276- Paint Fence  **My SubmissionsQuestion Editorial Solution

Total Accepted: 10079 Total Submissions: 31886 Difficulty: Easy

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.

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    public int numWays(int n, int k) {
     /* idea:  e.g.   n = 3, k = 2 (r,w)
         two fences, two color: (r, r), (r, w) (w, r), (w, w)
         diff2 = k * (k - 1) = 2 * ( 2- 1)  = 2
         same2 = k = 2
         total2 = diff2 + same2 = 2 + 2 = 4
         
         three fences, two color:
         same3 = diff2;
         diff3 = (total) * (k-1) = (diff2 + same2) * (k -1)
         ref: https://discuss.leetcode.com/topic/23426/o-n-time-java-solution-o-1-space
     */
       if(n == 0) {
           return 0;
       } else if(n == 1) {
           return k;
       }
       
      int diffCounts = k * (k -1) ; // n = 2
      int sameCounts = k;
      
      for (int i = 2 ; i < n; i++) {  // n > 2
          int temp = diffCounts;
          diffCounts = (diffCounts + sameCounts) * ( k - 1);
          sameCounts = temp;
      }
        return diffCounts + sameCounts;
    }