LeetCode Online Judge 题目C# 练习 - Unique Binary Search Trees

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 

 1         public static int UniqueBinarySearchTrees(int n)
 2         {
 3             if (n <= 1)
 4                 return 1;
 5 
 6             int left, right, sum = 0;
 7 
 8             for (int i = 1; i <= n; i++)
 9             {
10                 // BST, smaller than the root go left
11                 left = UniqueBinarySearchTrees(i - 1);
12                 // greater than the root go right
13                 right = UniqueBinarySearchTrees(n - i);
14 
15                 sum += left * right;
16             }
17 
18             return sum;
19         }

代码分析：

　　关于树的，十有八九用递归。