Unique Binary Search Trees

1. Title

Unique Binary Search Trees

2.   Http address

https://leetcode.com/problems/unique-binary-search-trees/

3. The question

Given n, how many structurally unique BST's (binary search trees) that store values 1...n?

For example,
Given n = 3, there are a total of 5 unique BST's.

   1         3     3      2      1
    \       /     /      / \      \
     3     2     1      1   3      2
    /     /       \                 \
   2     1         2                 3

4 My code (AC)
 1 public class UniqueBinarySearchTrees {
 2 
 3     public static void main(String[] args) {
 4         // TODO Auto-generated method stub
 5         System.out.println(numTrees(50));
 6     }
 7     
 8     // Accepted
 9       public static int numTrees(int n) {
10           
11           if ( n == 0)
12               return 0;
13           if ( n == 1)
14               return 1;
15           if ( n == 2)
16               return 2;
17           if ( n == 3)
18                return 5;
19           int sum;
20           int opt[] = new int[n+1];
21           opt[1] = 1;
22           opt[2] = 2;        // n == 2;
23           opt[3] = 5;        // n == 3;
24           for( int i = 4; i <= n; i++)
25           {
26               // sum =  [opt(1) * opt(n-2) +   opt(3) * opt ( n-3)  ..... + opt（n-1) * opt(1)]  n = i -2;
27               sum = 0;
28               for( int j = 1; j <= i - 2; j++)
29               {
30                   sum += opt[j] * opt[i-j-1];
31               }
32              opt[i] = 2 * opt[i-1] + sum;
33           }
34           return opt[n];
35         }
36 
37 }

 

posted @ 2015-11-01 18:01  ordi  阅读(100)  评论(0)  编辑  收藏  举报