leetcode 265 Paint House II

problem:

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?

解題思路：

WTF！！！！！！！！！！！！！！！！！！！！！！！！！！！！！！！！！！！！
想不出來。這裡原來的3種顏色變成了K種，按照之前的寫法無法達到nk.去看了看大神的想法.晚點再補程式碼。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。。

The idea is similar to the problem Paint House I, for each house and each color, the minimum cost of painting the house with that color should be the minimum cost of painting previous houses, and make sure the previous house doesn't paint with the same color.

We can use min1 and min2 to track the indices of the 1st and 2nd smallest cost till previous house, if the current color's index is same as min1, then we have to go with min2, otherwise we can safely go with min1.

The code below modifies the value of costs[][] so we don't need extra space.