题目描述：

Given n, generate all structurally unique BST‘s (binary search trees) that store values 1...n.

For example,
Given n = 3, your program should return all 5 unique BST‘s shown below.

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

思路分析：分别让1-n做root。当root为i时，左子树由1~i-1组成，右子树由i+1~n组成。采用递归的方法分别对左右子树求解，再将左右子树所有可能的解组合在一起，即可得到所有可能的BST。

代码：

vector<TreeNode *> getTrees(int start,int end)
{
    vector<TreeNode *> result;
    if(start > end)
    {
        result.push_back(NULL);
        return result;
    }
        
    if(start == end)
    {
        TreeNode * new_node = new TreeNode(start);
        result.push_back(new_node);
        return result;
    }
    for(int i = start;i <= end ;i++)
    {
        vector<TreeNode *> left = getTrees(start,i-1);
        vector<TreeNode *> right = getTrees(i+1,end);
        for(TreeNode * left_node:left)
            for(TreeNode * right_node:right)
        {
            TreeNode * new_node = new TreeNode(i);
            new_node->left = left_node;
            new_node->right = right_node;
            result.push_back(new_node);
        }
    }
    return result;
}

vector<TreeNode *> Solution::generateTrees(int n)
{
    return getTrees(1,n);
}

LeetCode:Unique Binary Search Trees II