here 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 anx3cost matrix. For example,costs[0][0]is the cost of painting house0with color red;costs[1][2]is the cost of painting house1with color green, and so on... Find the minimum cost to paint all houses.

Notice

All costs are positive integers.

Have you met this question in a real interview?

Yes

Example

Givencosts=[[14,2,11],[11,14,5],[14,3,10]]return10

house 0 is blue, house 1 is green, house 2 is blue,2 + 5 + 3 = 10

DP.

set f[n][0], f[n][1], f[n][2] represents the min sum for the first n houses and the n - 1th house is painted with red, blue, green

public class Solution {
    /**
     * @param costs n x 3 cost matrix
     * @return an integer, the minimum cost to paint all houses
     */
    public int minCost(int[][] costs) {
        // Write your code here
        if (costs == null || costs.length == 0 || costs[0] == null || costs[0].length == 0) {
            return 0;
        }

        int n = costs.length;
        int m = costs[0].length;

        int[][] f = new int[2][m];
        int now, old = 0;
        int i, j, k;
        for (i = 1; i <= n; i++) {
            old = now;
            now = 1 - now;
            for (j = 0; j < m; j++) {
                f[now][j] = Integer.MAX_VALUE;
                for (k = 0; k < m; k++) {
                    if (j == k) {
                        continue;
                    }
                    f[now][j] = Math.min(f[now][j], f[old][k] + costs[i - 1][j]);
                }
            }
        }

        return Math.min(f[now][0], Math.min(f[now][1], f[now][2]));
    }
}