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.

樣例:

Given n=3, k=2 return 6

     post 1,   post 2, post 3
way1    0         0       1 
way2    0         1       0
way3    0         1       1
way4    1         0       0
way5    1         0       1
way6    1         1       0

分析：

影響第n種的顏色的是第n-1與第n-2種顏色的，因此可能性都為k-1種
因此得到如下遞推式:maxWays[n] = (k - 1) * (maxWays[n - 1] + maxWays[n - 2]);

public class Solution {
    /**
     * @param n non-negative integer, n posts
     * @param k non-negative integer, k colors
     * @return an integer, the total number of ways
     */
   public int numWays(int n, int k) {
        if(n == 0 || k == 0)
            return 0;
        if(n == 1)
            return k;
        
        int[] maxWays = new int[n + 1];
        maxWays[0] = 0;
        maxWays[1] = k;
        maxWays[2] = k * k;
        for(int i = 3;i <= n;i ++)
        {
            maxWays[i] = (k - 1) * (maxWays[i - 1] + maxWays[i - 2]);
        }
        
        return maxWays[n];
    }
}