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.

Solution

public class Solution {
    public int minCost(int[][] costs) {
        if (costs == null || costs.length == 0 || costs[0].length != 3) return 0;

        int n = costs.length;
        int[][] dp = new int[n][3];

        for (int i = 0; i <= 2; i++) {
            dp[0][i] = costs[0][i];
        }

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