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word_ladder.py
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word_ladder.py
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"""
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)