Match a pattern and String using backtracking (#9861)

* Fix: Issue 9588

* Fix: Issue 9588

* [pre-commit.ci] auto fixes from pre-commit.com hooks

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* Fix: Issue 9588

* Fix: Issue #9588

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Fix: Issue #9588

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Fix: Issue #9588

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* fix: issue #9793

* fix: issue #9793

* fix: issue #9588

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* fix: issue #9844

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* fix: issue #9844

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* fix: issue #9844

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* fix: issue #9844

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

---------

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>

backtracking/match_word_pattern.py

@@ -0,0 +1,61 @@
+def match_word_pattern(pattern: str, input_string: str) -> bool:
+    """
+    Determine if a given pattern matches a string using backtracking.
+
+    pattern: The pattern to match.
+    input_string: The string to match against the pattern.
+    return: True if the pattern matches the string, False otherwise.
+
+    >>> match_word_pattern("aba", "GraphTreesGraph")
+    True
+
+    >>> match_word_pattern("xyx", "PythonRubyPython")
+    True
+
+    >>> match_word_pattern("GG", "PythonJavaPython")
+    False
+    """
+
+    def backtrack(pattern_index: int, str_index: int) -> bool:
+        """
+        >>> backtrack(0, 0)
+        True
+
+        >>> backtrack(0, 1)
+        True
+
+        >>> backtrack(0, 4)
+        False
+        """
+        if pattern_index == len(pattern) and str_index == len(input_string):
+            return True
+        if pattern_index == len(pattern) or str_index == len(input_string):
+            return False
+        char = pattern[pattern_index]
+        if char in pattern_map:
+            mapped_str = pattern_map[char]
+            if input_string.startswith(mapped_str, str_index):
+                return backtrack(pattern_index + 1, str_index + len(mapped_str))
+            else:
+                return False
+        for end in range(str_index + 1, len(input_string) + 1):
+            substr = input_string[str_index:end]
+            if substr in str_map:
+                continue
+            pattern_map[char] = substr
+            str_map[substr] = char
+            if backtrack(pattern_index + 1, end):
+                return True
+            del pattern_map[char]
+            del str_map[substr]
+        return False
+
+    pattern_map: dict[str, str] = {}
+    str_map: dict[str, str] = {}
+    return backtrack(0, 0)
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()