is_match algorithm

dynamic_programming/is_match.py

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+"""You are given a string s and a pattern p. Write a function to determine if the pattern p matches the entire string s.
+The pattern p may contain the special characters:"""
+
+"""  ? which matches any single character.
+     * which matches any sequence of characters (including the empty sequence).
+ Return True if p matches the entire string s; otherwise, return False."""
+
+"""Example :
+Input: s = "aa", p = "a"
+Output: False
+Explanation: The pattern "a" does not match the entire string "aa"."""
+
+
+def is_match(s, p):
+    m, n = len(s), len(p)
+
+    # Initialize a DP table where dp[i][j] represents whether s[:i] matches p[:j]
+    dp = [[False] * (n + 1) for _ in range(m + 1)]
+    dp[0][0] = True  # Empty pattern matches empty string
+
+    # Fill the first row (when s is empty)
+    for j in range(1, n + 1):
+        if p[j - 1] == "*":
+            dp[0][j] = dp[0][j - 1]  # '*' can match an empty sequence
+
+    # Fill the DP table
+    for i in range(1, m + 1):
+        for j in range(1, n + 1):
+            if p[j - 1] == "*":
+                # '*' can match zero or more of the previous characters
+                dp[i][j] = dp[i - 1][j] or dp[i][j - 1]
+            elif p[j - 1] == "?" or s[i - 1] == p[j - 1]:
+                # '?' matches any single character, or if characters match exactly
+                dp[i][j] = dp[i - 1][j - 1]
+
+    # The result is whether the entire string s matches the entire pattern p
+    return dp[m][n]
+
+
+# Take user input for string and pattern
+s = input("Enter the string: ")
+p = input("Enter the pattern: ")
+
+# Print the result
+print("Does the pattern match the string?", is_match(s, p))