1368. Minimum Cost to Make at Least One Valid Path in a Grid

Given an m x n grid. Each cell of the grid has a sign pointing to the next cell you should visit if you are currently in this cell. The sign of grid[i][j] can be:

- 1 which means go to the cell to the right. (i.e go from grid[i][j] to grid[i][j + 1])
- 2 which means go to the cell to the left. (i.e go from grid[i][j] to grid[i][j - 1])
- 3 which means go to the lower cell. (i.e go from grid[i][j] to grid[i + 1][j])
- 4 which means go to the upper cell. (i.e go from grid[i][j] to grid[i - 1][j])
Notice that there could be some signs on the cells of the grid that point outside the grid.

You will initially start at the upper left cell (0, 0). A valid path in the grid is a path that starts from the upper left cell (0, 0) and ends at the bottom-right cell (m - 1, n - 1) following the signs on the grid. The valid path does not have to be the shortest.

You can modify the sign on a cell with cost = 1. You can modify the sign on a cell one time only.

Return the minimum cost to make the grid have at least one valid path.

- Time : O(nlogn)
- Space : O(n)

1 | class Solution { |