276. Paint Fence

Posted 2020-08-21 鱼与海洋

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.

 

分析：第一块与第二块相同 lastsame ＝ k

         第一块与第二块不相同   lastdiff ＝ k * k－1

         第三块 两种情况 1.当1，2是相同颜色  same ＝ k   2. 1，2块不同颜色 diff ＝ k * (k-1)

               temp = lastsame * (k-1) + lastdiff * (k-1)

               lastsame  = last last diff (上两块fense颜色必须不同)

               lastdiff = temp （上两块可相同可不同，第三块与第二块必须不同）

 

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