1091. Shortest Path in Binary Matrix

Problem Link

Description

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Given an n x n binary matrix grid, return the length of the shortest clear path in the matrix. If there is no clear path, return -1.

A clear path in a binary matrix is a path from the top-left cell (i.e., (0, 0)) to the bottom-right cell (i.e., (n - 1, n - 1)) such that:

• All the visited cells of the path are 0.
• All the adjacent cells of the path are 8-directionally connected (i.e., they are different and they share an edge or a corner).

The length of a clear path is the number of visited cells of this path.

 

Example 1:

Input: grid = [[0,1],[1,0]]
Output: 2

Example 2:

Input: grid = [[0,0,0],[1,1,0],[1,1,0]]
Output: 4

Example 3:

Input: grid = [[1,0,0],[1,1,0],[1,1,0]]
Output: -1

 

Constraints:

• n == grid.length
• n == grid[i].length
• 1 <= n <= 100
• grid[i][j] is 0 or 1

Solution

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Python3

class Solution:
    def shortestPathBinaryMatrix(self, grid: List[List[int]]) -> int:
        n = len(grid)
        bfs = deque([])
 
        if grid[0][0] == 0:
            bfs.append((0, 0))
            grid[0][0] = 1
        
        count = 1
 
        while bfs:
            N = len(bfs)
 
            for _ in range(N):
                x, y = bfs.popleft()
 
                if x == y == n - 1: return count
 
                for dx in range(x - 1, x + 2):
                    for dy in range(y - 1, y + 2):
                        if 0 <= dx < n and 0 <= dy < n and grid[dx][dy] == 0:
                            grid[dx][dy] = 1
                            bfs.append((dx, dy))
 
            count += 1
        
        return -1