Package g1301_1400.s1368_minimum_cost_to_make_at_least_one_valid_path_in_a_grid

Class Solution

  • public class Solution
extends Object
    1368 - Minimum Cost to Make at Least One Valid Path in a Grid.

    Hard

    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.

    Example 1:

    Input: grid = [[1,1,1,1],[2,2,2,2],[1,1,1,1],[2,2,2,2]]

    Output: 3

    Explanation: You will start at point (0, 0). The path to (3, 3) is as follows. (0, 0) –> (0, 1) –> (0, 2) –> (0, 3) change the arrow to down with cost = 1 –> (1, 3) –> (1, 2) –> (1, 1) –> (1, 0) change the arrow to down with cost = 1 –> (2, 0) –> (2, 1) –> (2, 2) –> (2, 3) change the arrow to down with cost = 1 –> (3, 3) The total cost = 3.

    Example 2:

    Input: grid = [[1,1,3],[3,2,2],[1,1,4]]

    Output: 0

    Explanation: You can follow the path from (0, 0) to (2, 2).

    Example 3:

    Input: grid = [[1,2],[4,3]]

    Output: 1

    Constraints:

    • m == grid.length
    • n == grid[i].length
    • 1 <= m, n <= 100
    • 1 <= grid[i][j] <= 4

    • Constructor Detail

      • Solution

        public Solution()

    • Method Detail

      • minCost

        public int minCost​(int[][] grid)