Shortest Path in a Grid with Obstacles Elimination
You are given an m x n integer matrix grid where each cell is either 0 (empty) or 1 (obstacle). You can move up, down, left, or right from and to an empty cell in one step.
Return the minimum number of steps to walk from the upper left corner (0, 0) to the lower right corner (m - 1, n - 1) given that you can eliminate at most k obstacles. If it is not possible to find such a walk, return -1.
Example 1
0 0 0 1 1 0 0 0 0 0 1 1 0 0 0
Input
grid = [[0,0,0],[1,1,0],[0,0,0],[0,1,1],[0,0,0]], k = 1Output
6The shortest path without eliminating any obstacle is 10, while eliminating the obstacle at position (3,2) gives a path of 6 steps.
Example 2
0 1 1 1 1 1 1 0 0
Input
grid = [[0,1,1],[1,1,1],[1,0,0]], k = 1Output
-1We need to eliminate at least two obstacles to find such a walk.
Constraints
- m == grid.length
- n == grid[i].length
- 1 <= m, n <= 40
- 1 <= k <= m * n
- grid[i][j] is either 0 or 1.
- grid[0][0] == grid[m - 1][n - 1] == 0