MediumNo. 2304
Minimum Path Cost in a Grid — LeetCode 2304 Python Solution
- Pattern
- Matrix and Grid
- Topics
- Array, Dynamic Programming, Matrix
- Reading time
- 2 min
- Source
- leetcode.com
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
- Time
- O(m × n2)
- Space · auxiliary
- O(n)
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.
Related problems
| No. | Problem | Difficulty |
|---|---|---|
| 0063 | Unique Paths II | Medium |
| 0064 | Minimum Path Sum | Medium |
| 0085 | Maximal Rectangle | Hard |
| 0174 | Dungeon Game | Hard |
| 0221 | Maximal Square | Medium |
| 0329 | Longest Increasing Path in a Matrix | Hard |
Frequently asked questions
- How hard is LeetCode 2304. Minimum Path Cost in a Grid?
LeetCode 2304. Minimum Path Cost in a Grid is rated Medium on LeetCode.
- What is the time complexity of LeetCode 2304. Minimum Path Cost in a Grid?
The Python solution on this page runs in O(m × n2).
- What is the space complexity of LeetCode 2304. Minimum Path Cost in a Grid?
The Python solution on this page uses O(n) auxiliary space.
- What topics does LeetCode 2304. Minimum Path Cost in a Grid cover?
LeetCode 2304. Minimum Path Cost in a Grid is tagged Array, Dynamic Programming and Matrix on LeetCode.