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

/** * Definition for binary tree * struct TreeNode { *     int val; *     TreeNode *left; *     TreeNode *right; *     TreeNode(int x) : val(x), left(NULL), right(NULL) {} * }; */struct TreeNode{	int val;	TreeNode *left;	TreeNode *right;	TreeNode(int x) : val(x), left(NULL), right(NULL) {}};class Solution {public:    std::vector
     
       generateTrees(int n) {        return dfs(0,n-1);    }private:	std::vector
      
        dfs(int n, int m)	{		std::vector
       
         res;		if(n > m)		{			res.push_back(NULL);			return res;		}		for (int i = n; i <= m; i++)		{			std::vector
        
          left = dfs(n,i-1);			std::vector
         
           right= dfs(i+1,m);			for (int j = 0; j < left.size(); j++)			{				for (int k = 0; k < right.size(); k++)				{					TreeNode *node = new TreeNode(i+1);					res.push_back(node);					node->left = left[j];					node->right= right[k];				}			}		}		return res;	}};