276. Paint Fence

There is a fence with n posts, each post can be painted with one of the k colors.

You have to paint all the posts such that no more than two adjacent fence posts have the same color.

Return the total number of ways you can paint the fence.

Note:
n and k are non-negative integers.

 此题用动态规划来解题，遇到动态规划题目时候，先找状态方程，假设要求第i个post的颜色种类，那么需要知道什么呢，条件是不能有超过两个相邻的fence的颜色相同的，那么就要分两种情况考虑了，第一种是如果前两个颜色不同，那么后面的颜色就是前面的颜色种类*k，还有一种就是如果前面两个颜色相同，后面的颜色就是（k-1）种了，代码如下：

 

public class Solution {

    public int numWays(int n, int k) {

        if(n==0) return 0;

        else if(n==1) return k;

        int same = k;

        int different =k*(k-1);

        for(int i=2;i<n;i++){

            int temp = different;

            different  =(different+same)*(k-1);

            same = temp;

        }

        return different+same;

    }

}