diff --git a/DIRECTORY.md b/DIRECTORY.md index 56ab8377f..cdbbac684 100644 --- a/DIRECTORY.md +++ b/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 diff --git a/backtracking/word_ladder.py b/backtracking/word_ladder.py new file mode 100644 index 000000000..7d9fd00f6 --- /dev/null +++ b/backtracking/word_ladder.py @@ -0,0 +1,100 @@ +""" +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 +""" + +import string + + +def backtrack( + current_word: str, path: list[str], end_word: str, word_set: set[str] +) -> list[str]: + """ + Helper function to perform backtracking to find the transformation + from the current_word to the end_word. + + Parameters: + current_word (str): The current word in the transformation sequence. + path (list[str]): The list of transformations from begin_word to current_word. + end_word (str): The target word for transformation. + word_set (set[str]): The set 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 from current_word to end_word. + + Example: + >>> backtrack("hit", ["hit"], "cog", {"hot", "dot", "dog", "lot", "log", "cog"}) + ['hit', 'hot', 'dot', 'lot', 'log', 'cog'] + + >>> backtrack("hit", ["hit"], "cog", {"hot", "dot", "dog", "lot", "log"}) + [] + + >>> backtrack("lead", ["lead"], "gold", {"load", "goad", "gold", "lead", "lord"}) + ['lead', 'lead', 'load', 'goad', 'gold'] + + >>> backtrack("game", ["game"], "code", {"came", "cage", "code", "cade", "gave"}) + ['game', 'came', 'cade', 'code'] + """ + + # 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 string.ascii_lowercase: # Try changing each letter + transformed_word = current_word[:i] + c + current_word[i + 1 :] + if transformed_word in word_set: + word_set.remove(transformed_word) + # Recur with the new word added to the path + result = backtrack( + transformed_word, [*path, transformed_word], end_word, word_set + ) + if result: # valid transformation found + return result + word_set.add(transformed_word) # backtrack + + return [] # No valid transformation found + + +def word_ladder(begin_word: str, end_word: str, word_set: set[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("hit", "cog", ["hot", "dot", "dog", "lot", "log", "cog"]) + ['hit', 'hot', 'dot', 'lot', 'log', 'cog'] + + >>> word_ladder("hit", "cog", ["hot", "dot", "dog", "lot", "log"]) + [] + + >>> word_ladder("lead", "gold", ["load", "goad", "gold", "lead", "lord"]) + ['lead', 'lead', 'load', 'goad', 'gold'] + + >>> word_ladder("game", "code", ["came", "cage", "code", "cade", "gave"]) + ['game', 'came', 'cade', 'code'] + """ + + if end_word not in word_set: # no valid transformation possible + return [] + + # Perform backtracking starting from the begin_word + return backtrack(begin_word, [begin_word], end_word, word_set)