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.

Solution:

The last two fences could be either the same color or different color.

Therefore, at any fence i, the number of ways to paint is the way ends with two same color + the way ends with two different colors.

The time complexity is O(n) and the space complexity is O(1).



Color:

public class Solution {
    public int numWays(int n, int k) {
        if (n == 0) {
            return 0;
        }
        if (n == 1) {
            return k;
        }
        int diff = k * (k - 1);
        int same = k;
        for (int i = 2; i < n; i++) {
            int tmpdiff = diff;
            diff = (diff + same) * (k - 1);
            same = tmpdiff;
        }
        return same + diff;
    }
}