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.
1 public class Solution { 2 public int NumWays(int n, int k) { 3 if (n < 1 || k < 1) return 0; 4 if (n == 1) return k; 5 6 int dpSame = k, dpDifferent = k * (k - 1); 7 8 for (int i = 2; i < n; i++) 9 { 10 var tmp = dpSame; 11 dpSame = dpDifferent; 12 dpDifferent = (tmp + dpDifferent) * (k - 1); 13 } 14 15 return dpSame + dpDifferent; 16 } 17 18 private int DFS(int n, int k, int start, int cur, bool sameColor) 19 { 20 if (start >= n) 21 { 22 return cur; 23 } 24 25 if (sameColor) 26 { 27 return DFS(n, k, start + 1, cur * (k - 1), false); 28 } 29 else 30 { 31 return DFS(n, k, start + 1, cur, true) + DFS(n, k, start + 1, cur * (k - 1), false); 32 } 33 } 34 } 35 36 // DFS, timeout 37 public class Solution1 { 38 public int NumWays(int n, int k) { 39 if (n < 1 || k < 1) return 0; 40 41 return DFS(n, k, 1, k, false); 42 } 43 44 private int DFS(int n, int k, int start, int cur, bool sameColor) 45 { 46 if (start >= n) 47 { 48 return cur; 49 } 50 51 if (sameColor) 52 { 53 return DFS(n, k, start + 1, cur * (k - 1), false); 54 } 55 else 56 { 57 return DFS(n, k, start + 1, cur, true) + DFS(n, k, start + 1, cur * (k - 1), false); 58 } 59 } 60 }
