Minimum Path Cost in a Grid — LeetCode 2304 Python Solution

The problem

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.

Example

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.

Python solution

class Solution:
    def minPathCost(self, grid: List[List[int]], moveCost: List[List[int]]) -> int:
        m, n = len(grid), len(grid[0])
        f = grid[0]
        for i in range(1, m):
            g = [inf] * n
            for j in range(n):
                for k in range(n):
                    g[j] = min(g[j], f[k] + moveCost[grid[i - 1][k]][j] + grid[i][j])
            f = g
        return min(f)

Complexity

Pattern: Matrix and Grid

Treat a 2-D grid as a graph whose neighbours are the four adjacent cells. LeetCode 2304. Minimum Path Cost in a Grid is filed here because LeetCode tags it Matrix, which is the vocabulary this hub collects.

The matrix and grid guide has the Python template for the pattern and the 216 LeetCode problems that use it.

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