Create Palindrome_partitioning.py

backtracking/Palindrome_partitioning.py

@@ -0,0 +1,55 @@
+def is_palindrome(s: str) -> bool:
+    """
+    Helper function to check if a given string is a palindrome.
+
+    Args:
+    s (str): The string to check.
+
+    Returns:
+    bool: True if s is a palindrome, False otherwise.
+    """
+    return s == s[::-1]
+
+
+def backtrack(start: int, path: list, result: list, s: str):
+    """
+    Backtracking function to find all palindrome partitions of the string s.
+
+    Args:
+    start (int): Starting index of the substring to consider.
+    path (list): The current path (partition) being constructed.
+    result (list): The final list of all valid palindrome partitions.
+    s (str): The input string.
+    """
+    # If we've reached the end of the string, add the current path to the result
+    if start == len(s):
+        result.append(path[:])  # Add a copy of the current path to the result
+        return
+
+    # Try every possible partition starting from 'start'
+    for end in range(start + 1, len(s) + 1):
+        # If the current substring is a palindrome, we can proceed
+        if is_palindrome(s[start:end]):
+            path.append(s[start:end])  # Choose the current palindrome substring
+            backtrack(end, path, result, s)  # Explore further partitions
+            path.pop()  # Backtrack and remove the last chosen partition
+
+
+def partition(s: str) -> list:
+    """
+    Main function to find all palindrome partitions of a string.
+
+    Args:
+    s (str): The input string.
+
+    Returns:
+    list: A list of lists containing all valid palindrome partitions.
+    """
+    result = []  # List to store all partitions
+    backtrack(0, [], result, s)  # Start the backtracking process
+    return result
+
+
+# Example usage:
+s = "aab"
+print(partition(s))  # Output: [['a', 'a', 'b'], ['aa', 'b']]