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Pattern Matching with Wildcards

What is Pattern Matching with Wildcards?​

Pattern Matching with Wildcards is an advanced search algorithm that extends traditional pattern matching by allowing wildcard characters ('*') to represent any sequence of characters (including empty sequence) during the search process. This approach is useful for flexible and efficient text searching in various applications.

Algorithm Steps​

  1. Initialization:

    • Prepare the pattern with wildcards and the text to search within.
  2. Pattern Matching:

    • Iterate through the pattern and text character by character.
    • Handle wildcard characters ('*') to match any sequence of characters or positions.
  3. Matching Strategy:

    • Use dynamic programming or a recursive approach to efficiently handle wildcard expansion and pattern matching.

Complexity Analysis​

  • Time Complexity: Depends on the specific implementation. It can range from O(m×n))O(m \times n) ) to O(m+n)O(m + n), where mm is the length of the pattern and nn is the length of the text.
  • Space Complexity: O(m×n))O(m \times n) ) in worst cases due to the potential recursion depth or dynamic programming table.

Example​

Given a pattern with wildcards and a text:


pattern = "acd"
text = "abcd"

Using Pattern Matching with Wildcards:

  • Match the pattern against the text, considering '*' as a wildcard that matches any sequence of characters.

Implementation​

def pattern_matching_with_wildcards(pattern, text):
# Dynamic programming approach
m, n = len(pattern), len(text)
dp = [[False] * (n + 1) for _ in range(m + 1)]
dp[0][0] = True

# Handle initial wildcard characters
for i in range(1, m + 1):
if pattern[i - 1] == '*':
dp[i][0] = dp[i - 1][0]

# Fill dp table
for i in range(1, m + 1):
for j in range(1, n + 1):
if pattern[i - 1] == '*':
dp[i][j] = dp[i - 1][j] or dp[i][j - 1]
elif pattern[i - 1] == '?' or pattern[i - 1] == text[j - 1]:
dp[i][j] = dp[i - 1][j - 1]

return dp[m][n]

# Example usage:
pattern = "a*c*d"
text = "abcd"

if pattern_matching_with_wildcards(pattern, text):
print(f"Pattern '{pattern}' matches text '{text}'")
else:
print(f"Pattern '{pattern}' does not match text '{text}'")

Conclusion

Pattern Matching with Wildcards is a versatile algorithm that allows for flexible matching of patterns containing wildcard characters ('*') against text sequences. It is useful in various applications such as text processing, file search utilities, and more where flexible and efficient pattern matching is required.