Min Cost Path
Detailed guide and Python implementation for the 'Min Cost Path' problem.
Problem Statement
Write a function min_cost_path(cost, m, n) that finds the minimum cost to reach cell (m, n) from cell (0, 0) in a 2D cost matrix cost. You can only move down, right, and diagonally down-right from a cell.
- •1 <= len(cost), len(cost[0]) <= 100
- •0 <= cost[i][j] <= 1000
- •0 <= m < len(cost)
- •0 <= n < len(cost[0])
Examples
min_cost_path([[1, 2, 3], [4, 8, 2], [1, 5, 3]], 2, 2)
8
The path with minimum cost is (0,0) -> (0,1) -> (1,2) -> (2,2) with total cost 1 + 2 + 2 + 3 = 8.
min_cost_path([[1, 2, 3], [4, 8, 2], [1, 5, 3]], 1, 1)
9
The path with minimum cost is (0,0) -> (1,1) with total cost 1 + 8 = 9.
Need a Hint?
Edge Cases to Watch
- Empty input structures
- Single element inputs
- Large numerical bounds
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