Python/backtracking/word_search.py
Kamil 7b996e2c22
backtracking -> word_search - replacing the example in doctest (#10188)
* Replacing the generator with numpy vector operations from lu_decomposition.

* Revert "Replacing the generator with numpy vector operations from lu_decomposition."

This reverts commit ad217c6616.

* Replacing the example in doctest with a less resource-intensive example.
2023-10-10 00:16:02 -04:00

163 lines
4.3 KiB
Python

"""
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 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 exits_word(
board: list[list[str]],
word: str,
row: int,
column: int,
word_index: int,
visited_points_set: set[int],
) -> bool:
"""
Return True if it's possible to search the word suffix
starting from the word_index.
>>> exits_word([["A"]], "B", 0, 0, 0, set())
False
"""
if board[row][column] != word[word_index]:
return False
if word_index == len(word) - 1:
return True
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)
if exits_word(board, word, next_i, next_j, word_index + 1, visited_points_set):
return True
visited_points_set.remove(key)
return False
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([["B", "A", "A"], ["A", "A", "A"], ["A", "B", "A"]], "ABB")
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."
)
len_board = len(board)
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."
)
len_board_column = len(board[0])
for i in range(len_board):
for j in range(len_board_column):
if exits_word(
board, word, i, j, 0, {get_point_key(len_board, len_board_column, i, j)}
):
return True
return False
if __name__ == "__main__":
import doctest
doctest.testmod()