# Paint House

## Problem

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 is the cost of painting house 0 with color red; costs is the cost of painting house 1 with color green, and so on... Find the minimum cost to paint all houses.

Notice: All costs are positive integers.

## Example

Given costs = [[14,2,11],[11,14,5],[14,3,10]] return 10

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

## Code - Java

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) {
int n = costs.length;
if (n == 0) return 0;
int[][] sum = new int[n];
for (int i = 0; i < 3; i++) {
sum[i] = costs[i];
}

for (int i = 1; i < n; i++) {

for (int j = 0; j < 3; j++) {
int min = Integer.MAX_VALUE;
for (int k = 0; k < 3; k++) {
if (j != k && sum[i - 1][k] < min) {
min = sum[i - 1][k];
}
}
sum[i][j] = min + costs[i][j];
}
}
int min = Integer.MAX_VALUE;
for (int i = 0; i < 3; i++) {
min = Math.min(min, sum[n - 1][i]);
}
return min;
}
}

## Online Judge

LintCode 515: http://www.lintcode.com/en/problem/paint-house/