1 \leq N \leq 10^5$
- $1 \leq A1, A2, A3...An \leq 10^7$
-----Sample Input:-----
1
5
10 2 1000 50 1000
-----Sample Output:-----
Accepted
-----Explanation:-----
- As the given list of items have 2 items whose price sum up to the age times 100 of Annabelle i.e. 1000+1000 = (20 *100)
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
test = int(input())
ANS = list()
for i in range(test):
n = int(input())
items = sorted(list(map(int, input().split())))
c = 1
for j in range(len(items)):
if items[j] < 2000:
t = 2000 - items[j]
if t in items[j+1:]:
ANS.append("Accepted")
c = 2
break
else:
pass
else:
break
if c==1:
ANS.append("Rejected")
for ans in ANS:
print(ans)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Given positive integers N, K and M, solve the following problem for every integer x between 1 and N (inclusive):
- Find the number, modulo M, of non-empty multisets containing between 0 and K (inclusive) instances of each of the integers 1, 2, 3 \cdots, N such that the average of the elements is x.
-----Constraints-----
- 1 \leq N, K \leq 100
- 10^8 \leq M \leq 10^9 + 9
- M is prime.
- All values in input are integers.
-----Input-----
Input is given from Standard Input in the following format:
N K M
-----Output-----
Use the following format:
c_1
c_2
:
c_N
Here, c_x should be the number, modulo M, of multisets such that the average of the elements is x.
-----Sample Input-----
3 1 998244353
-----Sample Output-----
1
3
1
Consider non-empty multisets containing between 0 and 1 instance(s) of each of the integers between 1 and 3. Among them, there are:
- one multiset such that the average of the elements is k = 1: \{1\};
- three multisets such that the average of the elements is k = 2: \{2\}, \{1, 3\}, \{1, 2, 3\};
- one multiset such that the average of the elements is k = 3: \{3\}.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
N,K,M=map(int,input().split());R=range;T=[[1]]
for i in R(1,N):
q=K*i
if i>~i+N:T+=[y:=T[-1][:len(T[~i+N])]]
else:T+=[y:=T[-1][:]+[0]*q]
p=len(y)-i
for j in R(p):y[j+i]+=y[j]%M
for j in R(p-q):y[~j]-=y[~j-i-q]%M
for i in R(N):print(sum(T[i][j]*T[~i+N][j]for j in R(len(T[i])))*-~K%M-1)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Chef played an interesting game yesterday. This game is played with two variables $X$ and $Y$; initially, $X = Y = 0$. Chef may make an arbitrary number of moves (including zero). In each move, he must perform the following process:
- Choose any positive integer $P$ such that $P \cdot P > Y$.
- Change $X$ to $P$.
- Add $P \cdot P$ to $Y$.
Unfortunately, Chef has a bad memory and he has forgotten the moves he made. He only remembers the value of $X$ after the game finished; let's denote it by $X_f$. Can you tell him the maximum possible number of moves he could have made in the game?
-----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 $X_f$.
-----Output-----
For each test case, print a single line containing one integer — the maximum number of moves Chef could have made.
-----Constraints-----
- $1 \le T \le 10^5$
- $1 \le X_f \le 10^9$
-----Example Input-----
3
3
8
9
-----Example Output-----
3
5
6
-----Explanation-----
Example case 2: One possible sequence of values of $X$ is $0 \rightarrow 1 \rightarrow 2 \rightarrow 3 \rightarrow 5 \rightarrow 8$.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
from math import sqrt
T = int(input())
ans = []
for _ in range(T):
X = int(input())
count = 0
x = 0
y = 0
while(x<=X):
p = int(sqrt(y))
count += 1
if(p*p>y):
x = p
y += p**2
else:
x = p+1
y += (p+1)**2
if(x<=X):
ans.append(count)
else:
ans.append(count-1)
for i in ans:
print(i)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
-----Problem-----
Suppose there is a circle. There are N Juice shops on that circle. Juice shops are numbered 0 to N-1 (both inclusive). You have two pieces of information corresponding to each of the juice shop:
(1) the amount of Juice that a particular Juice shop can provide and
(2) the distance from that juice shop to the next juice shop.
Initially, there is a man with a bottle of infinite capacity carrying no juice. He can start the tour at any of the juice shops. Calculate the first point from where the man will be able to complete the circle. Consider that the man will stop at every Juice Shop. The man will move one kilometer for each litre of the juice.
-----Input-----
-
The first line will contain the value of N.
-
The next N lines will contain a pair of integers each, i.e. the amount of juice that a juice shop can provide(in litres) and the distance between that juice shop and the next juice shop.
-----Output-----
An integer which will be the smallest index of the juice shop from which he can start the tour.
-----Constraints-----
-
1 ≤ N ≤ 105
-
1 ≤ amt of juice, distance ≤ 109
-----Sample Input-----
3
1 5
10 3
3 4
-----Sample Output-----
1
-----Explanation-----
He can start the tour from the SECOND Juice shop.
p { text-align:justify }
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
import re,sys
def isCirlePossible(juices,distances):
if juices == [] or distances == []:
return -1;
total_juice_consumed = 0
juice_consumed = 0
start=0
for i in range(0,len(juices)):
diff = juices[i] - distances[i]
if juice_consumed >= 0:
juice_consumed += diff
else:
juice_consumed = diff
start = i
total_juice_consumed += diff
return start
juices = []
distances = []
numLines = int(input())
for each in range(0,numLines):
line = input()
result = [int(x) for x in re.findall('\d+',line)]
if len(result) == 2:
juices.append(result[0])
distances.append(result[1])
print(isCirlePossible(juices,distances))
return
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Shaun was given $N$ pairs of parenthesis ( ) by his teacher who gave him a difficult task.The task consists of two steps. First,Shaun should colour all $N$ pairs of parenthesis each with different color but opening and closing bracket of a particular pair should be of same colour. Then,Shaun should report to his teacher the number of ways he can arrange all $2*N$ brackets such that sequence form is valid. Teacher defined valid sequence by these rules:
- Any left parenthesis '(' must have a corresponding right parenthesis ')'.
- Any right parenthesis ')' must have a corresponding left parenthesis '('.
- Left parenthesis '(' must go before the corresponding right parenthesis ')'.
Note: Shaun could match opening and closing brackets of different colours.
Since number of ways can be large, Shaun would report the answer as modulo 1000000007 ($10^9 + 7$).
-----Input:-----
- First line will contain $T$, number of testcases. Then the testcases follow.
- Each testcase contains of a single line of input, one integer $N$.
-----Output:-----
For each testcase, output in a single line answer given by Shaun to his teacher modulo 1000000007.
-----Constraints-----
- $1 \leq T \leq 100000$
- $1 \leq N \leq 100000$
-----Sample Input:-----
3
1
2
3
-----Sample Output:-----
1
6
90
-----EXPLANATION:-----
Here numbers from $1$ to $N$ have been used to denote parenthesis.A unique number corresponds to a unique pair of parenthesis.
-In the first test case , you can use only one color to color the parenthesis you could arrange it only in one way i.e, 1 1
-In the second test case you can use two colors and the possible ways of arranging it are
1 1 2 2
1 2 2 1
1 2 1 2
2 2 1 1
2 1 1 2
2 1 2 1
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
mod = 1000000007
fac = [1,1]
maxn = (10**5)+5
for i in range(2,maxn):
x = (fac[-1]*i)%mod
fac.append(x)
pre = [1]
for i in range(2,maxn):
x = 2*i-1
x = (pre[-1]*x)%mod
pre.append(x)
for _ in range(int(input())):
n = int(input())
x = fac[n]
y = pre[n-1]
print((x*y)%mod)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Polycarp analyzes the prices of the new berPhone. At his disposal are the prices for $n$ last days: $a_1, a_2, \dots, a_n$, where $a_i$ is the price of berPhone on the day $i$.
Polycarp considers the price on the day $i$ to be bad if later (that is, a day with a greater number) berPhone was sold at a lower price. For example, if $n=6$ and $a=[3, 9, 4, 6, 7, 5]$, then the number of days with a bad price is $3$ — these are days $2$ ($a_2=9$), $4$ ($a_4=6$) and $5$ ($a_5=7$).
Print the number of days with a bad price.
You have to answer $t$ independent data sets.
-----Input-----
The first line contains an integer $t$ ($1 \le t \le 10000$) — the number of sets of input data in the test. Input data sets must be processed independently, one after another.
Each input data set consists of two lines. The first line contains an integer $n$ ($1 \le n \le 150000$) — the number of days. The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 10^6$), where $a_i$ is the price on the $i$-th day.
It is guaranteed that the sum of $n$ over all data sets in the test does not exceed $150000$.
-----Output-----
Print $t$ integers, the $j$-th of which should be equal to the number of days with a bad price in the $j$-th input data set.
-----Example-----
Input
5
6
3 9 4 6 7 5
1
1000000
2
2 1
10
31 41 59 26 53 58 97 93 23 84
7
3 2 1 2 3 4 5
Output
3
0
1
8
2
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 = list(map(int, input().split()))
m = 10 ** 9
c = 0
for i in range(n - 1, -1, -1):
if A[i] <= m:
m = A[i]
else:
c += 1
print(c)
```
|
|
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. A group of disjoint subarrays in it will be a collection of subarrays of the array. Formally a group of subarrays consisting of K subarrays can be denoted by 2 * K indices, [i1, j1], [i2, j2] , ..., [iK, jK], such that i1 ≤ j1 < i2 ≤ j2 < ... < iK ≤ jK.
For example, in array A = {5, 6, 7}. A group of subarrays could be the subarrays denoted by indices [1, 1], [2, 3]. The subarray corresponding to indices [1, 1] will be {5}. The subarray corresponding to indices [2, 3] will be {6, 7}. So, we have i1 = 1, j1 = 1, i2 = 2, j2 = 3 and K = 2. You can check that the indices satisfy the property i1 ≤ j1 < i2 ≤ j2.
Note that the group of subarrays [1, 2] and [2, 3] won't be disjoint, as it does not satisfy the property j1 < i2. In other words, the index 2 is common in two subarrays, which should not happen.
Let M denote the maximum value of K in a group of K disjoint subarrays of array A, such that there are not two elements (not indices) common in those subarrays. This means, that if the group contained subarrays [A[i1], A[j1], [A[i2], A[j2]] , ..., A[[iK, jK]], then there should not be an element which is present in more than one subarrays.
You have to find maximum number of group of disjoint subarrays that number of subarrays in those groups are equal to M. As the answer could be large, output it 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.
First line of the each test case contains a single integer N denoting number of elements in array A.
Second line of each test case contains N space separated integers denoting the elements of the array A
-----Output-----
For each test case, output a single line corresponding to maximum number of group of disjoint subarrays of array A.
-----Constraints-----
- 1 ≤ T, N ≤ 105
- 1 ≤ Ai ≤ n
- Sum of N over all the test cases in a single file won't exceed 105
-----Subtasks-----
Subtask #1 (30 points)
- 1 ≤ T, N ≤ 103
- 1 ≤ Ai ≤ n
- Sum of N over all the test cases in a single file won't exceed 103
Subtask #2 (70 points)
- original constraints
-----Example-----
Input
3
2
3 4
3
1 2 2
5
1 1 2 2 2
Output:
1
3
18
-----Explanation-----
Example case 1. M will be equal to 2. The subarrays will be {[1, 1], [2, 2]}.
Example case 2. M will be equal to 3. The subarrays will be {[1, 1], [2, 2]}, {[1, 1], [3, 3]} and {[1, 1], [2, 3]}. Note that {[2, 2], [3, 3]} won't be a non-intersecting subarray as A[2] = 2 and A[3] = 2. So, 2 is common in both these subarrays.
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 k in range(t):
n=int(input())
l=[int(i) for i in input().split()]
m={}
count=1
for i in range(1,n):
if l[i]==l[i-1]:
count+=1
else:
if l[i-1] not in m:
m[l[i-1]]=(count*(count+1))/2
else:
m[l[i-1]]+=(count*(count+1))/2
count=1
if(l[n-1]) not in m:
m[l[n-1]]=(count*(count+1))/2
else:
m[l[n-1]]+=(count*(count+1))/2
s=1
for x in m:
s=(s*m[x])%(1000000007)
print(s)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
В Берляндском государственном университете локальная сеть между серверами не всегда работает без ошибок. При передаче двух одинаковых сообщений подряд возможна ошибка, в результате которой эти два сообщения сливаются в одно. При таком слиянии конец первого сообщения совмещается с началом второго. Конечно, совмещение может происходить только по одинаковым символам. Длина совмещения должна быть положительным числом, меньшим длины текста сообщения.
Например, при передаче двух сообщений «abrakadabra» подряд возможно, что оно будет передано с ошибкой описанного вида, и тогда будет получено сообщение вида «abrakadabrabrakadabra» или «abrakadabrakadabra» (в первом случае совмещение произошло по одному символу, а во втором — по четырем).
По полученному сообщению t определите, возможно ли, что это результат ошибки описанного вида работы локальной сети, и если возможно, определите возможное значение s.
Не следует считать ошибкой ситуацию полного наложения друга на друга двух сообщений. К примеру, если получено сообщение «abcd», следует считать, что в нём ошибки нет. Аналогично, простое дописывание одного сообщения вслед за другим не является признаком ошибки. Например, если получено сообщение «abcabc», следует считать, что в нём ошибки нет.
-----Входные данные-----
В единственной строке выходных данных следует непустая строка t, состоящая из строчных букв латинского алфавита. Длина строки t не превосходит 100 символов.
-----Выходные данные-----
Если сообщение t не может содержать ошибки, выведите «NO» (без кавычек) в единственную строку выходных данных.
В противном случае в первой строке выведите «YES» (без кавычек), а в следующей строке выведите строку s — возможное сообщение, которое могло привести к ошибке. Если возможных ответов несколько, разрешается вывести любой из них.
-----Примеры-----
Входные данные
abrakadabrabrakadabra
Выходные данные
YES
abrakadabra
Входные данные
acacacaca
Выходные данные
YES
acaca
Входные данные
abcabc
Выходные данные
NO
Входные данные
abababab
Выходные данные
YES
ababab
Входные данные
tatbt
Выходные данные
NO
-----Примечание-----
Во втором примере подходящим ответом также является строка acacaca.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
s = input()
t = 0
if len(s)%2==0:
n = (len(s)-1)//2+1
else:
n = (len(s)-1)//2
for i in range(n, len(s)-1):
a = i
b = len(s)-i-1
if s[:a+1]==s[b:]:
print('YES')
print(s[:a+1])
t = 1
break
if t==0:
print('NO')
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Ram and Shyam are playing a game of Truth and Dare. In this game, Shyam will ask Ram to perform tasks of two types:
- Truth task: Ram has to truthfully answer a question.
- Dare task: Ram has to perform a given task.
Each task is described by an integer. (If a truth task and a dare task are described by the same integer, they are still different tasks.) You are given four lists of tasks:
- $T_{r, 1}, T_{r, 2}, \dots, T_{r, t_r}$: the truth tasks Ram can perform.
- $D_{r, 1}, D_{r, 2}, \dots, D_{r, d_r}$: the dare tasks Ram can perform.
- $T_{s, 1}, T_{s, 2}, \dots, T_{s, t_s}$: the truth tasks Shyam can ask Ram to perform.
- $D_{s, 1}, D_{s, 2}, \dots, D_{s, d_s}$: the dare tasks Shyam can ask Ram to perform.
Note that the elements of these lists are not necessarily distinct, each task may be repeated any number of times in each list.
Shyam wins the game if he can find a task Ram cannot perform. Ram wins if he performs all tasks Shyam asks him to. Find the winner of the game.
Let's take an example where Ram can perform truth tasks $3$, $2$ and $5$ and dare tasks $2$ and $100$, and Shyam can give him truth tasks $2$ and $3$ and a dare task $100$. We can see that whichever truth or dare tasks Shyam asks Ram to perform, Ram can easily perform them, so he wins. However, if Shyam can give him dare tasks $3$ and $100$, then Ram will not be able to perform dare task $3$, so Shyam wins.
-----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 $t_r$.
- The second line contains $t_r$ space-separated integers $T_{r, 1}, T_{r, 2}, \dots, T_{r, t_r}$.
- The third line contains a single integer $d_r$.
- The fourth line contains $d_r$ space-separated integers $D_{r, 1}, D_{r, 2}, \dots, D_{r, d_r}$.
- The fifth line contains a single integer $t_s$.
- The sixth line contains $t_s$ space-separated integers $T_{s, 1}, T_{s, 2}, \dots, T_{s, t_s}$.
- The seventh line contains a single integer $d_s$.
- The eighth line contains $d_s$ space-separated integers $D_{s, 1}, D_{s, 2}, \dots, D_{s, d_s}$.
-----Output-----
For each test case, print a single line containing the string "yes" if Ram wins the game or "no" otherwise.
-----Constraints-----
- $1 \le T \le 100$
- $1 \le t_r, d_r, t_s, d_s \le 100$
- $1 \le T_{r, i} \le 100$ for each valid $i$
- $1 \le D_{r, i} \le 100$ for each valid $i$
- $1 \le T_{s, i} \le 100$ for each valid $i$
- $1 \le D_{s, i} \le 100$ for each valid $i$
-----Example Input-----
4
2
1 2
3
1 3 2
1
2
2
3 2
2
1 2
3
1 3 2
1
2
3
3 2 4
3
3 2 5
2
2 100
1
2
1
100
2
1 2
3
1 3 2
1
2
3
3 2 2
-----Example Output-----
yes
no
yes
yes
-----Explanation-----
Example case 1: Ram's truth tasks are $[1, 2]$ and his dare tasks are $[1, 3, 2]$. Shyam's truth tasks are $[2]$ and his dare tasks are $[3, 2]$. Ram can perform all tasks Shyam gives him.
Example case 2: Ram's truth tasks are $[1, 2]$ and his dare tasks are $[1, 3, 2]$. Shyam's truth tasks are $[2]$ and his dare tasks are $[3, 2, 4]$. If Shyam asks Ram to perform dare task $4$, Ram will not be able to do it.
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())):
tr=int(input())
trl=list(map(int,input().split()))
dr = int(input())
drl = list(map(int, input().split()))
ts = int(input())
tsl = list(map(int, input().split()))
ds = int(input())
dsl = list(map(int, input().split()))
for item in tsl:
if item in trl:
res=1
continue
else:
res=0
break
for item1 in dsl:
if item1 in drl:
res1=1
continue
else:
res1=0
break
if res==1 and res1==1:
print("yes")
else:
print("no")
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
You are given an empty grid with $N$ rows (numbered $1$ through $N$) and $M$ columns (numbered $1$ through $M$). You should fill this grid with integers in a way that satisfies the following rules:
- For any three cells $c_1$, $c_2$ and $c_3$ such that $c_1$ shares a side with $c_2$ and another side with $c_3$, the integers written in cells $c_2$ and $c_3$ are distinct.
- Let's denote the number of different integers in the grid by $K$; then, each of these integers should lie between $1$ and $K$ inclusive.
- $K$ should be minimum possible.
Find the minimum value of $K$ and a resulting (filled) grid. 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 and only line of each test case contains two space-separated integers $N$ and $M$.
-----Output-----
- For each test case, print $N+1$ lines.
- The first line should contain a single integer — the minimum $K$.
- Each of the following $N$ lines should contain $M$ space-separated integers between $1$ and $K$ inclusive. For each valid $i, j$, the $j$-th integer on the $i$-th line should denote the number in the $i$-th row and $j$-th column of the grid.
-----Constraints-----
- $1 \le T \le 500$
- $1 \le N, M \le 50$
- the sum of $N \cdot M$ over all test cases does not exceed $7 \cdot 10^5$
-----Subtasks-----
Subtask #1 (100 points): original constraints
-----Example Input-----
2
1 1
2 3
-----Example Output-----
1
1
3
1 1 2
2 3 3
-----Explanation-----
Example case 1: There is only one cell in the grid, so the only valid way to fill it is to write $1$ in this cell. Note that we cannot use any other integer than $1$.
Example case 2: For example, the integers written in the neighbours of cell $(2, 2)$ are $1$, $2$ and $3$; all these numbers are pairwise distinct and the integer written inside the cell $(2, 2)$ does not matter. Note that there are pairs of neighbouring cells with the same integer written in them, but this is OK.
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):
m,n = [int(d) for d in input().split()]
if m == 1:
arr = []
if n%4 == 0:
print(2)
arr = [[1,1,2,2]*(n//4)]
elif n%4 == 1:
if n == 1:
print(1)
arr = [[1]]
else:
print(2)
arr = [[1,1,2,2]*(n//4) + [1]]
elif n%4 == 2:
if n == 2:
print(1)
arr = [[1,1]]
else:
print(2)
arr = [[1,1,2,2]*(n//4) + [1,1]]
elif n%4 == 3:
print(2)
arr = [[1,1,2,2]*(n//4) + [1,1,2]]
elif m == 2:
if n%3 == 0:
print(3)
a1 = [1,2,3]*(n//3)
arr = [a1,a1]
elif n%3 == 1:
if n == 1:
print(1)
arr = [[1],[1]]
else:
print(3)
a1 = [1,2,3]*(n//3) + [1]
arr = [a1,a1]
elif n%3 == 2:
if n == 2:
print(2)
arr = [[1,2],[1,2]]
else:
print(3)
a1 = [1,2,3]*(n//3) + [1,2]
arr = [a1,a1]
elif m == 3:
if n == 1:
print(2)
arr = [[1],[1],[2]]
elif n == 2:
print(3)
arr = [[1,1],[2,2],[3,3]]
elif n == 3:
print(4)
arr = [[1,3,4],[4,2,1],[4,2,1]]
elif n == 4:
print(4)
arr = [[1,3,4,2],[4,2,1,3],[4,2,1,3]]
else:
if n%4 == 0:
print(4)
a1 = [1,3,4,2]*(n//4)
a2 = [4,2,1,3]*(n//4)
arr = [a1,a2,a2]
elif n%4 == 1:
print(4)
a1 = [1,3,4,2]*(n//4) + [1]
a2 = [4,2,1,3]*(n//4) + [4]
arr = [a1,a2,a2]
elif n%4 == 2:
print(4)
a1 = [1,3,4,2]*(n//4) + [1,3]
a2 = [4,2,1,3]*(n//4) + [4,2]
arr = [a1,a2,a2]
elif n%4 == 3:
print(4)
a1 = [1,3,4,2]*(n//4) + [1,3,4]
a2 = [4,2,1,3]*(n//4) + [4,2,1]
arr = [a1,a2,a2]
else:
if n == 1:
print(2)
a1 = [1,3,4,2]*(n//4) + [1]
a2 = [4,2,1,3]*(n//4) + [2]
arr = []
i = 0
j = 0
c = 0
c1 = 0
for i in range(m):
if j == 0 and c < 3:
arr.append(a1)
c = c + 1
if c == 2:
j = 1
c = 0
else:
arr.append(a2)
c1 = c1 + 1
if c1 == 2:
j = 0
c1 = 0
elif n == 2:
print(3)
arr = []
a1 = [1,1]
a2 = [2,2]
a3 = [3,3]
if m%3 == 1:
arr = [a1,a2,a3]*(m//3) + [a1]
elif m%3 == 2:
arr = [a1,a2,a3]*(m//3) + [a1,a2]
elif m%3 == 0:
arr = [a1,a2,a3]*(m//3)
else:
print(4)
if n%4 == 0:
a1 = [1,3,4,2]*(n//4)
a2 = [4,2,1,3]*(n//4)
arr = []
i = 0
j = 0
c = 0
c1 = 0
for i in range(m):
if j == 0 and c < 3:
arr.append(a1)
c = c + 1
if c == 2:
j = 1
c = 0
else:
arr.append(a2)
c1 = c1 + 1
if c1 == 2:
j = 0
c1 = 0
elif n%4 == 1:
a1 = [1,3,4,2]*(n//4) + [1]
a2 = [4,2,1,3]*(n//4) + [4]
arr = []
i = 0
j = 0
c = 0
c1 = 0
for i in range(m):
if j == 0 and c < 3:
arr.append(a1)
c = c + 1
if c == 2:
j = 1
c = 0
else:
arr.append(a2)
c1 = c1 + 1
if c1 == 2:
j = 0
c1 = 0
elif n%4 == 2:
a1 = [1,3,4,2]*(n//4) + [1,3]
a2 = [4,2,1,3]*(n//4) + [4,2]
arr = []
i = 0
j = 0
c = 0
c1 = 0
for i in range(m):
if j == 0 and c < 3:
arr.append(a1)
c = c + 1
if c == 2:
j = 1
c = 0
else:
arr.append(a2)
c1 = c1 + 1
if c1 == 2:
j = 0
c1 = 0
elif n%4 == 3:
a1 = [1,3,4,2]*(n//4) + [1,3,4]
a2 = [4,2,1,3]*(n//4) + [4,2,1]
arr = []
i = 0
j = 0
c = 0
c1 = 0
for i in range(m):
if j == 0 and c < 3:
arr.append(a1)
c = c + 1
if c == 2:
j = 1
c = 0
else:
arr.append(a2)
c1 = c1 + 1
if c1 == 2:
j = 0
c1 = 0
for i in range(m):
for j in range(n):
print(arr[i][j],end = " ")
print()
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
In this problem we assume the Earth to be a completely round ball and its surface a perfect sphere. The length of the equator and any meridian is considered to be exactly 40 000 kilometers. Thus, travelling from North Pole to South Pole or vice versa takes exactly 20 000 kilometers.
Limak, a polar bear, lives on the North Pole. Close to the New Year, he helps somebody with delivering packages all around the world. Instead of coordinates of places to visit, Limak got a description how he should move, assuming that he starts from the North Pole. The description consists of n parts. In the i-th part of his journey, Limak should move t_{i} kilometers in the direction represented by a string dir_{i} that is one of: "North", "South", "West", "East".
Limak isn’t sure whether the description is valid. You must help him to check the following conditions: If at any moment of time (before any of the instructions or while performing one of them) Limak is on the North Pole, he can move only to the South. If at any moment of time (before any of the instructions or while performing one of them) Limak is on the South Pole, he can move only to the North. The journey must end on the North Pole.
Check if the above conditions are satisfied and print "YES" or "NO" on a single line.
-----Input-----
The first line of the input contains a single integer n (1 ≤ n ≤ 50).
The i-th of next n lines contains an integer t_{i} and a string dir_{i} (1 ≤ t_{i} ≤ 10^6, $\operatorname{dir}_{i} \in \{\text{North, South, West, East} \}$) — the length and the direction of the i-th part of the journey, according to the description Limak got.
-----Output-----
Print "YES" if the description satisfies the three conditions, otherwise print "NO", both without the quotes.
-----Examples-----
Input
5
7500 South
10000 East
3500 North
4444 West
4000 North
Output
YES
Input
2
15000 South
4000 East
Output
NO
Input
5
20000 South
1000 North
1000000 West
9000 North
10000 North
Output
YES
Input
3
20000 South
10 East
20000 North
Output
NO
Input
2
1000 North
1000 South
Output
NO
Input
4
50 South
50 North
15000 South
15000 North
Output
YES
-----Note-----
Drawings below show how Limak's journey would look like in first two samples. In the second sample the answer is "NO" because he doesn't end on the North Pole. [Image]
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
"""
Codeforces Good Bye 2016 Contest Problem B
Author : chaotic_iak
Language: Python 3.5.2
"""
################################################### SOLUTION
def main():
latitude = 0
n, = read()
for i in range(n):
l, d = read(str)
l = int(l)
if latitude == 0:
if d != "South":
return "NO"
if latitude == 20000:
if d != "North":
return "NO"
if d == "South":
latitude += l
elif d == "North":
latitude -= l
if not (0 <= latitude <= 20000):
return "NO"
if latitude != 0:
return "NO"
return "YES"
#################################################### HELPERS
def read(callback=int):
return list(map(callback, input().strip().split()))
def write(value, end="\n"):
if value is None: return
try:
if not isinstance(value, str):
value = " ".join(map(str, value))
except:
pass
print(value, end=end)
write(main())
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
One day Kefa found n baloons. For convenience, we denote color of i-th baloon as s_{i} — lowercase letter of the Latin alphabet. Also Kefa has k friends. Friend will be upset, If he get two baloons of the same color. Kefa want to give out all baloons to his friends. Help Kefa to find out, can he give out all his baloons, such that no one of his friens will be upset — print «YES», if he can, and «NO», otherwise. Note, that Kefa's friend will not upset, if he doesn't get baloons at all.
-----Input-----
The first line contains two integers n and k (1 ≤ n, k ≤ 100) — the number of baloons and friends.
Next line contains string s — colors of baloons.
-----Output-----
Answer to the task — «YES» or «NO» in a single line.
You can choose the case (lower or upper) for each letter arbitrary.
-----Examples-----
Input
4 2
aabb
Output
YES
Input
6 3
aacaab
Output
NO
-----Note-----
In the first sample Kefa can give 1-st and 3-rd baloon to the first friend, and 2-nd and 4-th to the second.
In the second sample Kefa needs to give to all his friends baloons of color a, but one baloon will stay, thats why answer is «NO».
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
alpha = [chr(ord('a')+i) for i in range(26)]
n,k = list(map(int,input().split()))
s = input()
arr = [s.count(alpha[i]) for i in range(26)]
print('YES' if max(arr) <= k else 'NO')
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
We say that a binary string (a string containing only characters '0' and '1') is pure if it does not contain either of the strings "0101" or "1010" as a subsequence.
Recall that string T is a subsequence of string S if we can delete some of the letters of S (possibly none) such that the resulting string will become T.
You are given a binary string $S$ with length $N$. We want to make this string pure by deleting some (possibly zero) characters from it. What is the minimum number of characters we have to delete?
-----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 $S$ with length $N$.
-----Output-----
For each test case, print a single line containing one integer — the minimum number of characters we have to delete from $S$.
-----Constraints-----
- $1 \le T \le 40$
- $1 \le N \le 1,000$
- $S$ contains only characters '0' and '1'
-----Example Input-----
4
010111101
1011100001011101
0110
111111
-----Example Output-----
2
3
0
0
-----Explanation-----
Example case 1: We can delete the first and third character of our string. There is no way to make the string pure by deleting only one character.
Example case 3: The given string is already pure, so the answer is zero.
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 math;
from math import gcd,sqrt,floor,factorial,ceil
from bisect import bisect_left,bisect_right
import bisect;
import sys;
from sys import stdin,stdout
import os
sys.setrecursionlimit(pow(10,7))
import collections
from collections import defaultdict,Counter
from statistics import median
# input=stdin.readline
# print=stdout.write
from queue import Queue
inf = float("inf")
from operator import neg;
mod=pow(10,9)+7
def fun(l):
m=[[l[0]]]
for i in range(1,n):
if m[-1][-1]==l[i]:
m[-1]+=[l[i]]
else:
m.append([l[i]])
count=[]
for i in range(len(m)):
count.append(len(m[i]))
return count;
def function(l1,index,prev,count):
tuple=(index,prev,count)
if tuple in dict:
return dict[tuple]
n=len(l1)
if index==n:
return 0;
if count>=3:
if index%2==prev:
dict[tuple]=function(l1,index+1,prev,count)
return function(l1,index+1,prev,count)
else:
dict[tuple]=l1[index]+function(l1,index+1,prev,count);
return dict[tuple]
if prev==None:
skip=l1[index]+function(l1,index+1,prev,count)
not_skip=function(l1,index+1,index%2,count+1)
maxa=min(skip,not_skip)
dict[tuple]=maxa
return maxa;
if index%2==prev:
dict[tuple]=function(l1,index+1,index%2,count)
return dict[tuple]
if index%2!=prev:
skip=l1[index]+function(l1,index+1,prev,count)
not_skip=function(l1,index+1,index%2,1+count)
maxa = min(skip, not_skip)
dict[tuple]=maxa
return maxa;
t=int(input())
for i in range(t):
s=input()
l=list(s)
n=len(l)
l=[int(i) for i in l]
l1=fun(l)
dict=defaultdict(int)
theta=function(l1,0,None,0)
print(theta)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
You are given a binary string $s$ (recall that a string is binary if each character is either $0$ or $1$).
Let $f(t)$ be the decimal representation of integer $t$ written in binary form (possibly with leading zeroes). For example $f(011) = 3, f(00101) = 5, f(00001) = 1, f(10) = 2, f(000) = 0$ and $f(000100) = 4$.
The substring $s_{l}, s_{l+1}, \dots , s_{r}$ is good if $r - l + 1 = f(s_l \dots s_r)$.
For example string $s = 1011$ has $5$ good substrings: $s_1 \dots s_1 = 1$, $s_3 \dots s_3 = 1$, $s_4 \dots s_4 = 1$, $s_1 \dots s_2 = 10$ and $s_2 \dots s_4 = 011$.
Your task is to calculate the number of good substrings of string $s$.
You have to answer $t$ independent queries.
-----Input-----
The first line contains one integer $t$ ($1 \le t \le 1000$) — the number of queries.
The only line of each query contains string $s$ ($1 \le |s| \le 2 \cdot 10^5$), consisting of only digits $0$ and $1$.
It is guaranteed that $\sum\limits_{i=1}^{t} |s_i| \le 2 \cdot 10^5$.
-----Output-----
For each query print one integer — the number of good substrings of string $s$.
-----Example-----
Input
4
0110
0101
00001000
0001000
Output
4
3
4
3
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
LOG = 20
def solve(s):
n = len(s)
res = 0
z = 0
for t in range(0, n):
if s[t] == '0':
z += 1
continue
for l in range(1, min(LOG, n - t + 1)):
x = int(s[t:t+l], 2)
# print(l, t, x, l + z)
if l + z >= x:
res += 1
# print(t, l, x, res, z)
z = 0
return res
t = int(input())
while t > 0:
t -= 1
s = input()
print(solve(s))
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Consider a sequence [a_1, a_2, ... , a_{n}]. Define its prefix product sequence $[ a_{1} \operatorname{mod} n,(a_{1} a_{2}) \operatorname{mod} n, \cdots,(a_{1} a_{2} \cdots a_{n}) \operatorname{mod} n ]$.
Now given n, find a permutation of [1, 2, ..., n], such that its prefix product sequence is a permutation of [0, 1, ..., n - 1].
-----Input-----
The only input line contains an integer n (1 ≤ n ≤ 10^5).
-----Output-----
In the first output line, print "YES" if such sequence exists, or print "NO" if no such sequence exists.
If any solution exists, you should output n more lines. i-th line contains only an integer a_{i}. The elements of the sequence should be different positive integers no larger than n.
If there are multiple solutions, you are allowed to print any of them.
-----Examples-----
Input
7
Output
YES
1
4
3
6
5
2
7
Input
6
Output
NO
-----Note-----
For the second sample, there are no valid sequences.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
def comp(x):
for i in range(2, x):
if x % i == 0:
return True
return False
N = int(input())
if N == 4:
print('YES', '1', '3', '2', '4', sep = '\n')
elif comp(N):
print('NO')
else:
print('YES', '1', sep = '\n')
if N > 1:
for i in range(2, N):
print((i - 1) * pow(i, N - 2, N) % N)
print(N)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Kuro has recently won the "Most intelligent cat ever" contest. The three friends then decided to go to Katie's home to celebrate Kuro's winning. After a big meal, they took a small break then started playing games.
Kuro challenged Katie to create a game with only a white paper, a pencil, a pair of scissors and a lot of arrows (you can assume that the number of arrows is infinite). Immediately, Katie came up with the game called Topological Parity.
The paper is divided into $n$ pieces enumerated from $1$ to $n$. Shiro has painted some pieces with some color. Specifically, the $i$-th piece has color $c_{i}$ where $c_{i} = 0$ defines black color, $c_{i} = 1$ defines white color and $c_{i} = -1$ means that the piece hasn't been colored yet.
The rules of the game is simple. Players must put some arrows between some pairs of different pieces in such a way that for each arrow, the number in the piece it starts from is less than the number of the piece it ends at. Also, two different pieces can only be connected by at most one arrow. After that the players must choose the color ($0$ or $1$) for each of the unpainted pieces. The score of a valid way of putting the arrows and coloring pieces is defined as the number of paths of pieces of alternating colors. For example, $[1 \to 0 \to 1 \to 0]$, $[0 \to 1 \to 0 \to 1]$, $[1]$, $[0]$ are valid paths and will be counted. You can only travel from piece $x$ to piece $y$ if and only if there is an arrow from $x$ to $y$.
But Kuro is not fun yet. He loves parity. Let's call his favorite parity $p$ where $p = 0$ stands for "even" and $p = 1$ stands for "odd". He wants to put the arrows and choose colors in such a way that the score has the parity of $p$.
It seems like there will be so many ways which satisfy Kuro. He wants to count the number of them but this could be a very large number. Let's help him with his problem, but print it modulo $10^{9} + 7$.
-----Input-----
The first line contains two integers $n$ and $p$ ($1 \leq n \leq 50$, $0 \leq p \leq 1$) — the number of pieces and Kuro's wanted parity.
The second line contains $n$ integers $c_{1}, c_{2}, ..., c_{n}$ ($-1 \leq c_{i} \leq 1$) — the colors of the pieces.
-----Output-----
Print a single integer — the number of ways to put the arrows and choose colors so the number of valid paths of alternating colors has the parity of $p$.
-----Examples-----
Input
3 1
-1 0 1
Output
6
Input
2 1
1 0
Output
1
Input
1 1
-1
Output
2
-----Note-----
In the first example, there are $6$ ways to color the pieces and add the arrows, as are shown in the figure below. The scores are $3, 3, 5$ for the first row and $5, 3, 3$ for the second row, both from left to right.
[Image]
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
n,p=list(map(int,input().split()))
nums=[0]+list(map(int,input().split()))
mod=10**9+7
f=[[[[0]*2 for _ in range(2)] for _ in range(2)] for _ in range(n+1)]
_2=[0]*(n+1)
_2[0]=1
for i in range(1,n+1):
_2[i]=(_2[i-1]<<1)%mod
f[0][0][0][0]=1
if nums[1]!=0:
f[1][1][0][1]+=1
if nums[1]!=1:
f[1][1][1][0]+=1
for i in range(2,n+1):
for j in range(2):
for ob in range(2):
for ow in range(2):
qwq=f[i-1][j][ob][ow]
if nums[i]!=0:
if ob:
f[i][j][ob][ow]=(f[i][j][ob][ow]+qwq*_2[i-2])%mod
f[i][j^1][ob][ow|1]=(f[i][j^1][ob][ow|1]+qwq*_2[i-2])%mod
else:
f[i][j^1][ob][ow|1]=(f[i][j^1][ob][ow|1]+qwq*_2[i-1])%mod
if nums[i]!=1:
if ow:
f[i][j][ob][ow]=(f[i][j][ob][ow]+qwq*_2[i-2])%mod
f[i][j^1][ob|1][ow]=(f[i][j^1][ob|1][ow]+qwq*_2[i-2])%mod
else:
f[i][j^1][ob|1][ow]=(f[i][j^1][ob|1][ow]+qwq*_2[i-1])%mod
ans=0
for i in range(2):
for j in range(2):
ans=(ans+f[n][p][i][j])%mod
print(ans)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Sometimes Sergey visits fast food restaurants. Today he is going to visit the one called PizzaKing.
Sergey wants to buy N meals, which he had enumerated by integers from 1 to N. He knows that the meal i costs Ci rubles. He also knows that there are M meal sets in the restaurant.
The meal set is basically a set of meals, where you pay Pj burles and get Qj meals - Aj, 1, Aj, 2, ..., Aj, Qj.
Sergey has noticed that sometimes he can save money by buying the meals in the meal sets instead of buying each one separately. And now he is curious about what is the smallest amount of rubles he needs to spend to have at least one portion of each of the meals.
-----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 pair of integer numbers N and M denoting the number of meals and the number of the meal sets.
The second line contains N space-separated integers C1, C2, ..., CN denoting the costs of the meals, bought separately.
Each of the following M lines starts with a pair of integer numbers Pi and Qi, denoting the cost of the meal set and the number of meals in it, followed with the integer numbers Ai, 1 Ai, 2, ..., Ai, Qi denoting the meal numbers.
-----Output-----
For each test case, output a single line containing the minimal total amount of money Sergey needs to spend in order to have at least one portion of each meal.
-----Constraints-----
- 1 ≤ Pi, Ci ≤ 106
- 1 ≤ M ≤ min{2N, 2 × 100000}
- No meal appears in the set twice or more times.
- Subtask 1 (16 points): 1 ≤ T ≤ 103, 1 ≤ N ≤ 8
- Subtask 2 (23 points): For each test file, either 1 ≤ T ≤ 10, 1 ≤ N ≤ 12 or the constraints for Subtask 1 are held.
- Subtask 3 (61 points): For each test file, either T = 1, 1 ≤ N ≤ 18 or the constraints for Subtask 1 or 2 are held.
-----Example-----
Input:1
3 3
3 5 6
11 3 1 2 3
5 2 1 2
5 2 1 3
Output:10
-----Explanation-----
Example case 1. If Sergey buys all the meals separately, it would cost him 3 + 5 + 6 = 14 rubles. He can buy all of them at once by buying the first meal set, which costs for 11 rubles, but the optimal strategy would be either to buy the second and the third meal set, thus, paying 5 + 5 = 10 rubles, or to buy the third meal set and the second meal separately by paying the same amount of 10 rubles.
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 t in range(T):
n, m = list(map(int, input().split()))
c = list(map(int, input().split()))
dp1 = [1e9]*((1 << n)+1)
for i in range(n):
dp1[1 << i] = c[i]
dp1[1 << (n-1)] = min(dp1[1 << (n-1)], sum(c))
for i in range(m):
l = list(map(int, input().split()))
cost = l[0]
s = l[1]
items = l[2:]
mask = 0
for j in items:
mask = mask | (1 << (j-1))
dp1[mask] = min(dp1[mask], cost)
for i in range((1<<n) - 1, -1, -1):
for j in range(n):
if i & (1<< j):
dp1[i ^ (1<<j)] = min(dp1[i ^ (1<<j)], dp1[i])
dp2 = [1e9]*((1 << n) + 1)
dp2[0] = 0
for i in range(1 << n):
submask = i
while submask > 0:
dp2[i] = min(dp2[i], dp2[i ^ submask] + dp1[submask])
submask = (submask-1) & i
print(dp2[(1 << n)-1])
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Today Tavas got his test result as an integer score and he wants to share it with his girlfriend, Nafas.
His phone operating system is Tavdroid, and its keyboard doesn't have any digits! He wants to share his score with Nafas via text, so he has no choice but to send this number using words. [Image]
He ate coffee mix without water again, so right now he's really messed up and can't think.
Your task is to help him by telling him what to type.
-----Input-----
The first and only line of input contains an integer s (0 ≤ s ≤ 99), Tavas's score.
-----Output-----
In the first and only line of output, print a single string consisting only from English lowercase letters and hyphens ('-'). Do not use spaces.
-----Examples-----
Input
6
Output
six
Input
99
Output
ninety-nine
Input
20
Output
twenty
-----Note-----
You can find all you need to know about English numerals in http://en.wikipedia.org/wiki/English_numerals .
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 == 0:
print('zero')
elif n == 1:
print('one')
elif n == 2:
print('two')
elif n == 3:
print('three')
elif n == 4:
print('four')
elif n == 5:
print('five')
elif n == 6:
print('six')
elif n == 7:
print('seven')
elif n == 8:
print('eight')
elif n == 9:
print('nine')
elif n == 10:
print('ten')
elif n == 11:
print('eleven')
elif n == 12:
print('twelve')
elif n == 13:
print('thirteen')
elif n == 14:
print('fourteen')
elif n == 15:
print('fifteen')
elif n == 16:
print('sixteen')
elif n == 17:
print('seventeen')
elif n == 18:
print('eighteen')
elif n == 19:
print('nineteen')
else:
if n // 10 == 2:
res = 'twenty'
elif n // 10 == 3:
res = 'thirty'
elif n // 10 == 4:
res = 'forty'
elif n // 10 == 5:
res = 'fifty'
elif n // 10 == 6:
res = 'sixty'
elif n // 10 == 7:
res = 'seventy'
elif n // 10 == 8:
res = 'eighty'
elif n // 10 == 9:
res = 'ninety'
if n % 10 == 1:
res += '-one'
elif n % 10 == 2:
res += '-two'
elif n % 10 == 3:
res += '-three'
elif n % 10 == 4:
res += '-four'
elif n % 10 == 5:
res += '-five'
elif n % 10 == 6:
res += '-six'
elif n % 10 == 7:
res += '-seven'
elif n % 10 == 8:
res += '-eight'
elif n % 10 == 9:
res += '-nine'
print(res)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
You are given a sequence of n integers a_1, a_2, ..., a_{n}.
Determine a real number x such that the weakness of the sequence a_1 - x, a_2 - x, ..., a_{n} - x is as small as possible.
The weakness of a sequence is defined as the maximum value of the poorness over all segments (contiguous subsequences) of a sequence.
The poorness of a segment is defined as the absolute value of sum of the elements of segment.
-----Input-----
The first line contains one integer n (1 ≤ n ≤ 200 000), the length of a sequence.
The second line contains n integers a_1, a_2, ..., a_{n} (|a_{i}| ≤ 10 000).
-----Output-----
Output a real number denoting the minimum possible weakness of a_1 - x, a_2 - x, ..., a_{n} - x. Your answer will be considered correct if its relative or absolute error doesn't exceed 10^{ - 6}.
-----Examples-----
Input
3
1 2 3
Output
1.000000000000000
Input
4
1 2 3 4
Output
2.000000000000000
Input
10
1 10 2 9 3 8 4 7 5 6
Output
4.500000000000000
-----Note-----
For the first case, the optimal value of x is 2 so the sequence becomes - 1, 0, 1 and the max poorness occurs at the segment "-1" or segment "1". The poorness value (answer) equals to 1 in this case.
For the second sample the optimal value of x is 2.5 so the sequence becomes - 1.5, - 0.5, 0.5, 1.5 and the max poorness occurs on segment "-1.5 -0.5" or "0.5 1.5". The poorness value (answer) equals to 2 in this case.
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 = int(sys.stdin.readline())
a = [int(x) for x in sys.stdin.readline().split()]
eps = 1e-12
def f(x):
mx = a[0] - x
tsmx = 0.0
mn = a[0] - x
tsmn = 0.0
for ai in a:
tsmx = max(tsmx + ai - x, ai - x)
mx = max(tsmx, mx)
tsmn = min(tsmn + ai - x, ai - x)
mn = min(tsmn, mn)
return abs(mx), abs(mn)
l = min(a)
r = max(a)
f1, f2 = f(l)
for i in range(0, 90):
m = (l + r) / 2
f1, f2 = f(m)
if f1 > f2:
l = m
else:
r = m
A, B = f(l)
print(min(A,B))
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
You want to build a temple for snakes. The temple will be built on a mountain range, which can be thought of as n blocks, where height of i-th block is given by hi. The temple will be made on a consecutive section of the blocks and its height should start from 1 and increase by exactly 1 each time till some height and then decrease by exactly 1 each time to height 1,
i.e. a consecutive section of 1, 2, 3, .. x-1, x, x-1, x-2, .., 1 can correspond to a temple. Also, heights of all the blocks other than of the temple should have zero height, so that the temple is visible to people who view it from the left side or right side.
You want to construct a temple. For that, you can reduce the heights of some of the blocks. In a single operation, you can reduce the height of a block by 1 unit. Find out minimum number of operations required to build a temple.
-----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 an integer n.
The next line contains n integers, where the i-th integer denotes hi
-----Output-----
For each test case, output a new line with an integer corresponding to the answer of that testcase.
-----Constraints-----
- 1 ≤ T ≤ 10
- 2 ≤ n ≤ 105
- 1 ≤ hi ≤ 109
-----Example-----
Input
3
3
1 2 1
4
1 1 2 1
5
1 2 6 2 1
Output
0
1
3
-----Explanation-----
Example 1. The entire mountain range is already a temple. So, there is no need to make any operation.
Example 2. If you reduce the height of the first block to 0. You get 0 1 2 1. The blocks 1, 2, 1 form a temple. So, the answer is 1.
Example 3. One possible temple can be 1 2 3 2 1. It requires 3 operations to build. This is the minimum amount you have to spend in order to build a temple.
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:
t -= 1
n = int(input())
arr = list(map(int, input().split()))
sumi = sum(arr)
prev = 1
for i in range(n):
arr[i] = min(arr[i], prev)
prev = arr[i] + 1
prev = 1
for i in range(n - 1, -1, -1):
arr[i] = min(arr[i], prev)
prev = arr[i] + 1
temp = 0
for i in range(n):
temp = max(temp, arr[i])
print(sumi -( temp*temp))
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Taru likes reading. Every month he gets a copy of the magazine "BIT". The magazine contains information about the latest advancements in technology. Taru
reads the book at night and writes the page number to which he has read on a piece of paper so that he can continue from there the next day. But sometimes
the page number is not printed or is so dull that it is unreadable. To make matters worse Taru's brother who is really naughty tears of some of the pages of
the Magazine and throws them in the dustbin. He remembers the number of leaves he had torn but he does not remember which page numbers got removed. When Taru
finds this out he is furious and wants to beat him up. His brother apologizes, and says he won't ever do this again. But Taru did not want to be easy on him
and he says "I will leave you only if you help me find the answer to this. I will tell you how many pages (Printed sides) were there in the Magazine plus the
pages on which the page numbers were not printed. You already know the number of leaves you tore (T). Can you tell me the expected sum of the page numbers
left in the Magazine?" Taru's brother replied "huh!! This is a coding problem". Please help Taru's brother.
Note: The magazine is like a standard book with all odd page numbers in front and the successive even page number on its back. If the book contains 6 pages,
Page number 1 and Page number 2 are front and back respectively. Tearing a leaf removes both the front and back page numbers.
-----Input-----
The first line contains the number of test cases t. 3t lines follow. The first line of each test case contains the number of pages (printed sides) in the
book. The second line's first integer is F, F integers follow which tell us the numbers of the page numbers not printed. The third line contains a single integer telling us the number of leaves Taru's brother tore.
-----Output-----
Output one real number correct up to 4 decimal digits which is equal to the expected sum of the page numbers left in the book.
-----Constraints-----
Number of printed Sides<=2000. All other values abide by the number of printed sides.
-----Example-----
Input:
2
10
2 1 2
2
10
1 8
0
Output:
31.2000
47.0000
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
import sys
rl=sys.stdin.readline
T=int(rl())
for t in range(T):
P=int(rl())
T=(P+1)//2
F=list(map(int,rl().split()))[1:]
numtorn=int(rl())
t=sum(range(1,P+1))-sum(F)
K=T-numtorn
print('%.4f' % (t*K/float(T)))
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Chef wants to organize a contest. Predicting difficulty levels of the problems can be a daunting task. Chef wants his contests to be balanced in terms of difficulty levels of the problems.
Assume a contest had total P participants. A problem that was solved by at least half of the participants (i.e. P / 2 (integer division)) is said to be cakewalk difficulty. A problem solved by at max P / 10 (integer division) participants is categorized to be a hard difficulty.
Chef wants the contest to be balanced. According to him, a balanced contest must have exactly 1 cakewalk and exactly 2 hard problems. You are given the description of N problems and the number of participants solving those problems. Can you tell whether the contest was balanced 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 two space separated integers, N, P denoting the number of problems, number of participants respectively.
The second line contains N space separated integers, i-th of which denotes number of participants solving the i-th problem.
-----Output-----
For each test case, output "yes" or "no" (without quotes) denoting whether the contest is balanced or not.
-----Constraints-----
- 1 ≤ T, N ≤ 500
- 1 ≤ P ≤ 108
- 1 ≤ Number of participants solving a problem ≤ P
-----Subtasks-----
- Subtask #1 (40 points): P is a multiple of 10
- Subtask #2 (60 points): Original constraints
-----Example-----
Input
6
3 100
10 1 100
3 100
11 1 100
3 100
10 1 10
3 100
10 1 50
4 100
50 50 50 50
4 100
1 1 1 1
Output
yes
no
no
yes
no
no
-----Explanation-----
Example case 1.: The problems are of hard, hard and cakewalk difficulty. There is 1 cakewalk and 2 hard problems, so the contest is balanced.
Example case 2.: The second problem is hard and the third is cakewalk. There is 1 cakewalk and 1 hard problem, so the contest is not balanced.
Example case 3.: All the three problems are hard. So the contest is not balanced.
Example case 4.: The problems are of hard, hard, cakewalk difficulty. The contest is balanced.
Example case 5.: All the problems are cakewalk. The contest is not balanced.
Example case 6.: All the problems are hard. The contest is not balanced.
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 z in range(t) :
n,p = [int(x) for x in input().split()]
a = [int(x) for x in input().split()]
c = [x for x in a if x >= p//2]
h = [x for x in a if x <= p//10]
if len(c)==1 and len(h)==2 :
print("yes")
else:
print("no")
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Vasya learned about integer subtraction in school. He is still not very good at it, so he is only able to subtract any single digit number from any other number (which is not necessarily single digit).
For practice, Vasya chose a positive integer n$n$ and wrote it on the first line in his notepad. After that, on the second line he wrote the result of subtraction of the first digit of n$n$ from itself. For example, if n=968$n = 968$, then the second line would contain 968−9=959$968 - 9 = 959$, while with n=5$n = 5$ the second number would be 5−5=0$5 - 5 = 0$. If the second number was still positive, then Vasya would write the result of the same operation on the following line, and so on. For example, if n=91$n = 91$, then the sequence of numbers Vasya would write starts as follows: 91,82,74,67,61,55,50,…$91, 82, 74, 67, 61, 55, 50, \ldots$. One can see that any such sequence eventually terminates with the number 0$0$.
Since then, Vasya lost his notepad. However, he remembered the total number k$k$ of integers he wrote down (including the first number n$n$ and the final number 0$0$). What was the largest possible value of n$n$ Vasya could have started with?
-----Input:-----
The first line contains T$T$ , number of test cases per file.
The only line in each testcase contains a single integer k−$k-$ the total number of integers in Vasya's notepad (2≤k≤1012$2 \leq k \leq 10^{12}$).
-----Output:-----
Print a single integer−$-$ the largest possible value of the starting number n$n$. It is guaranteed that at least one such number n$n$ exists, and the largest possible value is finite.
-----Constraints-----
- 1≤T≤34$1 \leq T \leq 34 $
- 2≤k≤1012$2 \leq k \leq 10^{12}$
-----Sample Input-----
3
2
3
100
-----Sample Output:-----
9
10
170
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 getAns(num):
if num<10:return 2
last=int(str(num)[0]);rem=int(str(num)[1:]);steps=2;p=len(str(num))-1
while True:
steps+=rem//last+1;rem=rem%last
if last>0:rem=rem+10**p-last
last=last-1
if last==0:
p=p-1;last=9
if(len(str(rem))==1):rem=0
else:rem=int(str(rem)[1:])
if rem==0: break
return steps
for awa in range(int(input())):
k=int(input())
if(k==1):print(0)
elif(k==2):print(9)
elif(k==3):print(10)
else:
low,high,ans = 0,10**18,0
while(low<=high):
mid=(low+high)//2;temp=getAns(mid)
if int(temp)==k:ans=max(ans,mid);low=mid+1
elif temp<k:low=mid+1
else:high=mid-1
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
AND gates and OR gates are basic components used in building digital circuits. Both gates have two input lines and one output line. The output of an AND gate is 1 if both inputs are 1, otherwise the output is 0. The output of an OR gate is 1 if at least one input is 1, otherwise the output is 0.
You are given a digital circuit composed of only AND and OR gates where one node (gate or input) is specially designated as the output. Furthermore, for any gate G and any input node I, at most one of the inputs to G depends on the value of node I.
Now consider the following random experiment. Fix some probability p in [0,1] and set each input bit to 1 independently at random with probability p (and to 0 with probability 1-p). The output is then 1 with some probability that depends on p. You wonder what value of p causes the circuit to output a 1 with probability 1/2.
-----Input-----
The first line indicates the number of test cases to follow (about 100).
Each test case begins with a single line containing a single integer n with 1 ≤ n ≤ 100 indicating the number of nodes (inputs and gates) in the circuit. Following this, n lines follow where the i'th line describes the i'th node. If the node is an input, the line simply consists of the integer 0. Otherwise, if the node is an OR gate then the line begins with a 1 and if the node is an AND gate then the line begins with a 2. In either case, two more integers a,b follow, both less than i, which indicate that the outputs from both a and b are used as the two input to gate i.
As stated before, the circuit will be such that no gate has both of its inputs depending on the value of a common input node.
Test cases are separated by a blank line including a blank line preceding the first test case.
-----Output-----
For each test case you are to output a single line containing the value p for which the output of node n is 1 with probability exactly 1/2 if the inputs are independently and randomly set to value 1 with probability p. The value p should be printed with exactly 5 digits after the decimal.
-----Example-----
Input:
4
1
0
3
0
0
1 1 2
3
0
0
2 1 2
5
0
0
0
2 1 2
1 3 4
Output:
0.50000
0.29289
0.70711
0.40303
-----Temporary Stuff-----
A horizontal rule follows.
***
Here's a definition list (with `definitionLists` option):
apples
: Good for making applesauce.
oranges
: Citrus!
tomatoes
: There's no "e" in tomatoe.
#PRACTICE
- This must be done
[http:codechef.com/users/dpraveen](http:codechef.com/users/dpraveen)
(0.8944272−0.44721360.4472136−0.8944272)(10005)(0.89442720.4472136−0.4472136−0.8944272)(10005)
\left(\begin{array}{cc}
0.8944272 & 0.4472136\\
-0.4472136 & -0.8944272
\end{array}\right)
\left(\begin{array}{cc}
10 & 0\\
0 & 5
\end{array}\right)
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
class node:
def __init__(self,a,b=0,c=0):
self.val=a
self.a=b
self.b=c
arr=[]
def finder(node,val):
if(arr[node].val==0):
return val
else:
a=finder(arr[node].a,val)
b=finder(arr[node].b,val)
if(arr[node].val==1):
return a+b-a*b
else:
return a*b
t=int(input())
while(t>0):
x=input()
n=int(input())
arr.append(node(0))
for i in range(0,n):
vals=input().split()
sz=len(vals)
for i in range(0,sz):
vals[i]=int(vals[i])
if(vals[0]==0):
next=node(0)
arr.append(next)
else:
next=node(vals[0],vals[1],vals[2])
arr.append(next)
lower=0.0
higher=1.0
eps=1e-9
while((higher-lower)>eps):
mid=(higher+lower)/2.0
if(finder(n,mid)>0.5):
higher=mid
else:
lower=mid
print("%.5f" %(higher))
arr=[]
# print(higher)
t-=1
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
You are given an integer sequence $A_1, A_2, \ldots, A_N$ and an integer $X$. Consider a $N \times N$ matrix $B$, where $B_{i,j} = A_i + A_j$ for each valid $i$ and $j$.
You need to find the number of square submatrices of $B$ such that the sum of their elements is $X$. Formally, find the number of quartets $(x_1, y_1, x_2, y_2)$ such that $1 \le x_1 \le x_2 \le N$, $1 \le y_1 \le y_2 \le N$, $x_2-x_1 = y_2-y_1$ and $\sum_{i=x_1}^{x_2}\sum_{j=y_1}^{y_2} B_{i,j} = X$.
-----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 $X$.
- 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 ― the number of square submatrices with sum $X$.
-----Constraints-----
- $1 \le T \le 100$
- $1 \le X \le 10^6$
- $1 \le N \le 10^5$
- $1 \le A_i \le 10^6$ for each valid $i$
- the sum of $N$ over all test cases does not exceed $10^6$
-----Subtasks-----
Subtask #1 (50 points): the sum of $N$ over all test cases does not exceed $1,000$
Subtask #2 (50 points): original constraints
-----Example Input-----
2
5 36
1 2 3 1 12
4 54
3 3 3 3
-----Example Output-----
6
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
import sys
input=sys.stdin.readline
for _ in range(int(input())):
n,x=list(map(int,input().split()))
l=[0]
pre=[0]*(n+1)
sum=0
i=1
for m in input().split():
l.append(int(m))
sum+=int(m)
pre[i]=sum
i+=1
dict={}
k=[]
i=1
while (i*i)<=x:
if x%i==0:
k.append(i)
if (i*i)!=x:
k.append(x//i)
else:
break
i+=1
ans=0
for a in k:
if a>n:
continue
z=x//a
for j in range(a,n+1):
s=pre[j]-pre[j-a]
if s>z:
continue
if s in dict:
dict[s]+=1
else:
dict[s]=1
for j in range(a,n+1):
s=pre[j]-pre[j-a]
if s>z:
continue
if (z-s) in dict:
ans+=dict[z-s]
for j in range(a,n+1):
s=pre[j]-pre[j-a]
if s>z:
continue
dict[s]=0
print(ans)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
You are given a sequence a1, a2, ..., aN. Find the smallest possible value of ai + aj, where 1 ≤ i < j ≤ N.
-----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 description consists of a single integer N.
The second line of each description contains N space separated integers - a1, a2, ..., aN respectively.
-----Output-----
For each test case, output a single line containing a single integer - the smallest possible sum for the corresponding test case.
-----Constraints-----
- T = 105, N = 2 : 13 points.
- T = 105, 2 ≤ N ≤ 10 : 16 points.
- T = 1000, 2 ≤ N ≤ 100 : 31 points.
- T = 10, 2 ≤ N ≤ 105 : 40 points.
- 1 ≤ ai ≤ 106
-----Example-----
Input:
1
4
5 1 3 4
Output:
4
-----Explanation-----
Here we pick a2 and a3. Their sum equals to 1 + 3 = 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
def __starting_point():
try:
for _ in range (int(input())):
element = int(input())
l = list(map(int,input().split()))
a=min(l)
l.remove(a)
b=min(l)
print(a+b)
except EOFError :
print('EOFError')
__starting_point()
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
You have $n$ barrels lined up in a row, numbered from left to right from one. Initially, the $i$-th barrel contains $a_i$ liters of water.
You can pour water from one barrel to another. In one act of pouring, you can choose two different barrels $x$ and $y$ (the $x$-th barrel shouldn't be empty) and pour any possible amount of water from barrel $x$ to barrel $y$ (possibly, all water). You may assume that barrels have infinite capacity, so you can pour any amount of water in each of them.
Calculate the maximum possible difference between the maximum and the minimum amount of water in the barrels, if you can pour water at most $k$ times.
Some examples: if you have four barrels, each containing $5$ liters of water, and $k = 1$, you may pour $5$ liters from the second barrel into the fourth, so the amounts of water in the barrels are $[5, 0, 5, 10]$, and the difference between the maximum and the minimum is $10$; if all barrels are empty, you can't make any operation, so the difference between the maximum and the minimum amount is still $0$.
-----Input-----
The first line contains one integer $t$ ($1 \le t \le 1000$) — the number of test cases.
The first line of each test case contains two integers $n$ and $k$ ($1 \le k < n \le 2 \cdot 10^5$) — the number of barrels and the number of pourings you can make.
The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($0 \le a_i \le 10^{9}$), where $a_i$ is the initial amount of water the $i$-th barrel has.
It's guaranteed that the total sum of $n$ over test cases doesn't exceed $2 \cdot 10^5$.
-----Output-----
For each test case, print the maximum possible difference between the maximum and the minimum amount of water in the barrels, if you can pour water at most $k$ times.
-----Example-----
Input
2
4 1
5 5 5 5
3 2
0 0 0
Output
10
0
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
def solve():
n, k = map(int,input().split())
lst = list(map(int,input().split()))
lst.sort()
ans = 0
for i in range(n - k - 1, n):
ans += lst[i]
print(ans)
for i in range(int(input())):
solve()
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Chef is the new king of the country Chefland. As first and most important responsibility he wants to reconstruct the road system of Chefland. There are N (1 to N) cities in the country and each city i has a population Pi. Chef wants to build some bi-directional roads connecting different cities such that each city is connected to every other city (by a direct road or through some other intermediate city) and starting from any city one can visit every other city in the country through these roads. Cost of building a road between two cities u and v is Pu x Pv. Cost to build the road system is the sum of cost of every individual road that would be built.
Help king Chef to find the minimum cost to build the new road system in Chefland such that every city is connected to each other.
-----Input-----
The first line of the input contains an integer T denoting the number of test cases. The description of T test cases follows.
First line contains an integer N denoting the number of cities in the country. Second line contains N space separated integers Pi, the population of i-th city.
-----Output-----
For each test case, print a single integer, the minimum cost to build the new road system on separate line.
-----Constraints-----
- 1 ≤ T ≤ 10
- 1 ≤ N ≤ 105
- 1 ≤ Pi ≤ 106
-----Example-----
Input:
2
2
5 10
4
15 10 7 13
Output:
50
266
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=list(map(int,input().split()))
a.sort()
s=sum(a)
if a[0]*(s-a[0])<=a[n-1]*(s-a[n-1]):
print(a[0]*(s-a[0]))
else:
print(a[n-1]*(s-a[n-1]))
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
-----Problem-----
Once THANMAY met PK who is from a different planet visiting earth. THANMAY was very fascinate to learn PK's language. The language contains only lowercase English letters and is based on a simple logic that only certain characters can follow a particular character.
Now he is interested in calculating the number of possible words of length L and ending at a particular character C. Help THANMAY to calculate this value.
-----Input-----
The input begins with 26 lines, each containing 26 space-separated integers. The integers can be either 0 or 1. The jth integer at ith line depicts whether jth English alphabet can follow ith English alphabet or not.
Next line contains an integer T. T is the number of queries.
Next T lines contains a character C and an integer L.
-----Output-----
For each query output the count of words of length L ending with the character C. Answer to each query must be followed by newline character.
The answer may be very large so print it modulo 1000000007.
-----Constraints-----
-
1 ≤ T ≤ 100
-
C is lowercase English alphabet.
-
2 ≤ L ≤ 10000000
-----Sample Input-----
0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2
c 3
b 2
-----Sample Output-----
1
2
-----Explanation-----
For query 1, Words of length 3 are: aba, acb, bab, bac, cba. The only word ending with 'c' is bac.
p { text-align:justify }
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
d = {}
for i in range(26):
char = chr(i+ord('a'))
d[char] = []
for i in range(26):
char = chr(i+ord('a'))
temp = list(map(int,input().strip().split()))
for j in range(26):
if (temp[j] == 1):
follow= chr(j+ord('a'))
d[follow].append(char)
def f(char,i,n,count):
if (i==n):
return count+1
else:
ans = 0
for c in d[char]:
ans+=f(c,i+1,n,0)
ans%=(10**9+7)
return ans
for q in range(int(input().strip())):
c, n = input().strip().split()
n = int(n)
print(f(c,1,n,0))
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Santa has to send presents to the kids. He has a large stack of $n$ presents, numbered from $1$ to $n$; the topmost present has number $a_1$, the next present is $a_2$, and so on; the bottom present has number $a_n$. All numbers are distinct.
Santa has a list of $m$ distinct presents he has to send: $b_1$, $b_2$, ..., $b_m$. He will send them in the order they appear in the list.
To send a present, Santa has to find it in the stack by removing all presents above it, taking this present and returning all removed presents on top of the stack. So, if there are $k$ presents above the present Santa wants to send, it takes him $2k + 1$ seconds to do it. Fortunately, Santa can speed the whole process up — when he returns the presents to the stack, he may reorder them as he wishes (only those which were above the present he wanted to take; the presents below cannot be affected in any way).
What is the minimum time required to send all of the presents, provided that Santa knows the whole list of presents he has to send and reorders the presents optimally? Santa cannot change the order of presents or interact with the stack of presents in any other way.
Your program has to answer $t$ different test cases.
-----Input-----
The first line contains one integer $t$ ($1 \le t \le 100$) — the number of test cases.
Then the test cases follow, each represented by three lines.
The first line contains two integers $n$ and $m$ ($1 \le m \le n \le 10^5$) — the number of presents in the stack and the number of presents Santa wants to send, respectively.
The second line contains $n$ integers $a_1$, $a_2$, ..., $a_n$ ($1 \le a_i \le n$, all $a_i$ are unique) — the order of presents in the stack.
The third line contains $m$ integers $b_1$, $b_2$, ..., $b_m$ ($1 \le b_i \le n$, all $b_i$ are unique) — the ordered list of presents Santa has to send.
The sum of $n$ over all test cases does not exceed $10^5$.
-----Output-----
For each test case print one integer — the minimum number of seconds which Santa has to spend sending presents, if he reorders the presents optimally each time he returns them into the stack.
-----Example-----
Input
2
3 3
3 1 2
3 2 1
7 2
2 1 7 3 4 5 6
3 1
Output
5
8
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
for tc in range(int(input())):
n,m = list(map(int, input().split()))
al = list(map(int, input().split()))
bl = list(map(int, input().split()))
aidx = {}
for i,e in enumerate(al):
aidx[e]=i
midx = -1
res = 0
for i,e in enumerate(bl):
idx = aidx[e]
if idx <= midx:
res += 1
else:
res += 2*(idx-i)+1
midx = max(midx, idx)
print(res)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
This is probably the simplest problem ever. You just need to count the number of ordered triples of different numbers (X1, X2, X3), where Xi could be any positive integer from 1 to Ni, inclusive (i = 1, 2, 3).
No, wait. I forgot to mention that numbers N1, N2, N3 could be up to 1018. Well, in any case it is still quite simple :)
By the way, because of this the answer could be quite large. Hence you should output it modulo 109 + 7. That is you need to find the remainder of the division of the number of required triples by 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. The only line of each test case contains three space-separated integers N1, N2, N3.
-----Output-----
For each test case, output a single line containing the number of required triples modulo 109 + 7.
-----Constraints-----
- 1 ≤ T ≤ 1000
- 1 ≤ Ni ≤ 1018
-----Example-----
Input:
5
3 3 3
2 4 2
1 2 3
25 12 2012
1 1 2013
Output:
6
4
1
578880
0
-----Explanation-----
Example case 1. We have the following triples composed of different numbers up to 3:
(1, 2, 3)
(1, 3, 2)
(2, 1, 3)
(2, 3, 1)
(3, 1, 2)
(3, 2, 1)
Example case 2. Here the triples are:
(1, 3, 2)
(1, 4, 2)
(2, 3, 1)
(2, 4, 1)
Example case 3. Here the only triple is (1, 2, 3).
Example case 4. Merry Christmas!
Example case 5. ... and Happy New Year! By the way here the answer is zero since the only choice for X1 and for is X2 is 1, so any such triple will have equal numbers.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
d=1000000007
for _ in range(int(input())):
l=sorted(list(map(int,input().split())))
ans=(l[0]%d)*((l[1]-1)%d)*((l[2]-2)%d)
print(ans%d)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Luba is surfing the Internet. She currently has n opened tabs in her browser, indexed from 1 to n from left to right. The mouse cursor is currently located at the pos-th tab. Luba needs to use the tabs with indices from l to r (inclusive) for her studies, and she wants to close all the tabs that don't belong to this segment as fast as possible.
Each second Luba can either try moving the cursor to the left or to the right (if the cursor is currently at the tab i, then she can move it to the tab max(i - 1, a) or to the tab min(i + 1, b)) or try closing all the tabs to the left or to the right of the cursor (if the cursor is currently at the tab i, she can close all the tabs with indices from segment [a, i - 1] or from segment [i + 1, b]). In the aforementioned expressions a and b denote the minimum and maximum index of an unclosed tab, respectively. For example, if there were 7 tabs initially and tabs 1, 2 and 7 are closed, then a = 3, b = 6.
What is the minimum number of seconds Luba has to spend in order to leave only the tabs with initial indices from l to r inclusive opened?
-----Input-----
The only line of input contains four integer numbers n, pos, l, r (1 ≤ n ≤ 100, 1 ≤ pos ≤ n, 1 ≤ l ≤ r ≤ n) — the number of the tabs, the cursor position and the segment which Luba needs to leave opened.
-----Output-----
Print one integer equal to the minimum number of seconds required to close all the tabs outside the segment [l, r].
-----Examples-----
Input
6 3 2 4
Output
5
Input
6 3 1 3
Output
1
Input
5 2 1 5
Output
0
-----Note-----
In the first test Luba can do the following operations: shift the mouse cursor to the tab 2, close all the tabs to the left of it, shift the mouse cursor to the tab 3, then to the tab 4, and then close all the tabs to the right of it.
In the second test she only needs to close all the tabs to the right of the current position of the cursor.
In the third test Luba doesn't need to do anything.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
n, pos, l, r = map(int, input().split())
if l > 1 and r < n:
if l <= pos and pos <= r:
if pos - l < r - pos:
print(pos - l + 1 + r - l + 1)
else:
print(r - pos + 1 + r - l + 1)
elif pos > r:
print(pos - r + 1 + r - l + 1)
else:
print(l - pos + 1 + r - l + 1)
elif l == 1 and r < n:
print(int(abs(pos - r)) + 1)
elif l > 1 and r == n:
print(int(abs(pos - l)) + 1)
else:
print(0)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Chef likes strings a lot but he likes palindromic strings even more. Today he found an old string s in his garage. The string is so old that some of its characters have faded and are unidentifiable now. Faded characters in the string are represented by '.' whereas other characters are lower case Latin alphabets i.e ['a'-'z'].
Chef being the palindrome lover decided to construct the lexicographically smallest palindrome by filling each of the faded character ('.') with a lower case Latin alphabet. Can you please help him completing the task?
-----Input-----
First line of input contains a single integer T denoting the number of test cases. T test cases follow.
First and the only line of each case contains string s denoting the old string that chef has found in his garage.
-----Output-----
For each test case, print lexicographically smallest palindrome after filling each faded character - if it possible to construct one. Print -1 otherwise.
-----Constraints-----
- 1 ≤ T ≤ 50
- 1 ≤ |s| ≤ 12345
- String s consists of ['a'-'z'] and '.' only.
-----Subtasks-----Subtask #1 (47 points)
- 1 ≤ T ≤ 50, 1 ≤ |S| ≤ 123
Subtask #2 (53 points)
- 1 ≤ T ≤ 50, 1 ≤ |S| ≤ 12345
-----Example-----Input
3
a.ba
cb.bc
a.b
Output
abba
cbabc
-1
-----Explanation-----
In example 1, you can create a palindrome by filling the faded character by 'b'.
In example 2, you can replace the faded character by any character from 'a' to 'z'. We fill it by 'a', as it will generate the lexicographically smallest palindrome.
In example 3, it is not possible to make the string s a palindrome.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
test=int(input())
for i in range(test):
s=input()
b=len(s)
list1=[]
for j in range(len(s)):
if s[j]=='.':
list1.append(j)
for i in list1:
if b-i-1 in list1 :
if i!=b-i-1 and ((s[i] and s[b-i-1]) != 'a' ):
s=s[:i]+'a'+s[i+1:b-i-1]+'a'+s[b-i:]
else:
s=s[:i]+'a'+s[i+1:]
else:
s=s[:i]+s[b-i-1]+s[i+1:]
if s==s[::-1]:
print(s)
else:
print(-1)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Since due to COVID 19, India has undergone a complete 21 day lockdown. So Amol was attending an online lecture where his professor asked him to solve a question. Amol was unable to solve the question so he asked you to solve the question and give him the correct answer.
The question was asked a such that his professor gave him a number M and a list of integers of length N (i.e. A1, A2,..... AN) and you have to find out all the subsets that add up to M and the total number of subsets will be the final answer.
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 of each test case contains a single integer M.
• The third line contains N space-separated integers A1, A2,..... AN.
Output:
For each test case, print a single line containing one integer ― the no. of subsets that adds upto M.
Constraints:
• 1≤T≤5
• 1≤N≤100
• 10≤M≤100
• 1≤Ai≤100
ExampleInput:
2
4
16
2 4 6 10
4
20
2 8 12 10
Output:
2
2
Explanation:
In the 1st example there are two subsets {2,4,10} and {6,10} that adds upto 16 so the output is 2.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
try:
def countsubsetsum(S,arr,n):
k=[[0 for i in range(S+1)] for i in range(n+1)]
for i in range(n+1):
for j in range(S+1):
if(j==0):
k[i][j]=1
elif(i==0):
k[i][j]=0
elif(arr[i-1]<=j):
k[i][j]=k[i-1][j-arr[i-1]]+k[i-1][j]
else:
k[i][j]=k[i-1][j]
return k[n][S]
for _ in range(int(input())):
m=int(input())
S=int(input())
arr=[int(i) for i in input().split()]
n=len(arr)
print(countsubsetsum(S, arr, n))
except EOFError as e:
pass
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Master Oogway has forseen that a panda named Po will be the dragon warrior, and the master of Chi. But he did not tell anyone about the spell that would make him the master of Chi, and has left Po confused. Now Po has to defeat Kai, who is the super villian, the strongest of them all. Po needs to master Chi, and he finds a spell which unlocks his powerful Chi. But the spell is rather strange. It asks Po to calculate the factorial of a number! Po is very good at mathematics, and thinks that this is very easy. So he leaves the spell, thinking it's a hoax. But little does he know that this can give him the ultimate power of Chi. Help Po by solving the spell and proving that it's not a hoax.
-----Input-----
First line of input contains an integer T denoting the number of test cases.
The next T lines contain an integer N.
-----Output-----
For each test case, print a single line containing the solution to the spell which is equal to factorial of N, i.e. N!. Since the output could be large, output it modulo 1589540031(Grand Master Oogway's current age).
-----Constraints-----
- 1 ≤ T ≤ 100000
- 1 ≤ N ≤ 100000
-----Example-----
Input:
4
1
2
3
4
Output:
1
2
6
24
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
arr = []
arr.append(1)
_ = 1
while _<=100002:
arr.append(_*arr[_-1]%1589540031)
_+=1
for _ in range(int(input())):
print(arr[int(input())])
```
|
|
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 sequence of integers $A_1, A_2, \ldots, A_N$. You may choose an arbitrary permutation $p_1, p_2, \ldots, p_N$ of the integers $1$ through $N$. Then, for each vertex $i$, you should assign the value $A_{p_i}$ to this vertex.
The profit of a path between two vertices $u$ and $v$ is the sum of the values assigned to the vertices on that path (including $u$ and $v$).
Let's consider only (undirected) paths that start at a leaf and end at a different leaf. Calculate the maximum possible value of the sum of profits of all such paths. Since this value could be very large, compute it modulo $10^9 + 7$.
-----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 $A_1, A_2, \ldots, A_N$.
- Each of the following $N−1$ lines contains two space-separated integers $u$ and $v$ denoting that vertices $u$ and $v$ are connected by an edge.
-----Output-----
For each test case, print a single line containing one integer — the maximum sum of profits, modulo $10^9 + 7$.
-----Constraints-----
- $1 \le T \le 1,000$
- $1 \le N \le 300,000$
- $1 \le A_i \le 10^9$ for each valid $i$
- the sum of $N$ over all test cases does not exceed $5 \cdot 10^5$
-----Example Input-----
2
4
1 2 3 4
1 2
2 3
2 4
5
1 2 3 4 5
1 2
2 3
3 4
4 5
-----Example Output-----
24
15
-----Explanation-----
Example case 1: $(1, 4, 2, 3)$ is one of the possible permutations that give the optimal answer. Then, the profits of paths between pairs of vertices $(1, 3)$, $(1, 4)$ and $(3, 4)$ are $7$, $8$ and $9$ respectively.
Example case 2: Here, any permutation could be chosen.
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())
M = 10 ** 9 + 7
for _ in range(T):
N = int(input())
A = list(map(int, input().split()))
if N == 1:
print(0)
continue
B = {}
C = {}
for i in range(N - 1):
u, v = input().split()
u = int(u) - 1
v = int(v) - 1
if u not in B:
B[u] = []
if v not in B:
B[v] = []
B[u].append(v)
B[v].append(u)
total_leaves = 0
for i in B:
if len(B[i]) == 1:
total_leaves += 1
S = [0]
visited = [False] * N
parent = [-1] * N
total_visits = [0] * N
while len(S) > 0:
current = S.pop(len(S) - 1)
if visited[current]:
p = parent[current]
if p != -1:
total_visits[p] += total_visits[current]
if p not in C:
C[p] = {}
C[p][current] = total_visits[current]
if current not in C:
C[current] = {}
C[current][p] = total_leaves - C[p][current]
else:
S.append(current)
visited[current] = True
for i, j in enumerate(B[current]):
if not visited[j]:
parent[j] = current
S.append(j)
if len(B[current]) == 1:
total_visits[current] = 1
p = parent[current]
if p != -1:
if p not in C:
C[p] = {}
C[p][current] = 1
D = {}
for i in C:
sum1 = 0
for j in C[i]:
sum1 += C[i][j]
D[i] = sum1
E = [0] * N
for i in C:
sum1 = 0
for j in C[i]:
D[i] -= C[i][j]
sum1 += C[i][j] * D[i]
E[i] = sum1
for i, j in enumerate(E):
if j == 0:
for k in C[i]:
E[i] = C[i][k]
E.sort()
E.reverse()
A.sort()
A.reverse()
E = [x % M for x in E]
A = [x % M for x in A]
ans = 0
for i, j in zip(E, A):
a = i * j
a %= M
ans += a
ans %= M
print(ans)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
A city of dimension N x N is constructed with grid of lanes. These lanes are fenced by government so that no one can cross any grid diagonally. Although a train
line runs diagonally from (0,0) to (N,N).
Our chef has a weird kind of phobia and is very afraid to cross the railway line. He is at point (0,0) and wants to get to the point (N,N). Calculate number of path
through which it is possible to reach to its destination travelling the minimum distance. .
Note that:
1. Since he is already at position (0,0) he can go to either part of grid (i.e. left or right part - divided by diagonal) but he will remain in that part for the whole path.
2. He is only afraid to "cross" the line, i.e. during the route he can go to position (m,m) where 0
3. You have to calculate the number of path possible. If there is more than one path then you have to print the number of path of minimum distances.
-----Input-----
The first line of the input contains an integer T denoting the number of test cases, for each test case enter the grid size i.e value of N.
-----Output-----
For each test case, output a single line with number of such paths possible.
(Note : If no such path possible print 0)
-----Constraints-----
- 1 <= T <= 100
- 0 <= N <= 30
-----Example-----
Input:
2
2
5
Output:
4
84
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
ar = []
ar.append(1)
for i in range(1, 31):
ar.append(ar[i-1]*(4*i-2)/(i+1))
t = int(input())
while(t>0):
n = int(input())
if(n==0):
print(0)
else:
print(ar[n]*2)
t=t-1
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
The Fibonacci sequence is defined as F(n) = F(n-1) + F(n-2). You have developed two sequences of numbers. The first sequence that uses the bitwise XOR operation instead of the addition method is called the Xoronacci number. It is described as follows:
X(n) = X(n-1) XOR X(n-2)
The second sequence that uses the bitwise XNOR operation instead of the addition method is called the XNoronacci number. It is described as follows:
E(n) = E(n-1) XNOR E(n-2)
The first and second numbers of the sequence are as follows:
X(1) = E(1) = a
X(2) = E(2) = b
Your task is to determine the value of max(X(n),E(n)), where n is the n th term of the Xoronacci and XNoronacci sequence.
-----Input:-----
The first line consists of a single integer T denoting the number of test cases.
The first and the only line of each test case consists of three space separated integers a, b and n.
-----Output:-----
For each test case print a single integer max(X(n),E(n)).
-----Constraints-----
- $1 \leq T \leq 1000$
- $2 \leq a,b,n \leq 1000000000000$
-----Sample Input:-----
1
3 4 2
-----Sample Output:-----
4
-----EXPLANATION:-----
Xoronacci Sequence : 3 4 7 …….
XNoronacci Sequence : 3 4 0 …….
Here n = 2. Hence max(X(2),E(2)) = 4
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
# Python3 program to find XNOR
# of two numbers
import math
def swap(a, b):
temp = a
a = b
b = temp
# log(n) solution
def xnor(a, b):
# Make sure a is larger
if (a < b):
swap(a, b)
if (a == 0 and b == 0):
return 1;
# for last bit of a
a_rem = 0
# for last bit of b
b_rem = 0
# counter for count bit and
# set bit in xnor num
count = 0
# for make new xnor number
xnornum = 0
# for set bits in new xnor
# number
while (a != 0):
# get last bit of a
a_rem = a & 1
# get last bit of b
b_rem = b & 1
# Check if current two
# bits are same
if (a_rem == b_rem):
xnornum |= (1 << count)
# counter for count bit
count = count + 1
a = a >> 1
b = b >> 1
return xnornum;
t= int(input())
for o in range(t):
a,b,n=map(int,input().split())
c=a^b
x=bin(c)
x=x.split("b")
x=x[1]
x=len(x)
d=xnor(a,b)
p=[a,b,c];r=[a,b,d]
k=n%3-1
if p[k]>r[k]:
print(p[k])
else :
print(r[k])
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Zookeeper is playing a game. In this game, Zookeeper must use bombs to bomb a string that consists of letters 'A' and 'B'. He can use bombs to bomb a substring which is either "AB" or "BB". When he bombs such a substring, the substring gets deleted from the string and the remaining parts of the string get concatenated.
For example, Zookeeper can use two such operations: AABABBA $\to$ AABBA $\to$ AAA.
Zookeeper wonders what the shortest string he can make is. Can you help him find the length of the shortest string?
-----Input-----
Each test contains multiple test cases. The first line contains a single integer $t$ $(1 \leq t \leq 20000)$ — the number of test cases. The description of the test cases follows.
Each of the next $t$ lines contains a single test case each, consisting of a non-empty string $s$: the string that Zookeeper needs to bomb. It is guaranteed that all symbols of $s$ are either 'A' or 'B'.
It is guaranteed that the sum of $|s|$ (length of $s$) among all test cases does not exceed $2 \cdot 10^5$.
-----Output-----
For each test case, print a single integer: the length of the shortest string that Zookeeper can make.
-----Example-----
Input
3
AAA
BABA
AABBBABBBB
Output
3
2
0
-----Note-----
For the first test case, you can't make any moves, so the answer is $3$.
For the second test case, one optimal sequence of moves is BABA $\to$ BA. So, the answer is $2$.
For the third test case, one optimal sequence of moves is AABBBABBBB $\to$ AABBBABB $\to$ AABBBB $\to$ ABBB $\to$ AB $\to$ (empty 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
import sys
readline = sys.stdin.readline
T = int(readline())
Ans = [None]*T
for qu in range(T):
S = [1 if s == 'A' else 0 for s in readline().strip()]
stack = []
for s in S:
if s:
stack.append(s)
else:
if stack and stack[-1] == 1:
stack.pop()
else:
stack.append(s)
stack2 = []
for s in stack:
if s:
stack2.append(s)
else:
if stack2 and stack2[-1] == 0:
stack2.pop()
else:
stack2.append(s)
Ans[qu] = len(stack2)
print('\n'.join(map(str, Ans)))
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Chef is multi-talented. He has developed a cure for coronavirus called COVAC-19. Now that everyone in the world is infected, it is time to distribute it throughout the world efficiently to wipe out coronavirus from the Earth. Chef just cooks the cure, you are his distribution manager.
In the world, there are $N$ countries (numbered $1$ through $N$) with populations $a_1, a_2, \ldots, a_N$. Each cure can be used to cure one infected person once. Due to lockdown rules, you may only deliver cures to one country per day, but you may choose that country arbitrarily and independently on each day. Days are numbered by positive integers. On day $1$, Chef has $x$ cures ready. On each subsequent day, Chef can supply twice the number of cures that were delivered (i.e. people that were cured) on the previous day. Chef cannot supply leftovers from the previous or any earlier day, as the cures expire in a day. The number of cures delivered to some country on some day cannot exceed the number of infected people it currently has, either.
However, coronavirus is not giving up so easily. It can infect a cured person that comes in contact with an infected person again ― formally, it means that the number of infected people in a country doubles at the end of each day, i.e. after the cures for this day are used (obviously up to the population of that country).
Find the minimum number of days needed to make the world corona-free.
-----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 $x$.
- 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 ― the minimum number of days.
-----Constraints-----
- $1 \le T \le 10^3$
- $1 \le N \le 10^5$
- $1 \le a_i \le 10^9$ for each valid $i$
- $1 \le x \le 10^9$
- the sum of $N$ over all test cases does not exceed $10^6$
-----Subtasks-----
Subtask #1 (20 points): $a_1 = a_2 = \ldots = a_N$
Subtask #2 (80 points): original constraints
-----Example Input-----
3
5 5
1 2 3 4 5
5 1
40 30 20 10 50
3 10
20 1 110
-----Example Output-----
5
9
6
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
import math
for i in range(int(input())):
n,x=list(map(int,input().split()))
l=list(map(int,input().split()))
l.sort()
flag=0
d=0
for j in range(n):
if l[j]>x:
for k in range(j,n):
if x<l[k]:
d+=(math.ceil(math.log(l[k]/x)/math.log(2))+1)
else:
d+=1
x=l[k]*2
flag=1
break
if flag==1:
print(j+d)
else:
print(n)
```
|
|
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(odd) 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-----
- $1 \leq T \leq 50$
- $1 \leq K \leq 50$
-----Sample Input:-----
4
1
3
5
7
-----Sample Output:-----
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
-----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
def func(num):
for i in range(num):
if i < num//2 + 1:
print(' '*i, end='')
print('*')
else:
print(' '*(num-i-1), end='')
print('*')
for _ in range(int(input())):
num = int(input())
func(num)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Nikita likes tasks on order statistics, for example, he can easily find the $k$-th number in increasing order on a segment of an array. But now Nikita wonders how many segments of an array there are such that a given number $x$ is the $k$-th number in increasing order on this segment. In other words, you should find the number of segments of a given array such that there are exactly $k$ numbers of this segment which are less than $x$.
Nikita wants to get answer for this question for each $k$ from $0$ to $n$, where $n$ is the size of the array.
-----Input-----
The first line contains two integers $n$ and $x$ $(1 \le n \le 2 \cdot 10^5, -10^9 \le x \le 10^9)$.
The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ $(-10^9 \le a_i \le 10^9)$ — the given array.
-----Output-----
Print $n+1$ integers, where the $i$-th number is the answer for Nikita's question for $k=i-1$.
-----Examples-----
Input
5 3
1 2 3 4 5
Output
6 5 4 0 0 0
Input
2 6
-5 9
Output
1 2 0
Input
6 99
-1 -1 -1 -1 -1 -1
Output
0 6 5 4 3 2 1
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
from math import pi
from cmath import exp
def fft(a, lgN, rot=1): # rot=-1 for ifft
N = 1<<lgN
assert len(a)==N
rev = [0]*N
for i in range(N):
rev[i] = (rev[i>>1]>>1)+(i&1)*(N>>1)
A = [a[rev[i]] for i in range(N)]
h = 1
while h<N:
w_m = exp((0+1j) * rot * (pi / h))
for k in range(0, N, h<<1):
w = 1
for j in range(h):
t = w * A[k+j+h]
A[k+j+h] = A[k+j]-t
A[k+j] = A[k+j]+t
w *= w_m
h = h<<1
return A if rot==1 else [x/N for x in A]
import sys
ints = (int(x) for x in sys.stdin.read().split())
n, x = (next(ints) for i in range(2))
r = [next(ints) for i in range(n)]
ac = [0]*(n+1)
for i in range(n): ac[i+1] = (r[i]<x) + ac[i]
# Multiset addition
min_A, min_B = 0, -ac[-1]
max_A, max_B = ac[-1], 0
N, lgN, m = 1, 0, 2*max(max_A-min_A+1, max_B-min_B+1)
while N<m: N,lgN = N<<1,lgN+1
a, b = [0]*N, [0]*N
for x in ac:
a[x-min_A] += 1
b[-x-min_B] += 1
c = zip(fft(a, lgN), fft(b, lgN))
c = fft([x*y for x,y in c], lgN, rot=-1)
c = [round(x.real) for x in c][-min_A-min_B:][:n+1]
c[0] = sum((x*(x-1))//2 for x in a)
print(*c, *(0 for i in range(n+1-len(c))), flush=True)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Nexus 4.O is going to be organized by ASME, GLA University. Shubhanshu, Head of Finance Team is working for it. He has $N$ number of bills of different values as $a$$1$,$ a$$2$, $a$$3$…$a$$n$.
He is interested in a game in which one has to do the addition of the bills. But due to privacy concerns, he cannot share the details with others.
He can only trust his best friend Avani with such a confidential thing. So, he asked her to play this game.
Rules of the game :
- Avani needs to answer $Q$ queries.
- Every $Q$$i$ query has 2 values $X$$i$ and $Y$$i$.
- Avani needs to find the sum of the values between $X$$i$ and $Y$$i$ (inclusive).
So, you need to help Avani in answering the $Q$ queries
-----Input:-----
- First line will contain $T$, number of testcases. Then the testcases follow.
- The first line of each test case contains the value $N$ and $Q$.
- The second line of each test case contains the $N$ space-separated values as $a$$1$,$ a$$2$, $a$$3$…$a$$n$.
- The next line of each test case containing $Q$ query with $X$$i$ and $Y$$i$.
-----Output:-----
For each test case, Print the total amount between $X$$i$ and $Y$$i$ for $Q$ number of queries.
-----Constraints-----
- $1 \leq T \leq 100$
- $1 \leq N \leq 10^5$
- $1 \leq Q \leq 10^5$
- $1 \leq a$$i$$ \leq 10^9$
-----Subtasks (25 points) :-----
- $1 \leq N \leq 10^2$.
- $1 \leq Q \leq 10^2$.
- $1 \leq a$$i$$ \leq 10^5$.
-----Subtasks (25 points) :-----
- $1 \leq N \leq 10^3$.
- $1 \leq Q \leq 10^3$.
- $1 \leq a$$i$$ \leq 10^5$.
-----Subtasks (50 points) :-----
- $Original Constraints$.
-----Sample Input:-----
1
8 3
1 2 3 4 5 6 7 8
2 3
1 6
5 8
-----Sample Output:-----
5
21
26
-----EXPLANATION:-----
$Q$$1$ : (2,3) 2+3=5
$Q$$2$ : (1,6) 1+2+3+4+5+6=21
$Q$$3$ : (5,8) 5+6+7+8=26
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):
l=list(map(int,input().split(' ')))
a=l[0]
b=l[1]
l1=list(map(int,input().split(' ')))
for i in range(b):
l2=list(map(int,input().split(' ')))
a1=l2[0]
b1=l2[1]
su=0
for j in range(a1-1,b1):
su=(su+l1[j])%1000000000
print(su)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Meliodas and Ban are fighting over chocolates. Meliodas has $X$ chocolates, while Ban has $Y$. Whoever has lesser number of chocolates eats as many chocolates as he has from the other's collection. This eatfest war continues till either they have the same number of chocolates, or atleast one of them is left with no chocolates.
Can you help Elizabeth predict the total no of chocolates they'll be left with at the end of their war?
-----Input:-----
- First line will contain $T$, number of testcases. Then the testcases follow.
- Each testcase contains of a single line of input, which contains two integers $X, Y$, the no of chocolates Meliodas and Ban have, respectively.
-----Output:-----
For each testcase, output in a single line the no of chocolates that remain after Ban and Meliodas stop fighting.
-----Constraints-----
- $1 \leq T \leq 100000$
- $0 \leq X,Y \leq 10^9$
-----Sample Input:-----
3
5 3
10 10
4 8
-----Sample Output:-----
2
20
8
-----EXPLANATION:-----
Denoting Meliodas as $M$, Ban as $B$.
Testcase 1:
$M$=5, $B$=3
Ban eates 3 chocolates of Meliodas.
$M$=2, $B$=3
Meliodas eats 2 chocolates of Ban.
$M$=2, $B$=1
Ban eates 1 chocolate of Meliodas.
$M$=1, $B$=1
Since they have the same no of candies, they stop quarreling.
Total candies left: 2
Testcase 2:
$M$=10, $B$=10
Since both of them had the same candies to begin with, there was no point in fighting.
Total candies left: 20
Testcase 3:
$M$=4, $B$=8
Meliodas eats 4 chocolates of Ban.
$M$=4, $B$=4
Since they have the same no of candies, they stop quarreling.
Total candies left: 8
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
from math import *
t=int(input())
for i in range(t):
m,b=input().split()
m=int(m)
b=int(b)
print(2*gcd(m,b))
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Ada is playing pawn chess with Suzumo.
Pawn chess is played on a long board with N$N$ squares in one row. Initially, some of the squares contain pawns.
Note that the colours of the squares and pawns do not matter in this game, but otherwise, the standard chess rules apply:
- no two pawns can occupy the same square at the same time
- a pawn cannot jump over another pawn (they are no knights!), i.e. if there is a pawn at square i$i$, then it can only be moved to square i−2$i-2$ if squares i−1$i-1$ and i−2$i-2$ are empty
- pawns cannot move outside of the board (outs are forbidden)
The players alternate turns; as usual, Ada plays first. In each turn, the current player must choose a pawn and move it either one or two squares to the left of its current position. The player that cannot make a move loses.
Can Ada always beat Suzumo? Remember that Ada is a chess grandmaster, so she always plays optimally.
-----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 and only line of each test case contains a single string S$S$ with length N$N$ describing the initial board from left to right. An empty square and a square containing a pawn are denoted by the characters '.' and 'P' respectively.
-----Output-----
For each test case, print a single line containing the string "Yes" if Ada wins the game or "No" otherwise (without quotes).
-----Constraints-----
- 1≤T≤500$1 \le T \le 500$
- 2≤N≤128$2 \le N \le 128$
- S$S$ contains only characters '.' and 'P'
-----Example Input-----
1
..P.P
-----Example Output-----
Yes
-----Explanation-----
Example case 1: Ada can move the first pawn two squares to the left; the board after this move looks like
P...P
and now, Suzumo can only move the second pawn. If he moves it one square to the left, Ada will move it two squares to the left on her next move, and if he moves it two squares to the left, Ada will move it one square to the left, so the board after Ada's next move will look like
PP...
and Suzumo cannot make any move here.
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())):
s = input().strip()
a = []
last = 0
for i in range(len(s)):
if s[i] == 'P':
a.append(i - last)
last = i + 1
x = 0
a = a[::-1]
for v in a[::2]:
x ^= v % 3
print('Yes' if x else 'No')
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Mohit's girlfriend is playing a game with Nicky. The description of the game is as follows:
- Initially on a table Player 1 will put N gem-stones.
- Players will play alternatively, turn by turn.
- At each move a player can take at most M gem-stones (at least 1 gem-stone must be taken) from the available gem-stones on the table.(Each gem-stone has same cost.)
- Each players gem-stone are gathered in player's side.
- The player that empties the table purchases food from it (using all his gem-stones; one gem-stone can buy one unit of food), and the other one puts all his gem-stones back on to the table. Again the game continues with the "loser" player starting.
- The game continues until all the gem-stones are used to buy food.
- The main objective of the game is to consume maximum units of food.
Mohit's girlfriend is weak in mathematics and prediction so she asks help from Mohit, in return she shall kiss Mohit. Mohit task is to predict the maximum units of food her girlfriend can eat, if, she starts first. Being the best friend of Mohit, help him in predicting the answer.
-----Input-----
- Single line contains two space separated integers N and M.
-----Output-----
- The maximum units of food Mohit's girlfriend can eat.
-----Constraints and Subtasks-----
- 1 <= M <= N <= 100
Subtask 1: 10 points
- 1 <= M <= N <= 5
Subtask 2: 20 points
- 1 <= M <= N <= 10
Subtask 3: 30 points
- 1 <= M <= N <= 50
Subtask 3: 40 points
- Original Constraints.
-----Example-----
Input:
4 2
Output:
2
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
r=[0,1,1,2,1,4,2,6,1,8,4]
n,m=[int(x) for x in input().split()]
if m==1:
while n%2!=1:
n=n/2
if n==1:
print(1)
else:
print(n-1)
elif (n+1)/2<m:
print(m)
else:
print(n-m)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
The entire network is under the inspection and direct control of the Decepticons. They have learned our language through the World Wide Web and can easily understand the messages which are being sent. Sam is trying to send the information to Autobots to locate “ALL SPARK” which is the only source of energy that can be used to create universe. He is bit cautious in sending the message. He is sending the messages in a form of special pattern of string that contains important message in form of substrings. But Decepticons have learnt to recognize the Data Mining and string comparison patterns. He is sending a big message in form of a string (say M) and let there are N smaller substrings. Decepticons have to find whether each of these N substrings is a sub-string of M. All strings consist of only alphanumeric characters.
-----Input-----
Input to the program consists of two line. The first line contains the string M (where size of M should be <=40). The next line contain a string S.
-----Output-----
Output should consist of a line with a character 'Y'/'N' indicating whether the string S is a sub-string of String M or not.
-----Example-----
Input:
techtrishna online event
onlin
Output:
Y
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
x = input()
y = input()
z = x.find(y)
if z == -1 :
print('N')
else :
print('Y')
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
The snakes want to build a temple for Lord Cobra. There are multiple strips of land that they are looking at, but not all of them are suitable. They need the strip of land to resemble a coiled Cobra. You need to find out which strips do so.
Formally, every strip of land, has a length. Suppose the length of the i-th strip is is Ni, then there will be Ni integers, Hi1, Hi2, .. HiNi, which represent the heights of the ground at various parts of the strip, in sequential order. That is, the strip has been divided into Ni parts and the height of each part is given. This strip is valid, if and only if all these conditions are satisfied:
- There should be an unique 'centre' part. This is where the actual temple will be built. By centre, we mean that there should be an equal number of parts to the left of this part, and to the right of this part.
- Hi1 = 1
- The heights keep increasing by exactly 1, as you move from the leftmost part, to the centre part.
- The heights should keep decreasing by exactly 1, as you move from the centre part to the rightmost part. Note that this means that HiNi should also be 1.
Your job is to look at every strip and find if it's valid or not.
-----Input-----
- The first line contains a single integer, S, which is the number of strips you need to look at. The description of each of the S strips follows
- The first line of the i-th strip's description will contain a single integer: Ni, which is the length and number of parts into which it has been divided.
- The next line contains Ni integers: Hi1, Hi2, .., HiNi. These represent the heights of the various parts in the i-th strip.
-----Output-----
- For each strip, in a new line, output "yes" if is a valid strip, and "no", if it isn't.
-----Constraints-----
- 1 ≤ S ≤ 100
- 3 ≤ Ni ≤ 100
- 1 ≤ Hij ≤ 100
-----Example-----
Input:
7
5
1 2 3 2 1
7
2 3 4 5 4 3 2
5
1 2 3 4 3
5
1 3 5 3 1
7
1 2 3 4 3 2 1
4
1 2 3 2
4
1 2 2 1
Output:
yes
no
no
no
yes
no
no
-----Explanation-----
In the first strip, all the conditions are satisfied, hence it is valid.
In the second strip, it does not start with a 1, and hence is invalid.
In the third strip, it keeps increasing even past the centre, instead of decreasing. Hence invalid.
The fourth strip does not increase and decrease by exactly 1. Hence invalid.
The fifth satisfies all conditions and hence is valid.
The sixth and seventh strip do not have a 'centre' part. Because for every part, there are either more parts to its right than its left, or more parts on its left than its right. Hence both the strips are invalid.
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 i in range(int(input())):
N=int(input())
L=list(map(int,input().split()))
l,h=0,N-1
flag=1
if L[l]!=1 and L[h]!=1:
flag=0
else:
while(l<h):
if (L[l]!=L[h]) or (L[l+1]-L[l]!=1 and L[h-1]-L[h]!=1):
flag=0
break
l+=1
h-=1
if flag:
print("yes")
else:
print("no")
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Given the values at the leaf nodes of a complete binary tree. The total number of nodes in the binary tree, is also given. Sum of the values at both the children of a node is equal to the value of the node itself. You can add any value or subtract any value from a node. Print the minimum change(difference made) in the sum of values of all the nodes in the tree, such that all the leaf nodes have the same value.
Note: If a value transfers from one node to another, then that is not a change, but if an extra is needed to be added or subtracted to the entire total value of the nodes, then that is a change.
Input Description:
Input will contain an integer N, the number of nodes in the tree on a newline, followed by N space separated integers representing the values at the leaf nodes of the tree.
Output Description:
Print the required value on a newline.
Constraints:
1<=N<=20000
1<=Value at each node in the leaves<=1000
Example 1:
Input:
1
50
Output:
0
Explanation: Since there is only one node, it is a leaf node itself and no change needs to be made.
Example 2:
Input:
3
200 800
Output:
0
Explanation: There are two leaf nodes, and they can be made to 500 500, since no change in the total was made so difference made is 0.
Example 3:
Input:
30
29 33 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Output:
6
Output: A total change of 6 needs to be changed to the entire value of the nodes, to get the leaf nodes equal.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
print(0)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Zaikia has $N$ sticks of distinct positive lengths $A_1,A_2,\dots,A_N$. For no good reason at all, he wants to know if there is a triplet of sticks which when connected end-to-end will form a non-trivial triangle. Here non-trivial refers to a triangle with positive area.
Help Zaikia know if such a triplet exists or not. If such a triplet exists, help him find the lexicographically largest applicable triplet.Input
- The first line contains an integer $N$.
- The second line contains $N$ space-seperated integers $A_1,A_2,\dots,A_N$. Output
- In the first line print YES if a triplet exists or NO if it doesn't.
- If such a triplet exists, then in the second line print the lexicographically largest applicable triplet.Constraints
- $3 \leq N \leq {2}\times{10}^{5}$
- $1 \leq A_i \leq {10}^{9}$ for each valid $i$Sample Input 1
5
4 2 10 3 5
Sample Output 1
YES
5 4 3
Explanation 1
There are three unordered triplets of sticks which can be used to create a triangle:
- $4,2,3$
- $4,2,5$
- $4,3,5$
Arranging them in lexicographically largest fashion
- $4,3,2$
- $5,4,2$
- $5,4,3$
Here $5,4,3$ is the lexicographically largest so it is the triplet which dristiron wantsSample Input 2
5
1 2 4 8 16
Sample Output 2
NO
Explanation 2
There are no triplets of sticks here that can be used to create a triangle.
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 combinations as c
n=int(input());l=list(map(int,input().split()))
l1=[]
if(n<3):
print("NO")
else:
l.sort()
for i in range(n-2):
if(l[i]+l[i+1]>l[i+2]):
l1.append([l[i+2],l[i+1],l[i]])
if(len(l1)!=0):
print("YES")
print(*max(l1))
else:
print("NO")
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
We have a graph with N vertices and M edges, and there are two people on the graph: Takahashi and Aoki.
The i-th edge connects Vertex U_i and Vertex V_i.
The time it takes to traverse this edge is D_i minutes, regardless of direction and who traverses the edge (Takahashi or Aoki).
Takahashi departs Vertex S and Aoki departs Vertex T at the same time. Takahashi travels to Vertex T and Aoki travels to Vertex S, both in the shortest time possible.
Find the number of the pairs of ways for Takahashi and Aoki to choose their shortest paths such that they never meet (at a vertex or on an edge) during the travel, modulo 10^9 + 7.
-----Constraints-----
- 1 \leq N \leq 100 000
- 1 \leq M \leq 200 000
- 1 \leq S, T \leq N
- S \neq T
- 1 \leq U_i, V_i \leq N (1 \leq i \leq M)
- 1 \leq D_i \leq 10^9 (1 \leq i \leq M)
- If i \neq j, then (U_i, V_i) \neq (U_j, V_j) and (U_i, V_i) \neq (V_j, U_j).
- U_i \neq V_i (1 \leq i \leq M)
- D_i are integers.
- The given graph is connected.
-----Input-----
Input is given from Standard Input in the following format:
N M
S T
U_1 V_1 D_1
U_2 V_2 D_2
:
U_M V_M D_M
-----Output-----
Print the answer.
-----Sample Input-----
4 4
1 3
1 2 1
2 3 1
3 4 1
4 1 1
-----Sample Output-----
2
There are two ways to choose shortest paths that satisfies the condition:
- Takahashi chooses the path 1 \rightarrow 2 \rightarrow 3, and Aoki chooses the path 3 \rightarrow 4 \rightarrow 1.
- Takahashi chooses the path 1 \rightarrow 4 \rightarrow 3, and Aoki chooses the path 3 \rightarrow 2 \rightarrow 1.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
# ARC090E
def hoge():
M = 10**9 + 7
import sys
input = lambda : sys.stdin.readline().rstrip()
n, m = map(int, input().split())
s, t = map(int, input().split())
s -= 1
t -= 1
from collections import defaultdict
ns = defaultdict(set)
for i in range(m):
u, v, d = map(int, input().split())
ns[u-1].add((v-1, d))
ns[v-1].add((u-1, d))
def _dijkstra(N, s, Edge):
import heapq
geta = 10**15
inf = geta
dist = [inf] * N
dist[s] = 0
Q = [(0, s)]
dp = [0]*N
dp[s] = 1
while Q:
dn, vn = heapq.heappop(Q)
if dn > dist[vn]:
continue
for vf, df in Edge[vn]:
if dist[vn] + df < dist[vf]:
dist[vf] = dist[vn] + df
dp[vf] = dp[vn]
heapq.heappush(Q, (dn + df,vf))
elif dist[vn] + df == dist[vf]:
dp[vf] = (dp[vf] + dp[vn]) % M
return dist, dp
def dijkstra(start):
import heapq
vals = [None] * n
nums = [None] * n
nums[start] = 1
h = [(0, start)] # (距離, ノード番号)
vals[start] = 0
while h:
val, u = heapq.heappop(h)
for v, d in ns[u]:
if vals[v] is None or vals[v]>val+d:
vals[v] = val+d
nums[v] = nums[u]
heapq.heappush(h, (vals[v], v))
elif vals[v] is not None and vals[v]==val+d:
nums[v] = (nums[v] + nums[u]) % M
return vals, nums
vals1, nums1 = dijkstra(s)
vals2, nums2 = dijkstra(t)
T = vals1[t]
c1 = 0 # 頂点で衝突するペアの数
c2 = 0 # エッジ(端点除く)で衝突するペアの数
for u in range(n):
if 2*vals1[u]==T and 2*vals2[u]==T:
c1 = (c1 + pow((nums1[u] * nums2[u]), 2, M)) % M
for v,d in ns[u]:
if (vals1[u]+d+vals2[v]==T) and (2*vals1[u] < T < 2*(vals1[u] + d)):
c2 = (c2 + (nums1[u] * nums2[v])**2) % M
print((nums1[t]*nums2[s] - (c1+c2)) % M)
hoge()
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
You are given an integer sequence $A_1, A_2, \ldots, A_N$. For any pair of integers $(l, r)$ such that $1 \le l \le r \le N$, let's define $\mathrm{OR}(l, r)$ as $A_l \lor A_{l+1} \lor \ldots \lor A_r$. Here, $\lor$ is the bitwise OR operator.
In total, there are $\frac{N(N+1)}{2}$ possible pairs $(l, r)$, i.e. $\frac{N(N+1)}{2}$ possible values of $\mathrm{OR}(l, r)$. Determine if all these values are pairwise distinct.
-----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 the string "YES" if all values of $\mathrm{OR}(l, r)$ are pairwise distinct or "NO" otherwise (without quotes).
-----Constraints-----
- $1 \le T \le 300$
- $1 \le N \le 10^5$
- $0 \le A_i \le 10^{18}$ for each valid $i$
- the sum of $N$ over all test cases does not exceed $3 \cdot 10^5$
-----Example Input-----
4
3
1 2 7
2
1 2
3
6 5 8
5
12 32 45 23 47
-----Example Output-----
NO
YES
YES
NO
-----Explanation-----
Example case 1: The values of $\mathrm{OR}(l, r)$ are $1, 2, 7, 3, 7, 7$ (corresponding to the contiguous subsequences $[1], [2], [7], [1,2], [2,7], [1,2,7]$ respectively). We can see that these values are not pairwise distinct.
Example case 2: The values of $\mathrm{OR}(l, r)$ are $1, 2, 3$ (corresponding to the contiguous subsequences $[1], [2], [1, 2]$ respectively) and they are pairwise distinct.
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())
arr = list(map(int,input().split()))
if n<=62:
st = set()
for i in range(n):
curr = 0
for j in range(i,n):
curr = curr|arr[j]
st.add(curr)
if len(st)==n*(n+1)//2:
print("YES")
else:
print("NO")
else:
print("NO")
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
You are working for the Gryzzl company, headquartered in Pawnee, Indiana.
The new national park has been opened near Pawnee recently and you are to implement a geolocation system, so people won't get lost. The concept you developed is innovative and minimalistic. There will be $n$ antennas located somewhere in the park. When someone would like to know their current location, their Gryzzl hologram phone will communicate with antennas and obtain distances from a user's current location to all antennas.
Knowing those distances and antennas locations it should be easy to recover a user's location... Right? Well, almost. The only issue is that there is no way to distinguish antennas, so you don't know, which distance corresponds to each antenna. Your task is to find a user's location given as little as all antennas location and an unordered multiset of distances.
-----Input-----
The first line of input contains a single integer $n$ ($2 \leq n \leq 10^5$) which is the number of antennas.
The following $n$ lines contain coordinates of antennas, $i$-th line contain two integers $x_i$ and $y_i$ ($0 \leq x_i,y_i \leq 10^8$). It is guaranteed that no two antennas coincide.
The next line of input contains integer $m$ ($1 \leq n \cdot m \leq 10^5$), which is the number of queries to determine the location of the user.
Following $m$ lines contain $n$ integers $0 \leq d_1 \leq d_2 \leq \dots \leq d_n \leq 2 \cdot 10^{16}$ each. These integers form a multiset of squared distances from unknown user's location $(x;y)$ to antennas.
For all test cases except the examples it is guaranteed that all user's locations $(x;y)$ were chosen uniformly at random, independently from each other among all possible integer locations having $0 \leq x, y \leq 10^8$.
-----Output-----
For each query output $k$, the number of possible a user's locations matching the given input and then output the list of these locations in lexicographic order.
It is guaranteed that the sum of all $k$ over all points does not exceed $10^6$.
-----Examples-----
Input
3
0 0
0 1
1 0
1
1 1 2
Output
1 1 1
Input
4
0 0
0 1
1 0
1 1
2
0 1 1 2
2 5 5 8
Output
4 0 0 0 1 1 0 1 1
4 -1 -1 -1 2 2 -1 2 2
-----Note-----
As you see in the second example, although initially a user's location is picked to have non-negative coordinates, you have to output all possible integer locations.
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
n = int(input())
x = [0]*n
y = [0]*n
for i in range(n):
x[i], y[i] = list(map(int, input().split()))
sx = sum(x)
sy = sum(y)
for i in range(n):
x[i] = n * x[i] - sx
y[i] = n * y[i] - sy
m = int(input())
d = [0]*n
e = [0]*n
HD = 0
def check(a, b):
nonlocal HD
HE = 0
for i in range(n):
HE ^= hash((a-x[i])*(a-x[i])+(b-y[i])*(b-y[i]))
return HD == HE
def sqrt(x):
nn = int(x)
if nn == 0:
return 0
fa, fb = divmod(nn.bit_length(), 2)
x = 2**(fa+fb)
while True:
y = (x + nn//x)//2
if y >= x:
return x
x = y
def hash(x):
return x * 9991 + 43
pans = []
def solve():
nonlocal d
d = list(map(int, input().split()))
c = 0
d = [p * n * n for p in d]
for i in range(n):
c += d[i] - x[i] * x[i] - y[i] * y[i]
assert(c % n == 0)
c //= n
ans = []
ax = x[0]
ay = y[0]
if ax is 0 and ay is 0:
ax = x[1]
ay = y[1]
rev = 0
if ay == 0:
ay = ax
ax = 0
rev = 1
d.sort()
nonlocal HD
HD = 0
for p in d:
HD ^= hash(p)
old = -1
for p in d:
if (p == old):
continue
old = p
a = c + ax * ax + ay * ay - p
if (a % 2 != 0):
continue
a //= 2
A = ax * ax + ay * ay
B = a * ax
C = a * a - ay * ay * c
D = B * B - A * C
if (D < 0):
continue
sD = sqrt(D)
if D != sD * sD:
continue
if (B + sD) % A == 0:
qx = (B + sD) // A
qy = (a - ax * qx) // ay
if rev:
t = qx
qx = qy
qy = t
if ((qx + sx) % n == 0 and (qy + sy) % n == 0 and check(qx, qy)):
qx = (qx + sx) // n
qy = (qy + sy) // n
ans.append([qx, qy])
if sD == 0:
continue
if (B - sD) % A == 0:
qx = (B - sD) // A
qy = (a - ax * qx) // ay
if rev:
t = qx
qx = qy
qy = t
if ((qx + sx) % n == 0 and (qy + sy) % n == 0 and check(qx, qy)):
qx = (qx + sx) // n
qy = (qy + sy) // n
ans.append([qx, qy])
ans.sort()
buf=[]
buf.append(len(ans))
for p in ans:
buf.append(p[0])
buf.append(p[1])
nonlocal pans
pans.append(" ".join(map(str,buf)))
while m > 0:
m -= 1
solve()
sys.stdout.write("\n".join(pans))
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
You are given two binary strings $S$ and $P$, each with length $N$. A binary string contains only characters '0' and '1'. For each valid $i$, let's denote the $i$-th character of $S$ by $S_i$.
You have to convert the string $S$ into $P$ using zero or more operations. In one operation, you should choose two indices $i$ and $j$ ($1 \leq i < j \leq N$) such that $S_i$ is '1' and $S_j$ is '0', and swap $S_i$ with $S_j$.
Determine if it is possible to convert $S$ into $P$ by performing some operations.
-----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 a single string $S$.
- The third line contains a single string $P$.
-----Output-----
For each test case, print a single line containing the string "Yes" if it is possible to convert $S$ into $P$ or "No" otherwise (without quotes).
-----Constraints-----
- $1 \leq T \leq 10^5$
- $1 \leq N \leq 10^5$
- $S$ and $P$ contain only characters '0' and '1'
- the sum of $N$ over all test cases does not exceed $10^5$
-----Subtasks-----
Subtask #1 (20 points):
- $N \leq 14$
- the sum of $N$ over all test cases does not exceed $100$
Subtask #2 (30 points): the sum of $N$ over all test cases does not exceed $1,000$
Subtask #3 (50 points): original constraints
-----Example Input-----
3
2
00
00
3
101
010
4
0110
0011
-----Example Output-----
Yes
No
Yes
-----Explanation-----
Example case 1: The strings are already equal.
Example case 2: It can be showed that it is impossible to convert $S$ into $P$.
Example case 3: You can swap $S_2$ with $S_4$. The strings will then be equal.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
def solve(s, p):
diffs = 0
for x, y in zip(s, p):
if x == y:
continue
if x == '0':
if diffs < 1:
return "No"
diffs -= 1
else:
diffs += 1
return "Yes" if diffs == 0 else "No"
for _ in range(int(input())):
l = int(input())
s = input().strip()
p = input().strip()
print(solve(s, p))
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Vasya's got a birthday coming up and his mom decided to give him an array of positive integers a of length n.
Vasya thinks that an array's beauty is the greatest common divisor of all its elements. His mom, of course, wants to give him as beautiful an array as possible (with largest possible beauty). Unfortunately, the shop has only one array a left. On the plus side, the seller said that he could decrease some numbers in the array (no more than by k for each number).
The seller can obtain array b from array a if the following conditions hold: b_{i} > 0; 0 ≤ a_{i} - b_{i} ≤ k for all 1 ≤ i ≤ n.
Help mom find the maximum possible beauty of the array she will give to Vasya (that seller can obtain).
-----Input-----
The first line contains two integers n and k (1 ≤ n ≤ 3·10^5; 1 ≤ k ≤ 10^6). The second line contains n integers a_{i} (1 ≤ a_{i} ≤ 10^6) — array a.
-----Output-----
In the single line print a single number — the maximum possible beauty of the resulting array.
-----Examples-----
Input
6 1
3 6 10 12 13 16
Output
3
Input
5 3
8 21 52 15 77
Output
7
-----Note-----
In the first sample we can obtain the array:
3 6 9 12 12 15
In the second sample we can obtain the next array:
7 21 49 14 77
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
n, k = map(int, input().split())
t = set(map(int, input().split()))
y = x = min(t)
t = list(t)
while True:
for i in t:
if i % x > k: x = i // (i // x + 1)
if y == x: break
y = x
print(y)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Mitya has a rooted tree with $n$ vertices indexed from $1$ to $n$, where the root has index $1$. Each vertex $v$ initially had an integer number $a_v \ge 0$ written on it. For every vertex $v$ Mitya has computed $s_v$: the sum of all values written on the vertices on the path from vertex $v$ to the root, as well as $h_v$ — the depth of vertex $v$, which denotes the number of vertices on the path from vertex $v$ to the root. Clearly, $s_1=a_1$ and $h_1=1$.
Then Mitya erased all numbers $a_v$, and by accident he also erased all values $s_v$ for vertices with even depth (vertices with even $h_v$). Your task is to restore the values $a_v$ for every vertex, or determine that Mitya made a mistake. In case there are multiple ways to restore the values, you're required to find one which minimizes the total sum of values $a_v$ for all vertices in the tree.
-----Input-----
The first line contains one integer $n$ — the number of vertices in the tree ($2 \le n \le 10^5$). The following line contains integers $p_2$, $p_3$, ... $p_n$, where $p_i$ stands for the parent of vertex with index $i$ in the tree ($1 \le p_i < i$). The last line contains integer values $s_1$, $s_2$, ..., $s_n$ ($-1 \le s_v \le 10^9$), where erased values are replaced by $-1$.
-----Output-----
Output one integer — the minimum total sum of all values $a_v$ in the original tree, or $-1$ if such tree does not exist.
-----Examples-----
Input
5
1 1 1 1
1 -1 -1 -1 -1
Output
1
Input
5
1 2 3 1
1 -1 2 -1 -1
Output
2
Input
3
1 2
2 -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
from collections import defaultdict, deque
n = int(input())
adj = [[] for _ in range(n)]
v = [0] * n
l = list(map(int, input().split()))
for i, f in enumerate(l):
adj[f - 1].append(i + 1)
s = list(map(int, input().split()))
Q = deque([(0, s[0], s[0])])
ans = 0
flag = False
possible = True
while Q and possible:
# print(Q)
flag = not flag
for _ in range(len(Q)):
cur, v, curs = Q.popleft()
if v < 0:
possible = False
ans = -1
break
ans += v
if flag:
for i in adj[cur]:
if len(adj[i]) <= 1:
Q.append((i, 0, curs))
else:
temp = min([s[k] for k in adj[i]])
Q.append((i, temp - curs, temp))
else:
for i in adj[cur]:
Q.append((i, s[i] - curs, s[i]))
print(ans)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Amit is going on a date and he wants to gift his date an array of positive numbers. But he is running short on money. He already has an array of numbers in design. Cost of an array of numbers is the sum of elements in it. But he wants to minimize the cost of making it.
So he does the following number of operations one by one for any number of times:
He chooses two adjacent elements ,replace them by one element with value = XOR of the two numbers. This operation reduces length of array (and elements are re-numerated accordingly)
Find the minimum amount of money that Amit needs to spend to gift his date.
-----Input:-----
- First line will contain $T$, number of testcases. Then the testcases follow.
- Each testcase contains of $2$ lines of input, first line contains a single integer $N$ and the second line contains $N$ elements - $A1,A2,A3,.....,AN$
-----Output:-----
For each testcase, output in a single line answer denoting the minimum cost
-----Constraints-----
- $1 \leq T \leq 10$
- $1 \leq N \leq 10^5$
- $0 \leq Ai \leq 10^9$ for $1\leq i \leq N$
-----Sample Input:-----
3
5
8 4 1 5 0
5
1 2 4 0 8
2
10 10
-----Sample Output:-----
8
15
0
-----EXPLANATION:-----
For first case,
This array is :
$[8,4,1,5,0] -> [8,4,4,0] -> [8,0,0]$. Sum=$8$ So the answer is 8.
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()))
su=l[0]
for i in range(1,n):
su^=l[i]
print(su)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Chef Ada is preparing $N$ dishes (numbered $1$ through $N$). For each valid $i$, it takes $C_i$ minutes to prepare the $i$-th dish. The dishes can be prepared in any order.
Ada has a kitchen with two identical burners. For each valid $i$, to prepare the $i$-th dish, she puts it on one of the burners and after $C_i$ minutes, removes it from this burner; the dish may not be removed from the burner before those $C_i$ minutes pass, because otherwise it cools down and gets spoiled. Any two dishes may be prepared simultaneously, however, no two dishes may be on the same burner at the same time. Ada may remove a dish from a burner and put another dish on the same burner at the same time.
What is the minimum time needed to prepare all dishes, i.e. reach the state where all dishes are prepared?
-----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 $C_1, C_2, \ldots, C_N$.
-----Output-----
For each test case, print a single line containing one integer ― the minimum number of minutes needed to prepare all dishes.
-----Constraints-----
- $1 \le T \le 1,000$
- $1 \le N \le 4$
- $1 \le C_i \le 5$ for each valid $i$
-----Subtasks-----
Subtask #1 (1 points): $C_1 = C_2 = \ldots = C_N$
Subtask #2 (99 points): original constraints
-----Example Input-----
3
3
2 2 2
3
1 2 3
4
2 3 4 5
-----Example Output-----
4
3
7
-----Explanation-----
Example case 1: Place the first two dishes on the burners, wait for two minutes, remove both dishes and prepare the last one on one burner.
Example case 2: Place the first and third dish on the burners. When the first dish is prepared, remove it and put the second dish on the same burner.
Example case 3: Place the third and fourth dish on the burners. When the third dish is prepared, remove it and put the second dish on the same burner. Similarly, replace the fourth dish (when it is prepared) by the first dish on the other burner.
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=[int(z) for z in input().split()]
c.sort()
c.reverse()
b1,b2=0,0
for i in range(n):
if b1<b2:
b1+=c[i]
elif b2<b1:
b2+=c[i]
else:
b1+=c[i]
print(max(b1,b2))
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
You are given a binary string $s$.
Find the number of distinct cyclical binary strings of length $n$ which contain $s$ as a substring.
The cyclical string $t$ contains $s$ as a substring if there is some cyclical shift of string $t$, such that $s$ is a substring of this cyclical shift of $t$.
For example, the cyclical string "000111" contains substrings "001", "01110" and "10", but doesn't contain "0110" and "10110".
Two cyclical strings are called different if they differ from each other as strings. For example, two different strings, which differ from each other by a cyclical shift, are still considered different cyclical strings.
-----Input-----
The first line contains a single integer $n$ ($1 \le n \le 40$) — the length of the target string $t$.
The next line contains the string $s$ ($1 \le |s| \le n$) — the string which must be a substring of cyclical string $t$. String $s$ contains only characters '0' and '1'.
-----Output-----
Print the only integer — the number of distinct cyclical binary strings $t$, which contain $s$ as a substring.
-----Examples-----
Input
2
0
Output
3
Input
4
1010
Output
2
Input
20
10101010101010
Output
962
-----Note-----
In the first example, there are three cyclical strings, which contain "0" — "00", "01" and "10".
In the second example, there are only two such strings — "1010", "0101".
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=[c=='1' for c in input()]
m=len(s)
z=[[0,0]]
for c in s:
ind = z[-1][c]
z[-1][c] = len(z)
z.append(z[ind][:])
assert(len(z) == m+1)
z[m][0] = z[m][1] = m # make it sticky
# how many things match directly
dp = [0 for _ in range(m+1)]
dp[0] = 1
for i in range(n):
ndp = [0 for _ in range(m+1)]
for i in range(m+1):
ndp[z[i][0]] += dp[i]
ndp[z[i][1]] += dp[i]
dp = ndp
res = dp[m]
for k in range(1, m):
s0 = 0
for c in s[-k:]:
s0 = z[s0][c]
dp = [0 for _ in range(m+1)]
dp[s0] = 1
for i in range(n - k):
ndp = [0 for _ in range(m+1)]
for i in range(m+1):
ndp[z[i][0]] += dp[i]
ndp[z[i][1]] += dp[i]
dp = ndp
for s1 in range(m): # skip m
v = dp[s1]
for c in s[-k:]:
if s1 == m: v = 0
s1 = z[s1][c]
if s1 == m: res += v
print(res)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
The $String$ Family gave birth to a new $Tripartite$ $trio$ $sisters$ and named them $Hema$, $Rekha$ and $Sushma$. Hema and Rekha are very fond of parties whereas Sushma hates them. One day Hema and Rekha asked their parents to buy them candies to distribute to people in their birthday party. (Remember Hema, Rekha and Sushma were born on the same day). But Sushma was uninterested in the party and only wanted candies for herself.
You will be given a list $P$ of possible number of candidates coming to the party. Were $P[i]$ denotes the count of people coming in the i th possibility. In each case every person should get maximum possible equal number of candies such that after distributing the candies, there are always $R$ candies remaining for Sushma. You have to calculate the minimum number of candies required to buy so that, in any possible situation of the given array, each person coming to party gets equal number of candies (at least 1 and maximum possible out of total) and there are always $R$ candies remaining for Sushma.
-----Input:-----
- First line will contain $T$, number of testcases. Then the testcases follow.
- First line of each test case contain $N$, number of possible count of people coming to party
- Next line contain $N$ spaced integers denoting the count of people
- Next line contain $R$ the number of candies always remaining after maximum equal distribution
-----Output:-----
For each testcase, output in a single line answer, the minimum number of candies required to buy.
-----Constraints-----
- $1 \leq T \leq 100$
- $1 \leq N \leq 10^4$
- $1 \leq P[i] \leq 41$
- $0 \leq R < min(P[i])$
-----Sample Input:-----
1
2
2 3
1
-----Sample Output:-----
7
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
from math import gcd
def compute_lcm(x, y):
lcm = (x*y)//gcd(x,y)
return lcm
def LCMofArray(a):
lcm = a[0]
for i in range(1,len(a)):
lcm = lcm*a[i]//gcd(lcm, a[i])
return lcm
for _ in range(int(input())):
lens = int(input())
arrs = [int(x) for x in input().split()]
rest = int(input())
print(LCMofArray(arrs) + rest)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
You are given two strings $s$ and $t$ both of length $n$ and both consisting of lowercase Latin letters.
In one move, you can choose any length $len$ from $1$ to $n$ and perform the following operation: Choose any contiguous substring of the string $s$ of length $len$ and reverse it; at the same time choose any contiguous substring of the string $t$ of length $len$ and reverse it as well.
Note that during one move you reverse exactly one substring of the string $s$ and exactly one substring of the string $t$.
Also note that borders of substrings you reverse in $s$ and in $t$ can be different, the only restriction is that you reverse the substrings of equal length. For example, if $len=3$ and $n=5$, you can reverse $s[1 \dots 3]$ and $t[3 \dots 5]$, $s[2 \dots 4]$ and $t[2 \dots 4]$, but not $s[1 \dots 3]$ and $t[1 \dots 2]$.
Your task is to say if it is possible to make strings $s$ and $t$ equal after some (possibly, empty) sequence of moves.
You have to answer $q$ independent test cases.
-----Input-----
The first line of the input contains one integer $q$ ($1 \le q \le 10^4$) — the number of test cases. Then $q$ test cases follow.
The first line of the test case contains one integer $n$ ($1 \le n \le 2 \cdot 10^5$) — the length of $s$ and $t$.
The second line of the test case contains one string $s$ consisting of $n$ lowercase Latin letters.
The third line of the test case contains one string $t$ consisting of $n$ lowercase Latin letters.
It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$ ($\sum n \le 2 \cdot 10^5$).
-----Output-----
For each test case, print the answer on it — "YES" (without quotes) if it is possible to make strings $s$ and $t$ equal after some (possibly, empty) sequence of moves and "NO" otherwise.
-----Example-----
Input
4
4
abcd
abdc
5
ababa
baaba
4
asdf
asdg
4
abcd
badc
Output
NO
YES
NO
YES
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 _ in range(q) :
n = int(input())
s = input()
t = input()
x = set(s)
y = set(t)
if x != y :
print("NO")
continue
if len(x) == n :
a = [0] * n
for i, c in enumerate(t) :
a[i] = s.find(c)
yeet = 0
vis = [False] * n
for i in range(n) :
if vis[i] :
continue
j = i
cyc = 0
while not vis[j] :
cyc += 1
vis[j] = True
j = a[j]
# print('>> ', i, cyc)
yeet += (cyc - 1) % 2
yeet %= 2
if yeet == 0 :
print("YES")
else :
print("NO")
continue
print("YES")
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Cherry has a string S$S$ consisting of lowercase English letters. Using this string, he formed a pyramid of infinite length with certain rules:
- N$N$-th row of pyramid contains N$N$ characters.
- Each row of pyramid begins with the first character of the string.
- The subsequent characters of the row are appended to the string in cyclic fashion, until the size of string for that Row is reached (See example pyramid for better understanding).
He has another string T$T$ of smaller (or equal) size.
You are asked Q$Q$ queries. Each query is provided with a row number N$N$. The answer to the query is number of occurrences of string T$T$ in that particular row of pyramid. No of occurrences of String T$T$ in a string V$V$ would mean that you'd need to find number of substrings Vi,Vi+1...Vj$V_i, V_{i+1} ... V_j$ which are equal to String T$T$, where i≤j$i \leq j$.
For eg: If the string is code, then the pyramid will be of the form:
c
co
cod
code
codec
codeco
codecod
codecode
codecodec
codecodeco
...
-----Input:-----
- The first line contains string S$S$ — consisting of lowercase English letters.
- The second line contains string T$T$ — consisting of lowercase English letters.
- Next line contains an integer Q$Q$ — the number of queries.
- Then follow Q$Q$ lines with queries descriptions. Each of them contains a single integer N$N$ denoting the row number of pyramid.
-----Output:-----
- Print Q$Q$ lines. The i$i$-th of them should contain a integer denoting occurrences of string T$T$ in that particular row.
-----Constraints-----
- 1≤|S|≤105$1 \leq |S| \leq 10^5$
- 1≤|T|≤|S|$1 \leq |T| \leq |S|$
- 1≤Q≤105$1 \leq Q \leq 10^5$
- 1≤N≤109$1 \leq N \leq 10^9$
-----Sample Input:-----
codechef
chefcode
3
4
12
1455
-----Sample Output:-----
0
1
181
-----Explanation:-----
Pyramid will be formed as explained in the statement.
Query 1: Row number 4 of the pyramid is code. The number of occurrences of chefcode in code is 0.
Query 2: Row number 12 of the pyramid is codechefcode. The number of occurrences of chefcode in codechefcode is 1.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
def search(arr, lenl, val):
s = 0
l = lenl - 1
total = 0
while (s <= l):
m = int((s + l) / 2)
if (arr[m] <= val):
total = m + 1
s = m + 1
else:
l = m - 1
return total
def kmpsearch(string, lps):
lis = []
lens = len(string)
lensh = lens // 2
l = 0
i = 0
while i < lens:
if string[i] == pat[l]:
l += 1
i += 1
elif l > 0:
l = lps[l - 1]
else:
i += 1
if l == lenp:
if i - l < lensh:
lis.append(i - l)
l = lps[l - 1]
return lis
def kmp(pat, lenp):
lps = [0]*(lenp)
l = 0
i = 1
while i < lenp:
if pat[i] == pat[l]:
l += 1
lps[i] = l
i += 1
elif l > 0:
l = lps[l-1]
else:
lps[i] = 0
i += 1
return lps
keyword = input()
pat = input()
q = int(input())
lenk = len(keyword)
lenp = len(pat)
k = keyword * 2
lis = kmpsearch(k, kmp(pat, lenp))
lenl = len(lis)
for _ in range(q):
n = int(input())
count = 0
q = n // lenk
r = n % lenk
count += search(lis, lenl, r - lenp)
if q >= 1:
count += search(lis, lenl, lenk + r - lenp)
if q >= 2:
count += (q - 1)*lenl
print(count)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Our Chef is doing what he is best at, COOKING A BARBECUE for his guests. He has invited all of us, and taking the help of his apprentice to smoke the barbecues. The chef has got BBQ sticks, each can take N fillings, and he presents N distinctly filled sticks in front his guests forming a N*N matrix
But here is the problem, he has got only two type of fillings, meat and capsicum, but still wants the N sticks to look "presentable", he is very particular about it. As a solution he fills the main diagonal of the N*N matrix with the same type of filling (either meat or capsicum) forming a "presentable" set
The Chef's apprentice is a fool, so the Chef asks him to cook M distinctly filled sticks ,so that the Chef is sure that among M there exist N sticks forming a "presentable" set. Your job is to determine smallest possible value of M.
-----Input-----
T, the number of test cases, followed by T lines.
Each line containing the positive integer N >= 4
-----Output-----
T lines of output, each line contain the positive integer M
-----Example-----
Input:
1
4
Output:
5
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
testcase = int(input())
for case in range(testcase):
n = int(input())
print(2**(n-2)+1)
print('\n')
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Gargi is thinking of a solution to a problem. Meanwhile, her friend asks her to solve another problem. Since Gargi is busy in her own problem, she seeks your help to solve the new problem.
You are given a string S containing characters a-z (lower case letters) only. You need to change the string to a new string consisting of only one letter from a-z.
For a given character S[i] in the string, if you change it to a character having lower ASCII value than the character S[i], you gain points equal to the difference in ASCII value of the old character and the new character. Similarly, for a given character S[j] in the string, if you change it to a character having higher ASCII value than the character S[j], you lose points equal to the difference in ASCII value of the old character and the new character.
However, Gargi does not like gaining or losing points. She has asked you to change the string in such a way that the total losing or gaining of points at the end of the string conversion is minimum.
Give Gargi the absolute value of the points you have at the end of the string conversion.
-----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 of the T test case contains a string S containing only lower case characters (a-z)
-----Output-----
For each test case, output a single line containing the answer.
-----Constraints-----
- 1 ≤ T ≤ 10
- 1 ≤ |S| ≤ 100000
-----Example-----
Input:
1
abba
Output:
2
-----Explanation-----
Example case 1. The new string can be aaaa where you have +2 points at the end of string conversion or it can be bbbb where you have -2 points at the end of string conversion. Hence the output is 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):
s = input().rstrip()
sumv = 0
for j in range(len(s)):
sumv += ord(s[j])
minv = 10 ** 8;
for i in range(ord('a'), ord('z') + 1):
val = abs(sumv - i * len(s))
if minv > val:
minv = val
print(minv)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
We have a tree with N vertices, whose i-th edge connects Vertex u_i and Vertex v_i.
Vertex i has an integer a_i written on it.
For every integer k from 1 through N, solve the following problem:
- We will make a sequence by lining up the integers written on the vertices along the shortest path from Vertex 1 to Vertex k, in the order they appear. Find the length of the longest increasing subsequence of this sequence.
Here, the longest increasing subsequence of a sequence A of length L is the subsequence A_{i_1} , A_{i_2} , ... , A_{i_M} with the greatest possible value of M such that 1 \leq i_1 < i_2 < ... < i_M \leq L and A_{i_1} < A_{i_2} < ... < A_{i_M}.
-----Constraints-----
- 2 \leq N \leq 2 \times 10^5
- 1 \leq a_i \leq 10^9
- 1 \leq u_i , v_i \leq N
- u_i \neq v_i
- The given graph is a tree.
- All values in input are integers.
-----Input-----
Input is given from Standard Input in the following format:
N
a_1 a_2 ... a_N
u_1 v_1
u_2 v_2
:
u_{N-1} v_{N-1}
-----Output-----
Print N lines. The k-th line, print the length of the longest increasing subsequence of the sequence obtained from the shortest path from Vertex 1 to Vertex k.
-----Sample Input-----
10
1 2 5 3 4 6 7 3 2 4
1 2
2 3
3 4
4 5
3 6
6 7
1 8
8 9
9 10
-----Sample Output-----
1
2
3
3
4
4
5
2
2
3
For example, the sequence A obtained from the shortest path from Vertex 1 to Vertex 5 is 1,2,5,3,4. Its longest increasing subsequence is A_1, A_2, A_4, A_5, with the length of 4.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
import bisect
import sys
sys.setrecursionlimit(10**7)
def dfs(v):
pos=bisect.bisect_left(dp,arr[v])
changes.append((pos,dp[pos]))
dp[pos]=arr[v]
ans[v]=bisect.bisect_left(dp,10**18)
for u in g[v]:
if checked[u]==0:
checked[u]=1
dfs(u)
pos,val=changes.pop()
dp[pos]=val
n=int(input())
arr=[0]+list(map(int,input().split()))
g=[[] for _ in range(n+1)]
for _ in range(n-1):
a,b=map(int,input().split())
g[a].append(b)
g[b].append(a)
ans=[0]*(n+1)
checked=[0]*(n+1)
checked[1]=1
dp=[10**18 for _ in range(n+1)]
changes=[]
dfs(1)
for i in range(1,n+1):
print(ans[i])
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
There are $n$ programmers that you want to split into several non-empty teams. The skill of the $i$-th programmer is $a_i$. You want to assemble the maximum number of teams from them. There is a restriction for each team: the number of programmers in the team multiplied by the minimum skill among all programmers in the team must be at least $x$.
Each programmer should belong to at most one team. Some programmers may be left without a team.
Calculate the maximum number of teams that you can assemble.
-----Input-----
The first line contains the integer $t$ ($1 \le t \le 1000$) — the number of test cases.
The first line of each test case contains two integers $n$ and $x$ ($1 \le n \le 10^5; 1 \le x \le 10^9$) — the number of programmers and the restriction of team skill respectively.
The second line of each test case contains $n$ integers $a_1, a_2, \dots , a_n$ ($1 \le a_i \le 10^9$), where $a_i$ is the skill of the $i$-th programmer.
The sum of $n$ over all inputs does not exceed $10^5$.
-----Output-----
For each test case print one integer — the maximum number of teams that you can assemble.
-----Example-----
Input
3
5 10
7 11 2 9 5
4 8
2 4 2 3
4 11
1 3 3 7
Output
2
1
0
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
__MULTITEST = True
## solve
def solve():
n, x = map(int, input().split())
a = list(map(int, input().split()))
a.sort()
group = 0
ptr = n-1
members = 0
currentMin = int(1e10)
while ptr > -1:
currentMin = min(currentMin, a[ptr])
members += 1
if currentMin * members >= x:
group += 1
members = 0
currentMin = int(1e10)
ptr -= 1
print(group)
## main
def __starting_point():
t = (int(input()) if __MULTITEST else 1)
for tt in range(t):
solve();
__starting_point()
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
You are given a directed graph of $n$ vertices and $m$ edges. Vertices are numbered from $1$ to $n$. There is a token in vertex $1$.
The following actions are allowed: Token movement. To move the token from vertex $u$ to vertex $v$ if there is an edge $u \to v$ in the graph. This action takes $1$ second. Graph transposition. To transpose all the edges in the graph: replace each edge $u \to v$ by an edge $v \to u$. This action takes increasingly more time: $k$-th transposition takes $2^{k-1}$ seconds, i.e. the first transposition takes $1$ second, the second one takes $2$ seconds, the third one takes $4$ seconds, and so on.
The goal is to move the token from vertex $1$ to vertex $n$ in the shortest possible time. Print this time modulo $998\,244\,353$.
-----Input-----
The first line of input contains two integers $n, m$ ($1 \le n, m \le 200\,000$).
The next $m$ lines contain two integers each: $u, v$ ($1 \le u, v \le n; u \ne v$), which represent the edges of the graph. It is guaranteed that all ordered pairs $(u, v)$ are distinct.
It is guaranteed that it is possible to move the token from vertex $1$ to vertex $n$ using the actions above.
-----Output-----
Print one integer: the minimum required time modulo $998\,244\,353$.
-----Examples-----
Input
4 4
1 2
2 3
3 4
4 1
Output
2
Input
4 3
2 1
2 3
4 3
Output
10
-----Note-----
The first example can be solved by transposing the graph and moving the token to vertex $4$, taking $2$ seconds.
The best way to solve the second example is the following: transpose the graph, move the token to vertex $2$, transpose the graph again, move the token to vertex $3$, transpose the graph once more and move the token to vertex $4$.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
import sys
input = sys.stdin.readline
import heapq
mod=998244353
n,m=list(map(int,input().split()))
E=[[] for i in range(n+1)]
E2=[[] for i in range(n+1)]
for i in range(m):
x,y=list(map(int,input().split()))
E[x].append(y)
E2[y].append(x)
TIME=[1<<29]*(n+1)
TIME[1]=0
def shuku(x,y):
return (x<<20)+y
Q=[]
ANS=[]
for k in range(n+1):
NQ=[]
if k<=1:
heapq.heappush(Q,shuku(0,1))
if k%2==0:
while Q:
#print(Q)
x=heapq.heappop(Q)
time=x>>20
town=x-(time<<20)
#print(x,time,town)
if TIME[town]<time:
continue
for to in E[town]:
if TIME[to]>time+1:
TIME[to]=time+1
heapq.heappush(Q,shuku(TIME[to],to))
heapq.heappush(NQ,shuku(TIME[to],to))
else:
while Q:
x=heapq.heappop(Q)
time=x>>20
town=x-(time<<20)
#print(x,time,town)
if TIME[town]<time:
continue
for to in E2[town]:
if TIME[to]>time+1:
TIME[to]=time+1
heapq.heappush(Q,shuku(TIME[to],to))
heapq.heappush(NQ,shuku(TIME[to],to))
#print(k,TIME)
Q=NQ
ANS.append(TIME[n])
if k>=100 and TIME[n]!=1<<29:
break
A=ANS[0]
for k in range(1,len(ANS)):
if ANS[k]==1<<29:
continue
if ANS[k-1]==1<<29:
A=(ANS[k]+pow(2,k,mod)-1)%mod
if k<60 and ANS[k-1]-ANS[k]>pow(2,k-1):
A=(ANS[k]+pow(2,k,mod)-1)%mod
print(A)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Tonight, Chef would like to hold a party for his $N$ friends.
All friends are invited and they arrive at the party one by one in an arbitrary order. However, they have certain conditions — for each valid $i$, when the $i$-th friend arrives at the party and sees that at that point, strictly less than $A_i$ other people (excluding Chef) have joined the party, this friend leaves the party; otherwise, this friend joins the party.
Help Chef estimate how successful the party can be — find the maximum number of his friends who could join the party (for an optimal choice of the order of arrivals).
-----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 — the maximum number of Chef's friends who could join the party.
-----Constraints-----
- $1 \le T \le 1,000$
- $1 \le N \le 10^5$
- the sum of $N$ over all test cases does not exceed $10^6$
-----Example Input-----
3
2
0 0
6
3 1 0 0 5 5
3
1 2 3
-----Example Output-----
2
4
0
-----Explanation-----
Example case 1: Chef has two friends. Both of them do not require anyone else to be at the party before they join, so they will both definitely join the party.
Example case 2: At the beginning, friends $3$ and $4$ can arrive and join the party, since they do not require anyone else to be at the party before they join. After that, friend $2$ can arrive; this friend would see that there are two people at the party and therefore also join. Then, friend $1$ will also join, so in the end, there would be $4$ people attending the party.
Example case 3: No one will attend the party because each of Chef's friends will find zero people at the party and leave, regardless of the order in which they arrive.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
test=int(input())
for _ in range(test):
n=int(input())
ls=list(map(int,input().split()))
ls.sort()
s=0
for i in range(n):
if s>=ls[i]:
s=s+1
else:
break
print(s)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Petya is preparing for his birthday. He decided that there would be $n$ different dishes on the dinner table, numbered from $1$ to $n$. Since Petya doesn't like to cook, he wants to order these dishes in restaurants.
Unfortunately, all dishes are prepared in different restaurants and therefore Petya needs to pick up his orders from $n$ different places. To speed up this process, he wants to order courier delivery at some restaurants. Thus, for each dish, there are two options for Petya how he can get it: the dish will be delivered by a courier from the restaurant $i$, in this case the courier will arrive in $a_i$ minutes, Petya goes to the restaurant $i$ on his own and picks up the dish, he will spend $b_i$ minutes on this.
Each restaurant has its own couriers and they start delivering the order at the moment Petya leaves the house. In other words, all couriers work in parallel. Petya must visit all restaurants in which he has not chosen delivery, he does this consistently.
For example, if Petya wants to order $n = 4$ dishes and $a = [3, 7, 4, 5]$, and $b = [2, 1, 2, 4]$, then he can order delivery from the first and the fourth restaurant, and go to the second and third on your own. Then the courier of the first restaurant will bring the order in $3$ minutes, the courier of the fourth restaurant will bring the order in $5$ minutes, and Petya will pick up the remaining dishes in $1 + 2 = 3$ minutes. Thus, in $5$ minutes all the dishes will be at Petya's house.
Find the minimum time after which all the dishes can be at Petya's home.
-----Input-----
The first line contains one positive integer $t$ ($1 \le t \le 2 \cdot 10^5$) — the number of test cases. Then $t$ test cases follow.
Each test case begins with a line containing one integer $n$ ($1 \le n \le 2 \cdot 10^5$) — the number of dishes that Petya wants to order.
The second line of each test case contains $n$ integers $a_1 \ldots a_n$ ($1 \le a_i \le 10^9$) — the time of courier delivery of the dish with the number $i$.
The third line of each test case contains $n$ integers $b_1 \ldots b_n$ ($1 \le b_i \le 10^9$) — the time during which Petya will pick up the dish with the number $i$.
The sum of $n$ over all test cases does not exceed $2 \cdot 10^5$.
-----Output-----
For each test case output one integer — the minimum time after which all dishes can be at Petya's home.
-----Example-----
Input
4
4
3 7 4 5
2 1 2 4
4
1 2 3 4
3 3 3 3
2
1 2
10 10
2
10 10
1 2
Output
5
3
2
3
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
def check(M):
sm = 0
for i in range(n):
if a[i] > M:
sm += b[i]
return sm <= M
gans = []
for _ in range(int(input())):
n = int(input())
a = list(map(int, input().split()))
b = list(map(int, input().split()))
L = 0
R = max(a)
while R - L > 1:
M = (L + R) // 2
if check(M):
R = M
else:
L = M
gans.append(R)
print(*gans, sep='\n')
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Devu is a disastrous oracle: his predictions about various events of your life are horrifying. Instead of providing good luck, he "blesses" you with bad luck. The secret behind his wickedness is a hidden omen which is a string of length m. On your visit to him, you can ask a lot of questions about your future, each of which should be a string of length m. In total you asked him n such questions, denoted by strings s1, s2, ... , sn of length m each. Each of the question strings is composed of the characters 'a' and 'b' only.
Amount of bad luck this visit will bring you is equal to the length of longest common subsequence (LCS) of all the question strings and the hidden omen string. Of course, as the omen string is hidden, you are wondering what could be the least value of bad luck you can get.
Can you find out what could be the least bad luck you can get? Find it fast, before Devu tells you any bad omens.
-----Input-----
The first line of the input contains an integer T denoting the number of test cases. The description of T test cases follows.
First line of each test case contains a single integer n denoting number of strings.
For each of next n lines, the ith line contains the string si.
-----Output-----
For each test case, output a single integer corresponding to the answer of the problem.
-----Constraints-----
- All the strings (including the hidden omen) contain the characters 'a' and 'b' only.
Subtask #1: (40 points)
- 1 ≤ T, n, m ≤ 14
Subtask #2: (60 points)
- 1 ≤ T, n, m ≤ 100
-----Example-----
Input:3
2
ab
ba
2
aa
bb
3
aabb
abab
baab
Output:1
0
2
-----Explanation-----
In the first example, the minimum value of LCS of all the strings is 1, the string by oracle can be one of these {aa, ab, ba, bb}.
In the second example, whatever string oracle has does not matter, LCS will always be zero.
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):
n = int(input())
m = 100
for i in range(0, n):
str = input()
p = min(str.count("a",0,len(str)),str.count("b",0,len(str)))
if (m > p):
m = p
print(m)
t = t-1
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Ravi is very good student in mathematics and he also like Even numbers very much .
On the other hand his friend Jhon like Odd numbers . Both of them are preparing for IIT JEE Advance .One day they are solving a question together the question was Find the sum of first $n$ terms of the given series $1^2+2.2^2+3^2+2.4^2+5^2+2.6^2+...........$
If the sum is odd then Jhon will be happy and will solve 2 more questions,and Ravi will not attempt more questions. If sum is even Ravi will be happy and will solve 2 more questions and Jhon will not attempt more questions.
So Your task is to decide who will solve more questions.
-----Input:-----
- First line will contain $n$, number of terms in the given series.
-----Output:-----
Output single line "Ravi" if he solve more questions or "Jhon" if he solve more questions.
-----Constraints-----
- $1 \leq n \leq 100$
-----Sample Input:-----
2
3
-----Sample Output:-----
Jhon
Ravi
-----EXPLANATION:-----
In the first test cases sum of 2 terms is 9 (according to the given series) which is an odd number so Jhon will solve 2 more questions and Ravi will not attempt more questions.
In second test case sum of 3 terms is 18 (according to the given series) which is an even number according to the given series so Ravi will solve 3 more questions and Jhon will not attempt more questions.
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
while True:
try:
m=int(input())
n=int(m/2)
a=m-n
sum_even= int(2*(2*n*(n+1)*(2*n+1))/3)
sum_odd= int(((4*a*a*a)-a)/3)
result=sum_odd+sum_even
if result%2==0:
print('Ravi')
else:
print('Jhon')
except:
break;
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Gildong recently learned how to find the longest increasing subsequence (LIS) in $O(n\log{n})$ time for a sequence of length $n$. He wants to test himself if he can implement it correctly, but he couldn't find any online judges that would do it (even though there are actually many of them). So instead he's going to make a quiz for you about making permutations of $n$ distinct integers between $1$ and $n$, inclusive, to test his code with your output.
The quiz is as follows.
Gildong provides a string of length $n-1$, consisting of characters '<' and '>' only. The $i$-th (1-indexed) character is the comparison result between the $i$-th element and the $i+1$-st element of the sequence. If the $i$-th character of the string is '<', then the $i$-th element of the sequence is less than the $i+1$-st element. If the $i$-th character of the string is '>', then the $i$-th element of the sequence is greater than the $i+1$-st element.
He wants you to find two possible sequences (not necessarily distinct) consisting of $n$ distinct integers between $1$ and $n$, inclusive, each satisfying the comparison results, where the length of the LIS of the first sequence is minimum possible, and the length of the LIS of the second sequence is maximum possible.
-----Input-----
Each test contains one or more test cases. The first line contains the number of test cases $t$ ($1 \le t \le 10^4$).
Each test case contains exactly one line, consisting of an integer and a string consisting of characters '<' and '>' only. The integer is $n$ ($2 \le n \le 2 \cdot 10^5$), the length of the permutation you need to find. The string is the comparison results explained in the description. The length of the string is $n-1$.
It is guaranteed that the sum of all $n$ in all test cases doesn't exceed $2 \cdot 10^5$.
-----Output-----
For each test case, print two lines with $n$ integers each. The first line is the sequence with the minimum length of the LIS, and the second line is the sequence with the maximum length of the LIS. If there are multiple answers, print any one of them. Each sequence should contain all integers between $1$ and $n$, inclusive, and should satisfy the comparison results.
It can be shown that at least one answer always exists.
-----Example-----
Input
3
3 <<
7 >><>><
5 >>><
Output
1 2 3
1 2 3
5 4 3 7 2 1 6
4 3 1 7 5 2 6
4 3 2 1 5
5 4 2 1 3
-----Note-----
In the first case, $1$ $2$ $3$ is the only possible answer.
In the second case, the shortest length of the LIS is $2$, and the longest length of the LIS is $3$. In the example of the maximum LIS sequence, $4$ '$3$' $1$ $7$ '$5$' $2$ '$6$' can be one of the possible LIS.
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 compress(array):
array2 = sorted(set(array))
memo = {value : index for index, value in enumerate(array2)}
for i in range(len(array)):
array[i] = memo[array[i]] + 1
return array
t = int(input())
base = 10 ** 6
for _ in range(t):
n, b = list(map(str, input().split()))
n = int(n)
ans = [0] * n
now = base
ans[0] = base
for i in range(n - 1):
if b[i] == ">":
now -= base
ans[i + 1] = now
else:
now += 1
ans[i + 1] = now
print(*compress(ans))
now = base
ans[0] = base
for i in range(n - 1):
if b[i] == ">":
now -= 1
ans[i + 1] = now
else:
now += base
ans[i + 1] = now
print(*compress(ans))
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
We have a sequence A of N non-negative integers.
Compute the sum of \prod _{i = 1} ^N \dbinom{B_i}{A_i} over all sequences B of N non-negative integers whose sum is at most M, and print it modulo (10^9 + 7).
Here, \dbinom{B_i}{A_i}, the binomial coefficient, denotes the number of ways to choose A_i objects from B_i objects, and is 0 when B_i < A_i.
-----Constraints-----
- All values in input are integers.
- 1 \leq N \leq 2000
- 1 \leq M \leq 10^9
- 0 \leq A_i \leq 2000
-----Input-----
Input is given from Standard Input in the following format:
N M
A_1 A_2 \ldots A_N
-----Output-----
Print the sum of \prod _{i = 1} ^N \dbinom{B_i}{A_i}, modulo (10^9 + 7).
-----Sample Input-----
3 5
1 2 1
-----Sample Output-----
8
There are four sequences B such that \prod _{i = 1} ^N \dbinom{B_i}{A_i} is at least 1:
- B = \{1, 2, 1\}, where \prod _{i = 1} ^N \dbinom{B_i}{A_i} = \dbinom{1}{1} \times \dbinom{2}{2} \times \dbinom{1}{1} = 1;
- B = \{2, 2, 1\}, where \prod _{i = 1} ^N \dbinom{B_i}{A_i} = \dbinom{2}{1} \times \dbinom{2}{2} \times \dbinom{1}{1} = 2;
- B = \{1, 3, 1\}, where \prod _{i = 1} ^N \dbinom{B_i}{A_i} = \dbinom{1}{1} \times \dbinom{3}{2} \times \dbinom{1}{1} = 3;
- B = \{1, 2, 2\}, where \prod _{i = 1} ^N \dbinom{B_i}{A_i} = \dbinom{1}{1} \times \dbinom{2}{2} \times \dbinom{2}{1} = 2.
The sum of these is 1 + 2 + 3 + 2 = 8.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
from functools import reduce
def modpow(a, n, m):
if n == 0:
return 1
tmp = modpow(a, n // 2, m)
if n % 2 == 0:
return tmp * tmp % m
else:
return tmp * tmp * a % m
def modinv(a, m):
return modpow(a, m - 2, m)
n, m = [int(_) for _ in input().split(' ')]
s = sum([int(_) for _ in input().split(' ')])
M = 1_000_000_007
product = lambda x1, x2: x1 * x2 % M
print((reduce(product, list(range(m - s + 1, m + n + 1))) * modinv(reduce(product, list(range(1, s + n + 1))), M) % M))
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
You have three piles of candies: red, green and blue candies: the first pile contains only red candies and there are $r$ candies in it, the second pile contains only green candies and there are $g$ candies in it, the third pile contains only blue candies and there are $b$ candies in it.
Each day Tanya eats exactly two candies of different colors. She is free to choose the colors of eaten candies: the only restriction that she can't eat two candies of the same color in a day.
Find the maximal number of days Tanya can eat candies? Each day she needs to eat exactly two candies.
-----Input-----
The first line contains integer $t$ ($1 \le t \le 1000$) — the number of test cases in the input. Then $t$ test cases follow.
Each test case is given as a separate line of the input. It contains three integers $r$, $g$ and $b$ ($1 \le r, g, b \le 10^8$) — the number of red, green and blue candies, respectively.
-----Output-----
Print $t$ integers: the $i$-th printed integer is the answer on the $i$-th test case in the input.
-----Example-----
Input
6
1 1 1
1 2 1
4 1 1
7 4 10
8 1 4
8 2 8
Output
1
2
2
10
5
9
-----Note-----
In the first example, Tanya can eat candies for one day only. She can eat any pair of candies this day because all of them have different colors.
In the second example, Tanya can eat candies for two days. For example, she can eat red and green candies on the first day, and green and blue candies on the second day.
In the third example, Tanya can eat candies for two days. For example, she can eat red and green candies on the first day, and red and blue candies on the second day. Note, that two red candies will remain uneaten.
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())
for _ in range(n):
a, b, c = list(map(int, input().split()))
print(min((a+b+c)//2, a+b, a+c, b+c))
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Every Friday Chef and his N - 1 friends go for a party. At these parties, they play board games. This Friday, they are playing a game named "Boats! Boats! Boats!". In this game players have to transport cookies between Venice and Constantinople. Each player has a personal storage. The players are numbered from 1 to N, Chef is numbered 1. Rules for determining a winner are very difficult, therefore Chef asks you to write a program, which will determine who is a winner.
There are 6 types of cookies. For each cookie in the storage player gets 1 point. Also player gets additional points if he packs his cookies in some boxes as follows:
- A box containing 4 different types of cookies fetches 1 additional point.
- A box containing 5 different types of cookies fetches 2 additional points.
- A box containing 6 different types of cookies fetches 4 additional points.
Obviously a cookie can be put into a single box.
For each player, you know the number of cookies in his storage (denoted by c[i]), also the types of cookies in the storage given denoted by type[i][j].
Your task is to determine the winner of this game. Output "tie" if there are two or more players with same maximum score, "chef" if only Chef has a maximum score, winner's index in all other cases.
-----Input-----
The first line of input contains a single integer T denoting the number of test cases. This will be followed by T test cases.
The first line of each test case contains an integer N denoting the number of players.
The second line of each test case contains an integer c[i] denoting the number of cookies in the i-th storage, followed by c[i] space-separated integers type[i][j] which denote the type if j-th cookie in the storage i-th.
-----Output-----
For each test case, output a single line containing the answer as specified in the statement.
-----Constraints and Subtasks-----Subtask #1 : (20 points)
- 1 ≤ T ≤ 10
- 1 ≤ N ≤ 100
- 1 ≤ c[i] ≤ 100
- 1 ≤ type[i][j] ≤ 3
Subtask #2 : (80 points)
- 1 ≤ T ≤ 10
- 1 ≤ N ≤ 100
- 1 ≤ c[i] ≤ 100
- 1 ≤ type[i][j] ≤ 6
-----Example-----
Input:
3
2
6 1 2 3 4 5 6
9 3 3 3 4 4 4 5 5 5
2
5 2 3 4 5 6
7 1 1 2 2 3 3 4
3
4 1 1 2 3
4 1 2 2 3
4 1 2 3 3
Output:
chef
2
tie
-----Explanation-----
Example case 1.
Chef has total 6 cookie, so he gets 6 points for that. Also, he can put all his cookies (as they are all distinct) in a bag of size 6. It will fetch him additional 4 points. So, Chef's total points will be 10.
The second player has 9 cookies, he gets 9 points for that. Other than this, he can't create a bag with either 4, 5 or 6 distinct cookies. So, his final score is 9.
10 > 9 - Chef wins.
Example case 2.
Chef has 5 + 2 (a bag with 5 different cookies) = 7.
The second player has 7 + 1(a bag with 4 different cookies) = 8.
7 < 8 - the second player wins.
Example case 3.
Every player has 4 cookies and can't create any bag of sweets. So, it's a tie.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
# cook your code here
for _ in range(eval(input())):
n=eval(input())
ind=0
m=-1
for i in range(n):
l=[int(x) for x in input().split()]
sc=l[0]
for j in range(1,len(l)):
sc+=int(l[j]>=4)+int(l[j]>=5)+2*int(l[j]>=6)
if sc==m:
ind=-2
if sc>m :
m=sc
ind=i+1
if (ind==-2):
print("tie")
elif (ind==1) :
print("chef")
else:
print(ind)
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
The chef is trying to solve some series problems, Chef wants your help to code it. Chef has one number N. Help the chef to find N'th number in the series.
0, 1, 5, 14, 30, 55 …..
-----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 $N$.
-----Output:-----
For each test case, output as the pattern.
-----Constraints-----
- $1 \leq T \leq 10^4$
- $1 \leq N \leq 10^4$
-----Sample Input:-----
3
1
7
8
-----Sample Output:-----
0
91
140
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=int(input())
if n==1:
print("0")
else:
n=n-2
l=(n+1)*(2*n+3)*(n+2)/6
print(int(l))
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Oleg the bank client and Igor the analyst are arguing again. This time, they want to pick a gift as a present for their friend, ZS the coder. After a long thought, they decided that their friend loves to eat carrots the most and thus they want to pick the best carrot as their present.
There are n carrots arranged in a line. The i-th carrot from the left has juiciness a_{i}. Oleg thinks ZS loves juicy carrots whereas Igor thinks that he hates juicy carrots. Thus, Oleg would like to maximize the juiciness of the carrot they choose while Igor would like to minimize the juiciness of the carrot they choose.
To settle this issue, they decided to play a game again. Oleg and Igor take turns to play the game. In each turn, a player can choose a carrot from either end of the line, and eat it. The game ends when only one carrot remains. Oleg moves first. The last remaining carrot will be the carrot that they will give their friend, ZS.
Oleg is a sneaky bank client. When Igor goes to a restroom, he performs k moves before the start of the game. Each move is the same as above (eat a carrot from either end of the line). After Igor returns, they start the game with Oleg still going first.
Oleg wonders: for each k such that 0 ≤ k ≤ n - 1, what is the juiciness of the carrot they will give to ZS if he makes k extra moves beforehand and both players play optimally?
-----Input-----
The first line of input contains a single integer n (1 ≤ n ≤ 3·10^5) — the total number of carrots.
The next line contains n space-separated integers a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 10^9). Here a_{i} denotes the juiciness of the i-th carrot from the left of the line.
-----Output-----
Output n space-separated integers x_0, x_1, ..., x_{n} - 1. Here, x_{i} denotes the juiciness of the carrot the friends will present to ZS if k = i.
-----Examples-----
Input
4
1 2 3 5
Output
3 3 5 5
Input
5
1000000000 1000000000 1000000000 1000000000 1
Output
1000000000 1000000000 1000000000 1000000000 1000000000
-----Note-----
For the first example,
When k = 0, one possible optimal game is as follows: Oleg eats the carrot with juiciness 1. Igor eats the carrot with juiciness 5. Oleg eats the carrot with juiciness 2. The remaining carrot has juiciness 3.
When k = 1, one possible optimal play is as follows: Oleg eats the carrot with juiciness 1 beforehand. Oleg eats the carrot with juiciness 2. Igor eats the carrot with juiciness 5. The remaining carrot has juiciness 3.
When k = 2, one possible optimal play is as follows: Oleg eats the carrot with juiciness 1 beforehand. Oleg eats the carrot with juiciness 2 beforehand. Oleg eats the carrot with juiciness 3. The remaining carrot has juiciness 5.
When k = 3, one possible optimal play is as follows: Oleg eats the carrot with juiciness 1 beforehand. Oleg eats the carrot with juiciness 2 beforehand. Oleg eats the carrot with juiciness 3 beforehand. The remaining carrot has juiciness 5.
Thus, the answer is 3, 3, 5, 5.
For the second sample, Oleg can always eat the carrot with juiciness 1 since he always moves first. So, the remaining carrot will always have juiciness 1000000000.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
def evens(A):
n = len(A)
l = n//2-1; r = n//2
if len(A)%2 == 1: l+= 1
ans = [max(A[l], A[r])]
while r < n-1:
l-= 1; r+= 1
ans.append(max(ans[-1], A[l], A[r]))
return ans
def interleave(A, B):
q = []
for i in range(len(B)): q+= [A[i], B[i]]
if len(A) != len(B): q.append(A[-1])
return q
n = int(input())
A = list(map(int,input().split()))
M = [min(A[i],A[i+1]) for i in range(n-1)]
ansA = evens(A)
ansM = evens(M) if n>1 else []
if n%2 == 0: print(*interleave(ansA, ansM[1:]), max(A))
else: print(*interleave(ansM, ansA[1:]), max(A))
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
Raj is suffering from shot term memory loss so he is unable to remember his laptop password but he has a list of some string and the only thing that he remember about his password is alphanumeric and also that all the characters are unique.
Given a list of strings, your task is to find a valid password.
-----Input-----
Each String contains lower case alphabets and 0-9.
-----Output-----
print "Invalid"(without quotes) if password is not valid else print "Valid"(without quotes) and stop processing input after it.
-----Constraints-----
1<=length of string <=100
-----Example-----
Input:
absdbads
asdjenfef
tyerbet
abc564
Output:
Invalid
Invalid
Invalid
Valid
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
import collections
while True:
d = input().strip()
myCounter = collections.Counter(d)
flag = 1
for x in list(myCounter.keys()):
if myCounter[x] > 1:
flag = 0
break
isAlp = sum([myCounter[x] for x in list(myCounter.keys()) if x.isalnum()])
if flag and isAlp:
print("Valid")
break
else:
print("Invalid")
```
|
|
open-r1/verifiable-coding-problems-python-10k
|
Solve the following coding problem using the programming language python:
The USA Construction Operation (USACO) recently ordered Farmer John to arrange a row of $n$ haybale piles on the farm. The $i$-th pile contains $a_i$ haybales.
However, Farmer John has just left for vacation, leaving Bessie all on her own. Every day, Bessie the naughty cow can choose to move one haybale in any pile to an adjacent pile. Formally, in one day she can choose any two indices $i$ and $j$ ($1 \le i, j \le n$) such that $|i-j|=1$ and $a_i>0$ and apply $a_i = a_i - 1$, $a_j = a_j + 1$. She may also decide to not do anything on some days because she is lazy.
Bessie wants to maximize the number of haybales in pile $1$ (i.e. to maximize $a_1$), and she only has $d$ days to do so before Farmer John returns. Help her find the maximum number of haybales that may be in pile $1$ if she acts optimally!
-----Input-----
The input consists of multiple test cases. The first line contains an integer $t$ ($1 \le t \le 100$) — the number of test cases. Next $2t$ lines contain a description of test cases — two lines per test case.
The first line of each test case contains integers $n$ and $d$ ($1 \le n,d \le 100$) — the number of haybale piles and the number of days, respectively.
The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ($0 \le a_i \le 100$) — the number of haybales in each pile.
-----Output-----
For each test case, output one integer: the maximum number of haybales that may be in pile $1$ after $d$ days if Bessie acts optimally.
-----Example-----
Input
3
4 5
1 0 3 2
2 2
100 1
1 8
0
Output
3
101
0
-----Note-----
In the first test case of the sample, this is one possible way Bessie can end up with $3$ haybales in pile $1$: On day one, move a haybale from pile $3$ to pile $2$ On day two, move a haybale from pile $3$ to pile $2$ On day three, move a haybale from pile $2$ to pile $1$ On day four, move a haybale from pile $2$ to pile $1$ On day five, do nothing
In the second test case of the sample, Bessie can do nothing on the first day and move a haybale from pile $2$ to pile $1$ on the second day.
The input will be stdin and you should print your solution to stdout
Now solve the problem and return the code.
|
```python
import sys
#sys.stdin=open("data.txt")
input=sys.stdin.readline
mii=lambda:list(map(int,input().split()))
for _ in range(int(input())):
n,d=mii()
a=list(mii())
ans=0
for i in range(n):
while d>=i and a[i]:
a[i]-=1
ans+=1
d-=i
print(ans)
```
|
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