LeetCode: 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.

public class PaintFence {

public static int numWays(int n, int k) {
int[] ways = new int[n+1];
//k colors, 0 fences
ways[0] = 0;
//k colors, 1 fence
//diff colors = 0, same color = k
ways[1] = k;
//k colors, 2 fences
//diff colors = k*(k-1)
//same color = k, total = diff + same
ways[2] = k*k;
//iteratively use the relation, ways[i] = ways
for(int i=3;i<=n; i++){
ways[i] = (ways[i-1] + ways[i-2])*(k-1);
}
return ways[n];
}

    public int numWays(int n, int k) {
        if(n <= 0) {
            return 0;
        }
     
        int sameColorCounts = 0;
        int differentColorCounts = k;
     
        for(int i = 2; i <= n; i++) {
            int temp = differentColorCounts;

            differentColorCounts = (sameColorCounts + differentColorCounts) * (k - 1);

            sameColorCounts = temp;
        }
     
        return sameColorCounts + differentColorCounts;
    }
}