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def levenshtein_with_wildcards(str1, str2, wildcard='?', verbose=False):
"""
Calculate the Levenshtein distance between two strings with support for wildcards.
Args:
str1 (str): The first string.
str2 (str): The second string.
wildcard (str, optional): The wildcard character. Defaults to '?'.
verbose (bool, optional): If True, prints the DP matrix and explains the process.
Returns:
int: The Levenshtein distance between the two strings.
list: If verbose=True, also returns a list of operations performed.
"""
m, n = len(str1), len(str2)
# Create a matrix of size (m+1) x (n+1)
dp = [[0] * (n + 1) for _ in range(m + 1)]
# Initialize the first row and column
for i in range(m + 1):
dp[i][0] = i
for j in range(n + 1):
dp[0][j] = j
# Fill the dp matrix
for i in range(1, m + 1):
for j in range(1, n + 1):
# If either character is a wildcard, treat it as a match (cost = 0)
if str1[i - 1] == wildcard or str2[j - 1] == wildcard:
dp[i][j] = dp[i - 1][j - 1] # No cost for wildcard matches
else:
cost = 0 if str1[i - 1] == str2[j - 1] else 1
dp[i][j] = min(
dp[i - 1][j] + 1, # deletion
dp[i][j - 1] + 1, # insertion
dp[i - 1][j - 1] + cost # substitution
)
if verbose:
operations = explain_match(str1, str2, dp, wildcard)
return dp[m][n], operations
return dp[m][n]
def explain_match(str1, str2, dp, wildcard='?'):
"""
Traces the optimal alignment path and explains each step of the matching process.
Args:
str1 (str): The first string.
str2 (str): The second string.
dp (list): The dynamic programming matrix.
wildcard (str, optional): The wildcard character. Defaults to '?'.
Returns:
list: A list of explanation strings for each operation performed.
"""
m, n = len(str1), len(str2)
operations = []
# Find the optimal path
i, j = m, n
path = []
while i > 0 or j > 0:
path.append((i, j))
if i == 0:
j -= 1
elif j == 0:
i -= 1
else:
substitution_cost = dp[i-1][j-1]
deletion_cost = dp[i-1][j]
insertion_cost = dp[i][j-1]
min_cost = min(substitution_cost, deletion_cost, insertion_cost)
if min_cost == substitution_cost:
i -= 1
j -= 1
elif min_cost == deletion_cost:
i -= 1
else:
j -= 1
path.append((0, 0))
path.reverse()
# Generate explanations for each step
for idx in range(1, len(path)):
prev_i, prev_j = path[idx-1]
curr_i, curr_j = path[idx]
# Diagonal move (match or substitution)
if curr_i > prev_i and curr_j > prev_j:
char1 = str1[curr_i-1]
char2 = str2[curr_j-1]
if char1 == wildcard or char2 == wildcard:
wildcard_char = char1 if char1 == wildcard else char2
match_char = char2 if char1 == wildcard else char1
operations.append(f"Wildcard match: '{wildcard_char}' matches any character, here '{match_char}'")
elif char1 == char2:
operations.append(f"Match: '{char1}' matches '{char2}'")
else:
operations.append(f"Substitution: Replace '{char1}' with '{char2}'")
# Horizontal move (insertion)
elif curr_i == prev_i and curr_j > prev_j:
operations.append(f"Insertion: Insert '{str2[curr_j-1]}'")
# Vertical move (deletion)
elif curr_i > prev_i and curr_j == prev_j:
operations.append(f"Deletion: Delete '{str1[curr_i-1]}'")
return operations
def print_match_summary(str1, str2, wildcard='?'):
"""
Prints a summary of the match between two strings, highlighting wildcards.
Args:
str1 (str): The first string.
str2 (str): The second string.
wildcard (str, optional): The wildcard character. Defaults to '?'.
"""
distance, operations = levenshtein_with_wildcards(str1, str2, wildcard, verbose=True)
print(f"Comparing '{str1}' and '{str2}' (wildcard: '{wildcard}')")
print(f"Edit distance: {distance}")
print("\nMatch process:")
for i, op in enumerate(operations):
print(f"Step {i+1}: {op}")
# Visual representation
alignment = []
i, j = 0, 0
aligned_str1 = ""
aligned_str2 = ""
match_indicators = ""
for op in operations:
if "match" in op or "Match" in op or "Substitution" in op:
aligned_str1 += str1[i]
aligned_str2 += str2[j]
if "Wildcard" in op:
match_indicators += "*" # Wildcard match
elif "Match" in op:
match_indicators += "|" # Exact match
else:
match_indicators += "X" # Substitution
i += 1
j += 1
elif "Insertion" in op:
aligned_str1 += "-"
aligned_str2 += str2[j]
match_indicators += " "
j += 1
elif "Deletion" in op:
aligned_str1 += str1[i]
aligned_str2 += "-"
match_indicators += " "
i += 1
print("\nAlignment:")
print(aligned_str1)
print(match_indicators)
print(aligned_str2)
print("\nLegend:")
print("| = exact match, * = wildcard match, X = substitution, - = gap (insertion/deletion)")
# Summary of wildcard matches
wildcard_matches = [op for op in operations if "Wildcard" in op]
if wildcard_matches:
print("\nWildcard matches:")
for match in wildcard_matches:
print(f"- {match}")
return distance, operations
# Example usage
if __name__ == "__main__":
# Basic examples
print_match_summary("hello", "hello") # 0 (identical strings)
print_match_summary("hello", "hallo") # 1 (one substitution)
print_match_summary("he?lo", "hello") # 0 (wildcard matches 'l')
print_match_summary("he?lo", "hallo") # 0 (wildcard matches 'a')
print_match_summary("h?llo", "hello") # 0 (wildcard matches 'e')
print_match_summary("h?llo", "hillo") # 0 (wildcard matches 'i')
print_match_summary("c?t", "cat") # 0 (wildcard matches 'a')
print_match_summary("c?t", "cut") # 0 (wildcard matches 'u')
print_match_summary("w?rd", "word") # 0 (wildcard matches 'o')
print_match_summary("d?g", "dog") # 0 (wildcard matches 'o') |