dist.py

def levenshtein_with_wildcard(str1, str2, wildcard_offsets_str1=None, wildcard_offsets_str2=None, verbose=False):
    """
    Calculate the Levenshtein distance between two strings with support for wildcards at specific positions.
    
    Args:
        str1 (str): The first string.
        str2 (str): The second string.
        wildcard_offsets_str1 (iterable, optional): Indices in str1 that are wildcards. Defaults to None.
        wildcard_offsets_str2 (iterable, optional): Indices in str2 that are wildcards. Defaults to None.
        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.
    """
    # Initialize empty sets if None
    wildcard_offsets_str1 = set(wildcard_offsets_str1 or [])
    wildcard_offsets_str2 = set(wildcard_offsets_str2 or [])
    
    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):
            # Check if either position is a wildcard
            is_str1_wildcard = (i - 1) in wildcard_offsets_str1
            is_str2_wildcard = (j - 1) in wildcard_offsets_str2
            
            # If either position is a wildcard, treat it as a match (cost = 0)
            if is_str1_wildcard or is_str2_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_offsets_str1, wildcard_offsets_str2)
        return dp[m][n], operations
    
    return dp[m][n]

def explain_match(str1, str2, dp, wildcard_offsets_str1, wildcard_offsets_str2):
    """
    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_offsets_str1 (set): Indices in str1 that are wildcards.
        wildcard_offsets_str2 (set): Indices in str2 that are wildcards.
        
    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_idx = curr_i-1
            char2_idx = curr_j-1
            char1 = str1[char1_idx]
            char2 = str2[char2_idx]
            
            is_str1_wildcard = char1_idx in wildcard_offsets_str1
            is_str2_wildcard = char2_idx in wildcard_offsets_str2
            
            if is_str1_wildcard and is_str2_wildcard:
                operations.append(f"Double wildcard: Position {char1_idx} in str1 and position {char2_idx} in str2 are both wildcards")
            elif is_str1_wildcard:
                operations.append(f"Wildcard match: Position {char1_idx} in str1 is a wildcard, matches '{char2}' at position {char2_idx} in str2")
            elif is_str2_wildcard:
                operations.append(f"Wildcard match: Position {char2_idx} in str2 is a wildcard, matches '{char1}' at position {char1_idx} in str1")
            elif char1 == char2:
                operations.append(f"Match: '{char1}' at position {char1_idx} matches '{char2}' at position {char2_idx}")
            else:
                operations.append(f"Substitution: Replace '{char1}' at position {char1_idx} with '{char2}' at position {char2_idx}")
        
        # Horizontal move (insertion)
        elif curr_i == prev_i and curr_j > prev_j:
            char_idx = curr_j-1
            operations.append(f"Insertion: Insert '{str2[char_idx]}' at position {char_idx} in str2")
        
        # Vertical move (deletion)
        elif curr_i > prev_i and curr_j == prev_j:
            char_idx = curr_i-1
            operations.append(f"Deletion: Delete '{str1[char_idx]}' at position {char_idx} in str1")
    
    return operations

def print_match_summary(str1, str2, wildcard_offsets_str1=None, wildcard_offsets_str2=None):
    """
    Prints a summary of the match between two strings, highlighting wildcards by their offsets.
    
    Args:
        str1 (str): The first string.
        str2 (str): The second string.
        wildcard_offsets_str1 (iterable, optional): Indices in str1 that are wildcards. Defaults to None.
        wildcard_offsets_str2 (iterable, optional): Indices in str2 that are wildcards. Defaults to None.
    """
    # Initialize empty lists if None
    wildcard_offsets_str1 = set(wildcard_offsets_str1 or [])
    wildcard_offsets_str2 = set(wildcard_offsets_str2 or [])
    
    distance, operations = levenshtein_with_wildcard(
        str1, str2, wildcard_offsets_str1, wildcard_offsets_str2, verbose=True
    )
    
    # Create visual representations of the strings with wildcard markers
    str1_visual = type(str1)()
    for i, char in enumerate(str1):
        if i in wildcard_offsets_str1:
            str1_visual += f"[{char}]"  # Mark wildcards with brackets
        else:
            str1_visual += char
    
    str2_visual = type(str2)()
    for i, char in enumerate(str2):
        if i in wildcard_offsets_str2:
            str2_visual += f"[{char}]"  # Mark wildcards with brackets
        else:
            str2_visual += char
    
    print(f"Comparing '{str1_visual}' and '{str2_visual}'")
    print(f"Wildcards in str1: {sorted(wildcard_offsets_str1)}")
    print(f"Wildcards in str2: {sorted(wildcard_offsets_str2)}")
    print(f"Edit distance: {distance}")
    print("\nMatch process:")
    
    for i, op in enumerate(operations):
        print(f"Step {i+1}: {op}")
    
    # Visual representation of the alignment
    i, j = 0, 0
    aligned_str1 = ""
    aligned_str2 = ""
    match_indicators = ""
    
    for op in operations:
        if "Match:" in op or "Substitution:" in op or "Wildcard match:" in op or "Double wildcard:" in op:
            is_str1_wildcard = i in wildcard_offsets_str1
            is_str2_wildcard = j in wildcard_offsets_str2
            
            # Add brackets around wildcards
            if is_str1_wildcard:
                aligned_str1 += f"[{str1[i]}]"
            else:
                aligned_str1 += str1[i]
                
            if is_str2_wildcard:
                aligned_str2 += f"[{str2[j]}]"
            else:
                aligned_str2 += str2[j]
            
            # Determine match indicator
            if "Wildcard match:" in op or "Double 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 += "-"
            
            if j in wildcard_offsets_str2:
                aligned_str2 += f"[{str2[j]}]"
            else:
                aligned_str2 += str2[j]
                
            match_indicators += " "
            j += 1
        elif "Deletion:" in op:
            if i in wildcard_offsets_str1:
                aligned_str1 += f"[{str1[i]}]"
            else:
                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), [c] = wildcard position")
    
    # Summary of wildcard matches
    wildcard_matches = [op for op in operations if "Wildcard match:" in op or "Double 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__":
    # Example 1: "hello" vs "hello" with no wildcards
    print_match_summary("hello", "hello")
    
    # Example 2: "hello" vs "hallo" with no wildcards - expect distance of 1
    print_match_summary("hello", "hallo")
    
    # Example 3: "hello" with 3rd position (index 2) as wildcard vs "hallo" - expect distance of 0
    print_match_summary("hello", "hallo", wildcard_offsets_str1=[2])
    
    # Example 4: "hello" vs "hillo" with 2nd position (index 1) as wildcard in str2 - expect distance of 0
    print_match_summary("hello", "hillo", wildcard_offsets_str2=[1])
    
    # Example 5: Multiple wildcards in str1
    print_match_summary("hello", "haxyz", wildcard_offsets_str1=[2, 3, 4])
    
    # Example 6: Wildcards in both strings at different positions
    print_match_summary("hello", "howdy", wildcard_offsets_str1=[2], wildcard_offsets_str2=[3, 4])