There are a row ofnhouses, 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 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.

tag: DP

class Solution {
    public int minCost(int[][] costs) {
        if (costs == null || costs.length == 0) return 0;
        int n = costs.length;
        int[][] dp = new int[n][3];
        if (n == 1) return Math.min(costs[0][0], Math.min(costs[0][1], costs[0][2]));

        dp[0][0] = costs[0][0];
        dp[0][1] = costs[0][1];
        dp[0][2] = costs[0][2];

        for (int i = 1; i < n; i++){
            dp[i][0] = Math.min(dp[i - 1][1], dp[i - 1][2]) + costs[i][0];
            dp[i][1] = Math.min(dp[i - 1][0], dp[i - 1][2]) + costs[i][1];
            dp[i][2] = Math.min(dp[i - 1][0], dp[i - 1][1]) + costs[i][2];
        }

        return Math.min(dp[n - 1][0], Math.min(dp[n - 1][1], dp[n - 1][2]));
    }
}