# Shortest Path in Binary Matrix

Updated: Mar 25, 2021

In an N by N square grid, each cell is either empty (0) or blocked (1).

A *clear path from top-left to bottom-right* has length k if and only if it is composed of cells C_1, C_2, ..., C_k such that:

Adjacent cells C_i and C_{i+1} are connected 8-directionally (ie., they are different and share an edge or corner)

C_1 is at location (0, 0) (ie. has value grid[0][0])

C_k is at location (N-1, N-1) (ie. has value grid[N-1][N-1])

If C_i is located at (r, c), then grid[r][c] is empty (ie. grid[r][c] == 0).

Return the length of the shortest such clear path from top-left to bottom-right. If such a path does not exist, return -1.

**Example 1:**

**Input****:**** **[[0,1],[1,0]]
**Output****:**** **2

**Example 2:**
**Input: **[[0,0,0],[1,1,0],[1,1,0]] **Output:** 4

**Note:**

1 <= grid.length == grid[0].length <= 100

grid[r][c] is 0 or 1

**Solution:**

```
class Solution {
public int shortestPathBinaryMatrix(int[][] grid) {
int n = grid.length;
int m = grid[0].length;
if(grid[0][0]==1||grid[n-1][m-1]==1)return -1;
if(n==1 && m==1 && grid[0][0]==0)return 1;
int res=1;
Queue<int[]> q = new LinkedList<>();
q.add(new int[]{0,0});
int[][] directions = new int[][]{{1,0},{-1,0},{0,1},{0,-1},
{1,1},{1,-1},{-1,1},{-1,-1}};
while(!q.isEmpty()){
int qsize = q.size();
for(int i=0;i<qsize;i++){
int[] arr = q.poll();
for(int j=0;j<8;j++){
int newx = arr[0]+directions[j][0];
int newy = arr[1]+directions[j][1];
if(newx<0||newy<0||newx>=n||newy>=m||
grid[newx][newy]==1)continue;
if(newx==n-1 && newy==m-1) return res+1;
grid[newx][newy] = 1;
q.add(new int[]{newx,newy});
}
}
res++;
}
return -1;
}
}
```