256 Paint House

There are a row of n houses, each house can be painted with one of the three colors: red, blue or green. The cost of painting each house with a certain color is different. You have to paint all the houses such that no two adjacent houses have the same color.
The cost of painting each house with a certain color is represented by a n* x *3 cost matrix. For example, costs[0][0] is the cost of painting house 0 with color red; costs[1][2] is the cost of painting house 1 with color green, and so on... Find the minimum cost to paint all houses.
Note:All costs are positive integers.

  dp[k][c] = Min(dp[k-1][(c+1)%3], dp[k-1][(c+2)%3]) + costs[k][c]

    public class Solution {
        public int minCost(int[][] costs) {
            if(costs != null && costs.length == 0) return 0;
            for(int i = 1; i < costs.length; i++){
                costs[i][0] = costs[i][0] +
                                Math.min(costs[i - 1][1], costs[i - 1][2]);
                costs[i][1] = costs[i][1] + 
                                Math.min(costs[i - 1][0], costs[i - 1][2]);
                costs[i][2] = costs[i][2] + 
                                Math.min(costs[i - 1][0], costs[i - 1][1]);
            }
            return Math.min(costs[costs.length - 1][0], 
                                  Math.min(costs[costs.length - 1][1], 
                                        costs[costs.length - 1][2]));
        }
    }