Skip to main content

Shortest Path in Binary Matrix

Problem statement

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

My solution

/**
* @param {number[][]} grid
* @return {number}
*/
var shortestPathBinaryMatrix = function(grid) {
const n = grid.length - 1;

const movements = [
{ x: 0, y: 1 },
{ x: 0, y: -1 },
{ y: 0, x: -1 },
{ y: 0, x: 1 },
{ x: 1, y: 1 },
{ x: 1, y: -1 },
{ y: 1, x: -1 },
{ y: -1, x: -1 },
]

if (grid[n][n] === 1 || grid[0][0] === 1) {
return -1
}

const queue = [{
x: 0,
y: 0,
count: 1
}]

grid[0][0] = 1

// let shorted =

while (queue.length) {
// console.log(queue)
const {x, y, count} = queue.shift()

if (x === n && y === n) {
return count
} else {
for (const {x: mayX, y: mayY} of movements) {
const newX = mayX + x;
const newY = mayY + y;

// console.log(newX, newY)

if (newX >= 0 && newY >= 0 && newX <= n && newY <= n && grid[newX][newY] === 0) {
queue.push({
x: newX,
y: newY,
count: count + 1
})
grid[newX][newY] = 1
}
}
}
}

return -1;
};