Given a cost matrix cost and a position (m, n) in cost, write a function that returns cost of minimum cost path to reach (m, n) from (0, 0). Each cell of the matrix represents a cost to traverse through that cell. Total cost of a path to reach (m, n) is sum of all the costs on that path (including both source and destination). You can only traverse down, right and diagonally lower cells from a given cell, i.e., from a given cell (i, j), cells (i+1, j), (i, j+1) and (i+1, j+1) can be traversed. You may assume that all costs are positive integers.
The path with minimum cost is highlighted in the following figure. The path is (0, 0) –> (0, 1) –> (1, 2) –> (2, 2). The cost of the path is 8 (1 + 2 + 2 + 3).
Please refer complete article on Dynamic Programming | Set 6 (Min Cost Path) for more details!
- Java Program for Min Cost Path
- Python Program for Min Cost Path
- Min Cost Path | DP-6
- Minimum odd cost path in a matrix
- Minimum Cost Path with Left, Right, Bottom and Up moves allowed
- C / C++ Program for Dijkstra's shortest path algorithm | Greedy Algo-7
- Minimum cost to fill given weight in a bag
- Minimum Cost Polygon Triangulation
- Minimum cost to buy N kilograms of sweet for M persons
- Find minimum adjustment cost of an array
- Minimum Cost To Make Two Strings Identical
- Minimum cost to reach a point N from 0 with two different operations allowed
- Minimum cost to form a number X by adding up powers of 2
- Find the minimum cost to reach destination using a train
- Minimum cost to make a string free of a subsequence