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from __future__ import annotations

def solve_maze(

maze: list[list[int]],

source_row: int,

source_column: int,

destination_row: int,

destination_column: int,

) -> list[list[int]]:

"""

This method solves the "rat in maze" problem.

Parameters :

- maze: A two dimensional matrix of zeros and ones.

- source_row: The row index of the starting point.

- source_column: The column index of the starting point.

- destination_row: The row index of the destination point.

- destination_column: The column index of the destination point.

Returns:

- solution: A 2D matrix representing the solution path if it exists.

Raises:

- ValueError: If no solution exists or if the source or

destination coordinates are invalid.

Description:

This method navigates through a maze represented as an n by n matrix,

starting from a specified source cell and

aiming to reach a destination cell.

The maze consists of walls (1s) and open paths (0s).

By providing custom row and column values, the source and destination

cells can be adjusted.

>>> maze = [[0, 1, 0, 1, 1],

... [0, 0, 0, 0, 0],

... [1, 0, 1, 0, 1],

... [0, 0, 1, 0, 0],

... [1, 0, 0, 1, 0]]

>>> solve_maze(maze,0,0,len(maze)-1,len(maze)-1) # doctest: +NORMALIZE_WHITESPACE

[[0, 1, 1, 1, 1],

[0, 0, 0, 0, 1],

[1, 1, 1, 0, 1],

[1, 1, 1, 0, 0],

[1, 1, 1, 1, 0]]

Note:

In the output maze, the zeros (0s) represent one of the possible

paths from the source to the destination.

>>> maze = [[0, 1, 0, 1, 1],

... [0, 0, 0, 0, 0],

... [0, 0, 0, 0, 1],

... [0, 0, 0, 0, 0],

... [0, 0, 0, 0, 0]]

>>> solve_maze(maze,0,0,len(maze)-1,len(maze)-1) # doctest: +NORMALIZE_WHITESPACE

[[0, 1, 1, 1, 1],

[0, 1, 1, 1, 1],

[0, 0, 0, 0, 0]]

>>> maze = [[0, 0, 0],

... [0, 1, 0],

... [1, 0, 0]]

>>> solve_maze(maze,0,0,len(maze)-1,len(maze)-1) # doctest: +NORMALIZE_WHITESPACE

[[0, 0, 0],

[1, 1, 0],

[1, 1, 0]]

>>> maze = [[1, 0, 0],

... [0, 1, 0],

... [1, 0, 0]]

>>> solve_maze(maze,0,1,len(maze)-1,len(maze)-1) # doctest: +NORMALIZE_WHITESPACE

[[1, 0, 0],

[1, 1, 0],

[1, 1, 0]]

>>> maze = [[1, 1, 0, 0, 1, 0, 0, 1],

... [1, 0, 1, 0, 0, 1, 1, 1],

... [0, 1, 0, 1, 0, 0, 1, 0],

... [1, 1, 1, 0, 0, 1, 0, 1],

... [0, 1, 0, 0, 1, 0, 1, 1],

... [0, 0, 0, 1, 1, 1, 0, 1],

... [0, 1, 0, 1, 0, 1, 1, 1],

... [1, 1, 0, 0, 0, 0, 0, 1]]

>>> solve_maze(maze,0,2,len(maze)-1,2) # doctest: +NORMALIZE_WHITESPACE

[[1, 1, 0, 0, 1, 1, 1, 1],

[1, 1, 1, 0, 0, 1, 1, 1],

[1, 1, 1, 1, 0, 1, 1, 1],

[1, 1, 1, 0, 0, 1, 1, 1],

[1, 1, 0, 0, 1, 1, 1, 1],

[1, 1, 0, 1, 1, 1, 1, 1],

[1, 1, 0, 1, 1, 1, 1, 1]]

>>> maze = [[1, 0, 0],

... [0, 1, 1],

... [1, 0, 1]]

>>> solve_maze(maze,0,1,len(maze)-1,len(maze)-1)

Traceback (most recent call last):

...

ValueError: No solution exists!

>>> maze = [[0, 0],

... [1, 1]]

>>> solve_maze(maze,0,0,len(maze)-1,len(maze)-1)

Traceback (most recent call last):

...

ValueError: No solution exists!

>>> maze = [[0, 1],

... [1, 0]]

>>> solve_maze(maze,2,0,len(maze)-1,len(maze)-1)

Traceback (most recent call last):

...

ValueError: Invalid source or destination coordinates

>>> maze = [[1, 0, 0],

... [0, 1, 0],

... [1, 0, 0]]

>>> solve_maze(maze,0,1,len(maze),len(maze)-1)

Traceback (most recent call last):

...

ValueError: Invalid source or destination coordinates

"""

size = len(maze)

# Check if source and destination coordinates are Invalid.

if not (0 <= source_row <= size - 1 and 0 <= source_column <= size - 1) or (

not (0 <= destination_row <= size - 1 and 0 <= destination_column <= size - 1)

raise ValueError("Invalid source or destination coordinates")

# We need to create solution object to save path.

solutions = [[1 for _ in range(size)] for _ in range(size)]

solved = run_maze(

maze, source_row, source_column, destination_row, destination_column, solutions

)

if solved:

return solutions

else:

raise ValueError("No solution exists!")

def run_maze(

maze: list[list[int]],

i: int,

j: int,

destination_row: int,

destination_column: int,

solutions: list[list[int]],

) -> bool:

"""

This method is recursive starting from (i, j) and going in one of four directions:

up, down, left, right.

If a path is found to destination it returns True otherwise it returns False.

Parameters

maze: A two dimensional matrix of zeros and ones.

i, j : coordinates of matrix

solutions: A two dimensional matrix of solutions.

Returns:

Boolean if path is found True, Otherwise False.

"""

size = len(maze)

# Final check point.

if i == destination_row and j == destination_column and maze[i][j] == 0:

solutions[i][j] = 0

return True

lower_flag = (not i < 0) and (not j < 0) # Check lower bounds

upper_flag = (i < size) and (j < size) # Check upper bounds

if lower_flag and upper_flag:

# check for already visited and block points.

block_flag = (solutions[i][j]) and (not maze[i][j])

if block_flag:

# check visited

solutions[i][j] = 0

# check for directions

if (

run_maze(maze, i + 1, j, destination_row, destination_column, solutions)

or run_maze(

maze, i, j + 1, destination_row, destination_column, solutions

)

or run_maze(

maze, i - 1, j, destination_row, destination_column, solutions

)

or run_maze(

maze, i, j - 1, destination_row, destination_column, solutions

)

return True

solutions[i][j] = 1

return False

if __name__ == "__main__":

import doctest

doctest.testmod(optionflags=doctest.NORMALIZE_WHITESPACE)

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