Package g2301_2400.s2304_minimum_path_cost_in_a_grid

Class Solution

  • public class Solution
extends Object
    2304 - Minimum Path Cost in a Grid.

    Medium

    You are given a 0-indexed m x n integer matrix grid consisting of distinct integers from 0 to m * n - 1. You can move in this matrix from a cell to any other cell in the next row. That is, if you are in cell (x, y) such that x < m - 1, you can move to any of the cells (x + 1, 0), (x + 1, 1), …, (x + 1, n - 1). Note that it is not possible to move from cells in the last row.

    Each possible move has a cost given by a 0-indexed 2D array moveCost of size (m * n) x n, where moveCost[i][j] is the cost of moving from a cell with value i to a cell in column j of the next row. The cost of moving from cells in the last row of grid can be ignored.

    The cost of a path in grid is the sum of all values of cells visited plus the sum of costs of all the moves made. Return the minimum cost of a path that starts from any cell in the first row and ends at any cell in the last row.

    Example 1:

    Input: grid = [[5,3],[4,0],[2,1]], moveCost = [[9,8],[1,5],[10,12],[18,6],[2,4],[14,3]]

    Output: 17

    Explanation: The path with the minimum possible cost is the path 5 -> 0 -> 1.

    • The sum of the values of cells visited is 5 + 0 + 1 = 6.

    • The cost of moving from 5 to 0 is 3.

    • The cost of moving from 0 to 1 is 8.

    So the total cost of the path is 6 + 3 + 8 = 17.

    Example 2:

    Input: grid = [[5,1,2],[4,0,3]], moveCost = [[12,10,15],[20,23,8],[21,7,1],[8,1,13],[9,10,25],[5,3,2]]

    Output: 6

    Explanation: The path with the minimum possible cost is the path 2 -> 3.

    • The sum of the values of cells visited is 2 + 3 = 5.

    • The cost of moving from 2 to 3 is 1.

    So the total cost of this path is 5 + 1 = 6.

    Constraints:

    • m == grid.length
    • n == grid[i].length
    • 2 <= m, n <= 50
    • grid consists of distinct integers from 0 to m * n - 1.
    • moveCost.length == m * n
    • moveCost[i].length == n
    • 1 <= moveCost[i][j] <= 100

    • Constructor Detail

      • Solution

        public Solution()

    • Method Detail

      • minPathCost

        public int minPathCost​(int[][] grid,
                       int[][] moveCost)