Minimum Path Cost in a Grid

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
5 3
4 0
2 1
Inputgrid = [[5,3],[4,0],[2,1]], moveCost = [[9,8],[1,5],[10,12],[18,6],[2,4],[14,3]]
Output17
The path with the minimum possible cost is 5 -> 0 -> 1, with cell values summing to 6 and move costs 3 and 8, for a total cost of 17.
Example 2
5 1 2
4 0 3
Inputgrid = [[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]]
Output6
The path with the minimum possible cost is 2 -> 3, with cell values summing to 5 and move cost 1, for a total cost of 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

Asked at 2 companies

</>

Your Solution

(Ctrl/Cmd + Enter)

Switching Language

Loading template...

Loading...

Sign in to save your progress

AI code evaluation

Get a correctness verdict, missed edge cases, and complexity analysis of your solution.

Sign in to evaluate