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, and you need to cost the least. Return the minimum cost.

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.

Example

Example 1:

Input: [[14,2,11],[11,14,5],[14,3,10]]
Output: 10
Explanation: Paint house 0 into blue, paint house 1 into green, paint house 2 into blue. Minimum cost: 2 + 5 + 3 = 10.

Example 2:

Input: [[1,2,3],[1,4,6]]
Output: 3

Notice

All costs are positive integers.

分析

从前一栋房子里另外几个颜色选最小

class Solution:
    """
    @param costs: n x 3 cost matrix
    @return: An integer, the minimum cost to paint all houses
    """
    def minCost(self, costs):
        # write your code here
        if not costs:
            return  0 
        n = len(costs)
        
        for i in range(1,n):
            costs[i][0] = costs[i][0] + min(costs[i-1][1],costs[i-1][2])
            costs[i][1] = costs[i][1] + min(costs[i-1][0],costs[i-1][2])
            costs[i][2] = costs[i][2] + min(costs[i-1][0],costs[i-1][1])
            
        return min(costs[n-1])