Competitive ProgrammingEasy

Min Cost Path

Detailed guide and Python implementation for the 'Min Cost Path' problem.

Problem Statement

Easy

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.

Constraints
  • 1 <= len(cost), len(cost[0]) <= 100
  • 0 <= cost[i][j] <= 1000
  • 0 <= m < len(cost)
  • 0 <= n < len(cost[0])

Examples

Example 1
Input
min_cost_path([[1, 2, 3], [4, 8, 2], [1, 5, 3]], 2, 2)
Output
8
Explanation

The path with minimum cost is (0,0) -> (0,1) -> (1,2) -> (2,2) with total cost 1 + 2 + 2 + 3 = 8.

Example 2
Input
min_cost_path([[1, 2, 3], [4, 8, 2], [1, 5, 3]], 1, 1)
Output
9
Explanation

The path with minimum cost is (0,0) -> (1,1) with total cost 1 + 8 = 9.

Need a Hint?
Consider using Dynamic Programming-specific data structures like sets or heaps.
Edge Cases to Watch
  • Empty input structures
  • Single element inputs
  • Large numerical bounds

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