Add word ladder algorithm in backtracking

DIRECTORY.md

@@ -22,6 +22,7 @@
   * [Rat In Maze](backtracking/rat_in_maze.py)
   * [Sudoku](backtracking/sudoku.py)
   * [Sum Of Subsets](backtracking/sum_of_subsets.py)
+  * [Word Ladder](backtracking/word_ladder.py)
   * [Word Search](backtracking/word_search.py)
 
 ## Bit Manipulation

backtracking/word_ladder.py

@@ -0,0 +1,76 @@
+"""
+Word Ladder is a classic problem in computer science.
+The problem is to transform a start word into an end word
+by changing one letter at a time.
+Each intermediate word must be a valid word from a given list of words.
+The goal is to find a transformation sequence
+from the start word to the end word.
+
+Wikipedia: https://en.wikipedia.org/wiki/Word_ladder
+"""
+
+
+def word_ladder_backtrack(
+    begin_word: str, end_word: str, word_list: list[str]
+) -> list[str]:
+    """
+    Solve the Word Ladder problem using Backtracking and return
+    the list of transformations from begin_word to end_word.
+
+    Parameters:
+    begin_word (str): The word from which the transformation starts.
+    end_word (str): The target word for transformation.
+    word_list (list[str]): The list of valid words for transformation.
+
+    Returns:
+    list[str]: The list of transformations from begin_word to end_word.
+               Returns an empty list if there is no valid transformation.
+
+    Example:
+    >>> word_ladder_backtrack("hit", "cog", ["hot", "dot", "dog", "lot", "log", "cog"])
+    ['hit', 'hot', 'dot', 'lot', 'log', 'cog']
+
+    >>> word_ladder_backtrack("hit", "cog", ["hot", "dot", "dog", "lot", "log"])
+    []
+
+    >>> word_ladder_backtrack("lead", "gold", ["load", "goad", "gold", "lead", "lord"])
+    ['lead', 'lead', 'load', 'goad', 'gold']
+
+    >>> word_ladder_backtrack("game", "code", ["came", "cage", "code", "cade", "gave"])
+    ['game', 'came', 'cade', 'code']
+    """
+
+    # Step 1: Convert the word_list to a set for faster lookup
+    word_set = set(word_list)
+
+    # Step 2: If end_word is not in the word_list, return an empty list
+    if end_word not in word_set:
+        return []
+
+    # Step 3: Backtracking function to find the word ladder
+    def backtrack(current_word, path):
+        # Base case: If the current word is the end word, return the path
+        if current_word == end_word:
+            return path
+
+        # Try all possible single-letter transformations
+        for i in range(len(current_word)):
+            for c in "abcdefghijklmnopqrstuvwxyz":  # Try changing each letter
+                transformed_word = current_word[:i] + c + current_word[i + 1 :]
+
+                # If the transformed word is valid and has not been visited
+                if transformed_word in word_set:
+                    # Remove it from the set to avoid revisiting
+                    word_set.remove(transformed_word)
+                    # Recur with the new word added to the path
+                    result = backtrack(transformed_word, [*path, transformed_word])
+                    if result:  # If we found a valid result, return it
+                        return result
+                    # Add it back to the set after exploring this path (backtrack)
+                    word_set.add(transformed_word)
+
+        # If no valid path is found, return an empty list
+        return []
+
+    # Step 4: Start backtracking from the begin_word
+    return backtrack(begin_word, [begin_word])