Leetcode 265 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?

Solution 1: a DP question. Can be solved with O(k) space and O(nk) time.

 public class Solution {  
   public int minCostII(int[][] costs) {  
     int n=costs.length;  
     if (n==0) return 0;  
     int k=costs[0].length;  
     //if (k<2) return 0;// n==1 and k==1 still works  
     int[] dp=new int[k];  
     for (int i=0; i<n; i++) {  
       if (i==0) {  
         for (int j=0; j<k; j++) dp[j]=costs[i][j];  
       }  
       else {  
         int m1=-1, m2=-1, v1=Integer.MAX_VALUE, v2=Integer.MAX_VALUE;  
         for (int j=0; j<k; j++) {  
           if (dp[j]<=v1) {  
             m2=m1;  
             m1=j;  
             v2=v1;  
             v1=dp[j];  
           }  
           else if (dp[j]<=v2) {  
             m2=j;  
             v2=dp[j];  
           }  
         }  
         for (int j=0; j<k; j++) dp[j]=costs[i][j]+((j==m1)?v2:v1);  
       }  
     }  
     int res=Integer.MAX_VALUE;  
     for (int j=0; j<k; j++) res=Math.min(res,dp[j]);  
     return res;  
   }  
 }