[LintCode] paint fence

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.

思路：在前面n-1个正确地用了k种颜色的情况下，第n个用k种不同颜色，减去 

在前n-3正确地使用了k种颜色的情况下，n-1,n-2,n三个用相同颜色(且这个颜色将与第n-3个不一样）

也就是递推为：numWays(n, k) = numWays(n - 1,k) * k - numWays(n - 3,k) * (k - 1)

代码如下（C++）(注意当n=3时，n-1,n-2是可以选择k种颜色的)

class Solution {
public:
    /**
     * @param n non-negative integer, n posts
     * @param k non-negative integer, k colors
     * @return an integer, the total number of ways
     */
    int numWays(int n, int k) {
        // Write your code here
        if (n == 1)
        return k;
        if (n == 2)
        return k * k;
        else if (k == 1 && n < 3 || n <= 0)
        return 1;
        else if (k == 1 && n > 2 )
        return 0;
        else if (n > 3){
        return (numWays(n - 1,k) * k - numWays(n - 3,k) * (k - 1)); 
        }
        else 
        return (numWays(n - 1,k) * k - numWays(n - 3,k) * k);
       
    }
    
};