Add backtrack word search in matrix (#8005)

* add backtracking word search

* updating DIRECTORY.md

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* review notes fixes

* additional fixes

* add tests

* small cleanup

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* small cleanup 2

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* Update backtracking/word_search.py

Co-authored-by: Christian Clauss <cclauss@me.com>

* Update backtracking/word_search.py

Co-authored-by: Christian Clauss <cclauss@me.com>

* Update backtracking/word_search.py

Co-authored-by: Christian Clauss <cclauss@me.com>

* Update backtracking/word_search.py

Co-authored-by: Christian Clauss <cclauss@me.com>

Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Christian Clauss <cclauss@me.com>

DIRECTORY.md

@@ -33,6 +33,7 @@
   * [Rat In Maze](backtracking/rat_in_maze.py)
   * [Sudoku](backtracking/sudoku.py)
   * [Sum Of Subsets](backtracking/sum_of_subsets.py)
+  * [Word Search](backtracking/word_search.py)
 
 ## Bit Manipulation
   * [Binary And Operator](bit_manipulation/binary_and_operator.py)

backtracking/word_search.py

@@ -0,0 +1,160 @@
+"""
+Author  : Alexander Pantyukhin
+Date    : November 24, 2022
+
+Task:
+Given an m x n grid of characters board and a string word,
+return true if word exists in the grid.
+
+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:
+---------
+|A|B|C|E|
+|S|F|C|S|
+|A|D|E|E|
+---------
+
+Word:
+"ABCCED"
+
+Result:
+True
+
+Implementation notes: Use backtracking approach.
+At each point, check all neighbors to try to find the next letter of the word.
+
+leetcode: https://leetcode.com/problems/word-search/
+
+"""
+
+
+def word_exists(board: list[list[str]], word: str) -> bool:
+    """
+    >>> word_exists([["A","B","C","E"],["S","F","C","S"],["A","D","E","E"]], "ABCCED")
+    True
+    >>> word_exists([["A","B","C","E"],["S","F","C","S"],["A","D","E","E"]], "SEE")
+    True
+    >>> word_exists([["A","B","C","E"],["S","F","C","S"],["A","D","E","E"]], "ABCB")
+    False
+    >>> word_exists([["A"]], "A")
+    True
+    >>> word_exists([["A","A","A","A","A","A"],
+    ...              ["A","A","A","A","A","A"],
+    ...              ["A","A","A","A","A","A"],
+    ...              ["A","A","A","A","A","A"],
+    ...              ["A","A","A","A","A","B"],
+    ...              ["A","A","A","A","B","A"]],
+    ...             "AAAAAAAAAAAAABB")
+    False
+    >>> word_exists([["A"]], 123)
+    Traceback (most recent call last):
+        ...
+    ValueError: The word parameter should be a string of length greater than 0.
+    >>> word_exists([["A"]], "")
+    Traceback (most recent call last):
+        ...
+    ValueError: The word parameter should be a string of length greater than 0.
+    >>> word_exists([[]], "AB")
+    Traceback (most recent call last):
+        ...
+    ValueError: The board should be a non empty matrix of single chars strings.
+    >>> word_exists([], "AB")
+    Traceback (most recent call last):
+        ...
+    ValueError: The board should be a non empty matrix of single chars strings.
+    >>> word_exists([["A"], [21]], "AB")
+    Traceback (most recent call last):
+        ...
+    ValueError: The board should be a non empty matrix of single chars strings.
+    """
+
+    # Validate board
+    board_error_message = (
+        "The board should be a non empty matrix of single chars strings."
+    )
+    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
+    if not isinstance(word, str) or len(word) == 0:
+        raise ValueError(
+            "The word parameter should be a string of length greater than 0."
+        )
+
+    traverts_directions = [(0, 1), (0, -1), (-1, 0), (1, 0)]
+    len_word = len(word)
+    len_board = len(board)
+    len_board_column = len(board[0])
+
+    # Returns the hash key of matrix indexes.
+    def get_point_key(row: int, column: int) -> int:
+        """
+        >>> len_board=10
+        >>> len_board_column=20
+        >>> get_point_key(0, 0)
+        200
+        """
+
+        return len_board * len_board_column * row + column
+
+    # Return True if it's possible to search the word suffix
+    # starting from the word_index.
+    def exits_word(
+        row: int, column: int, word_index: int, visited_points_set: set[int]
+    ) -> bool:
+        """
+        >>> board=[["A"]]
+        >>> word="B"
+        >>> exits_word(0, 0, 0, set())
+        False
+        """
+
+        if board[row][column] != word[word_index]:
+            return False
+
+        if word_index == len_word - 1:
+            return True
+
+        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(next_i, next_j)
+            if key in visited_points_set:
+                continue
+
+            visited_points_set.add(key)
+            if exits_word(next_i, next_j, word_index + 1, visited_points_set):
+                return True
+
+            visited_points_set.remove(key)
+
+        return False
+
+    for i in range(len_board):
+        for j in range(len_board_column):
+            if exits_word(i, j, 0, {get_point_key(i, j)}):
+                return True
+
+    return False
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()