Paint House II

There are a row of n houses, each house can be painted with one of the k colors. 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 k cost matrix. For example, costs[0][0] is the cost of painting house 0 with color 0; costs[1][2] is the cost of painting house 1 with color 2, and so on... Find the minimum cost to paint all houses.
Note:
All costs are positive integers.
Follow up:
Could you solve it in O(nk) runtime?

public class Solution {
    public int minCostII(int[][] costs) {
        if (costs == null || costs.length == 0 || costs[0].length == 0) {
            return 0;
        }
        int n = costs.length;
        int k = costs[0].length;
        int[] dp = new int[k];
        int min1 = 0;
        int min2 = 0;
        int id1 = 0;
        for (int i = 0; i < n; i++) {
            int nextMin1 = Integer.MAX_VALUE;
            int nextId1 = -1;
            int nextMin2 = Integer.MAX_VALUE;
           
            for (int j = 0; j < k; j++) {
                if (j != id1) {
                    dp[j] = min1 + costs[i][j];
                } else {
                    dp[j] = min2 + costs[i][j];
                }
               
                if (dp[j] < nextMin1) {
                    nextId1 = j;
                    nextMin2 = nextMin1;
                    nextMin1 = dp[j];
                } else if (dp[j] < nextMin2) {
                    nextMin2 = dp[j];
                }
            }
            min1 = nextMin1;
            min2 = nextMin2;
            id1 = nextId1;
        }
       
        return min1;
    }
}