create word search path retrieval with comprehensive doctests

Author: maknelso

backtracking/word_search_path.py

@@ -0,0 +1,167 @@
+"""
+Author  : Nelson Mak
+Date    : April 5, 2026
+
+Task:
+Given an m x n grid of characters board and a string word,
+return the first valid path of coordinates found that matches 
+the word in the grid. If the word does not exist, return None.
+
+The word can be constructed from letters of sequentially adjacent cells,
+where adjacent cells are horizontally or vertically neighboring.
+The same letter cell may not be used more than once.
+
+Example:
+
+Matrix:
+---------
+|C|A|T|
+|X|Y|S|
+|A|B|C|
+---------
+
+Word: "CATS"
+
+Result: [(0, 0), (0, 1), (0, 2), (1, 2)]
+
+Implementation notes: 
+1. Use a backtracking (DFS) approach to explore all possible paths.
+2. At each cell, recursively check neighbors, in this question it's (Up, Down, Left, Right).
+3. Maintain a 'visited' set for each coordinate
+   to ensure cells are not reused within the same search branch.
+4. If a path matches the word, return the list of coordinates. 
+5. If a branch fails, 'backtrack' by removing the current cell from 
+   the visited set and the path list to allow for other potential matches.
+
+Similar leetcode question that returns a bool: https://leetcode.com/problems/word-search/
+"""
+
+
+def get_point_key(len_board: int, len_board_column: int, row: int, column: int) -> int:
+    """
+    Returns the hash key of matrix indexes.
+
+    >>> get_point_key(10, 20, 1, 0)
+    200
+    """
+
+    return len_board * len_board_column * row + column
+
+
+def get_word_path(
+    board: list[list[str]],
+    word: str,
+    row: int,
+    column: int,
+    word_index: int,
+    visited_points_set: set[int],
+    current_path: list[tuple[int, int]],
+) -> list[tuple[int, int]] | None:
+    """
+    Return the coordinate path if it's possible to find the word in the grid.
+    """
+
+    if board[row][column] != word[word_index]:
+        return None
+
+    # Track current progress
+    new_path = current_path + [(row, column)]
+
+    # Base case
+    if word_index == len(word) - 1:
+        return new_path
+
+    traverts_directions = [(0, 1), (0, -1), (-1, 0), (1, 0)]
+    len_board = len(board)
+    len_board_column = len(board[0])
+    for direction in traverts_directions:
+        next_i = row + direction[0]
+        next_j = column + direction[1]
+
+        if not (0 <= next_i < len_board and 0 <= next_j < len_board_column):
+            continue
+
+        key = get_point_key(len_board, len_board_column, next_i, next_j)
+        if key in visited_points_set:
+            continue
+            
+        visited_points_set.add(key)
+        result = get_word_path(
+            board, word, next_i, next_j, word_index + 1, visited_points_set, new_path
+        )
+        
+        if result is not None:
+            return result
+        
+        # Backtrack: remove key to try other paths
+        visited_points_set.remove(key)
+
+    return None
+
+
+def word_search_path(board: list[list[str]], word: str) -> list[tuple[int, int]] | None:
+    """
+    >>> # 1. Word is found case
+    >>> word_search_path([["C","A","T"],["X","Y","S"],["A","B","C"]], "CATS")
+    [(0, 0), (0, 1), (0, 2), (1, 2)]
+
+    >>> # 2. Word is not found case
+    >>> word_search_path([["A","B"],["C","D"]], "ABCD") is None
+    True
+
+    >>> #  3. Word is a single char
+    >>> word_search_path([["A"]], "A")
+    [(0, 0)]
+
+    >>> # 4. Invalid board error (empty list)
+    >>> word_search_path([], "CAT")
+    Traceback (most recent call last):
+        ...
+    ValueError: The board should be a non empty matrix of single chars strings.
+
+    >>> # 5. Invalid word error
+    >>> word_search_path([["A"]], 123)
+    Traceback (most recent call last):
+        ...
+    ValueError: The word parameter should be a string of length greater than 0.
+    """
+    # Validation
+    board_error_message = (
+        "The board should be a non empty matrix of single chars strings."
+    )
+
+    # Validate board input
+    if not isinstance(board, list) or len(board) == 0:
+        raise ValueError(board_error_message)
+    
+    for row in board:
+        if not isinstance(row, list) or len(row) == 0:
+            raise ValueError(board_error_message)
+        for item in row:
+            if not isinstance(item, str) or len(item) != 1:
+                raise ValueError(board_error_message)
+
+    # Validate word input
+    if not isinstance(word, str) or len(word) == 0:
+        raise ValueError(
+            "The word parameter should be a string of length greater than 0."
+        )
+
+    rows = len(board)
+    cols = len(board[0])
+    # Main entry point
+    for r in range(rows):
+        for c in range(cols):
+            # Optimization: only trigger recursion if first char in board matches with first char in word input
+            if board[r][c] == word[0]:
+                key = get_point_key(rows, cols, r, c)
+                path_result = get_word_path(board, word, r, c, 0, {key}, [])
+                if path_result is not None:
+                    return path_result
+
+    return None
+
+
+if __name__ == "__main__":
+    import doctest
+    doctest.testmod()