LeetCode #256. Paint House

题目描述：

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.

Example:

Input: [[17,2,17],[16,16,5],[14,3,19]]
Output: 10
Explanation: Paint house 0 into blue, paint house 1 into green, paint house 2 into blue. 
             Minimum cost: 2 + 5 + 3 = 10.

class Solution {
public:
    int minCost(vector<vector<int>>& costs) {
        int n=costs.size();
        if(n==0) return 0;
        vector<vector<int>> dp(n,vector<int>(3,0));
        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]=costs[i][0]+min(dp[i-1][1],dp[i-1][2]);
            dp[i][1]=costs[i][1]+min(dp[i-1][0],dp[i-1][2]);
            dp[i][2]=costs[i][2]+min(dp[i-1][0],dp[i-1][1]);
        }
        return min(dp[n-1][0],min(dp[n-1][1],dp[n-1][2]));
    }
};