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 +1,100 @@
+"""
+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)

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 +1,100 @@
+"""
+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)

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 +1,100 @@
+"""
+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)

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 +1,100 @@
+"""
+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)

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 +1,100 @@
+"""
+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)

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 +1,100 @@
+"""
+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)

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 +1,100 @@
+"""
+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)

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 +1,100 @@
+"""
+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)