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119 lines
3.2 KiB
Python
119 lines
3.2 KiB
Python
from typing import List
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def solve_maze(maze: List[List[int]]) -> bool:
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"""
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This method solves the "rat in maze" problem.
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In this problem we have some n by n matrix, a start point and an end point.
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We want to go from the start to the end. In this matrix zeroes represent walls
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and ones paths we can use.
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Parameters :
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maze(2D matrix) : maze
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Returns:
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Return: True if the maze has a solution or False if it does not.
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>>> maze = [[0, 1, 0, 1, 1],
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... [0, 0, 0, 0, 0],
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... [1, 0, 1, 0, 1],
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... [0, 0, 1, 0, 0],
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... [1, 0, 0, 1, 0]]
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>>> solve_maze(maze)
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[1, 0, 0, 0, 0]
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[1, 1, 1, 1, 0]
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[0, 0, 0, 1, 0]
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[0, 0, 0, 1, 1]
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[0, 0, 0, 0, 1]
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True
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>>> maze = [[0, 1, 0, 1, 1],
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... [0, 0, 0, 0, 0],
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... [0, 0, 0, 0, 1],
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... [0, 0, 0, 0, 0],
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... [0, 0, 0, 0, 0]]
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>>> solve_maze(maze)
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[1, 0, 0, 0, 0]
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[1, 0, 0, 0, 0]
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[1, 0, 0, 0, 0]
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[1, 0, 0, 0, 0]
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[1, 1, 1, 1, 1]
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True
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>>> maze = [[0, 0, 0],
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... [0, 1, 0],
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... [1, 0, 0]]
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>>> solve_maze(maze)
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[1, 1, 1]
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[0, 0, 1]
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[0, 0, 1]
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True
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>>> maze = [[0, 1, 0],
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... [0, 1, 0],
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... [1, 0, 0]]
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>>> solve_maze(maze)
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No solution exists!
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False
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>>> maze = [[0, 1],
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... [1, 0]]
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>>> solve_maze(maze)
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No solution exists!
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False
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"""
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size = len(maze)
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# We need to create solution object to save path.
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solutions = [[0 for _ in range(size)] for _ in range(size)]
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solved = run_maze(maze, 0, 0, solutions)
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if solved:
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print("\n".join(str(row) for row in solutions))
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else:
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print("No solution exists!")
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return solved
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def run_maze(maze: List[List[int]], i: int, j: int, solutions: List[List[int]]) -> bool:
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"""
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This method is recursive starting from (i, j) and going in one of four directions:
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up, down, left, right.
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If a path is found to destination it returns True otherwise it returns False.
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Parameters:
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maze(2D matrix) : maze
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i, j : coordinates of matrix
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solutions(2D matrix) : solutions
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Returns:
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Boolean if path is found True, Otherwise False.
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"""
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size = len(maze)
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# Final check point.
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if i == j == (size - 1):
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solutions[i][j] = 1
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return True
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lower_flag = (not (i < 0)) and (not (j < 0)) # Check lower bounds
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upper_flag = (i < size) and (j < size) # Check upper bounds
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if lower_flag and upper_flag:
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# check for already visited and block points.
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block_flag = (not (solutions[i][j])) and (not (maze[i][j]))
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if block_flag:
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# check visited
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solutions[i][j] = 1
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# check for directions
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if (
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run_maze(maze, i + 1, j, solutions)
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or run_maze(maze, i, j + 1, solutions)
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or run_maze(maze, i - 1, j, solutions)
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or run_maze(maze, i, j - 1, solutions)
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):
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return True
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solutions[i][j] = 0
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return False
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return False
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if __name__ == "__main__":
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import doctest
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doctest.testmod()
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