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