Find the Safest Path in a Grid
You are given a 0-indexed 2D matrix grid of size n x n, where (r, c) represents:
- A cell containing a thief if
grid[r][c] = 1. - An empty cell if
grid[r][c] = 0.
You are initially positioned at cell (0, 0). In one move, you can move to any adjacent cell in the grid, including cells containing thieves.
The safeness factor of a path on the grid is defined as the minimum Manhattan distance from any cell in the path to any thief in the grid.
Return the maximum safeness factor of all paths leading to cell (n - 1, n - 1).
An adjacent cell of cell (r, c) is one of the cells (r, c + 1), (r, c - 1), (r + 1, c), and (r - 1, c) if it exists.
The Manhattan distance between two cells (a, b) and (x, y) is equal to |a - x| + |b - y|, where |val| denotes the absolute value of val.
Example 1
1 0 0 0 0 0 0 0 1
Input
grid = [[1,0,0],[0,0,0],[0,0,1]]Output
0All paths from (0, 0) to (n - 1, n - 1) go through the thieves in cells (0, 0) and (n - 1, n - 1).
Example 2
0 0 1 0 0 0 0 0 0
Input
grid = [[0,0,1],[0,0,0],[0,0,0]]Output
2The shown path has safeness factor 2 because its closest cell to the thief at (0, 2) is (0, 0), and no path has a higher safeness factor.
Constraints
- 1 <= grid.length == n <= 400
- grid[i].length == n
- grid[i][j] is either 0 or 1.
- There is at least one thief in the grid.