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

confused what"{1,#,2,3}"means? > read more on how binary tree is serialized on OJ.
OJ's Binary Tree Serialization:

The serialization of a binary tree follows a level order traversal, where '#' signifies a path terminator where no node exists below.

Here's an example:

   1
  / \
 2   3
    /
   4
    \
     5

The above binary tree is serialized as"{1,2,3,#,#,4,#,#,5}".

/**
 * Definition for binary tree
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 * };
 */
class Solution {
public:
    vector<TreeNode *> generateTrees(int n) {
        return helper(1,n);
    }
    
    vector<TreeNode*> helper(int left,int right){
        vector<TreeNode*> ret;
        if(left > right) {
            ret.push_back(nullptr);
            return ret;
        }
        for(int i = left;i <= right;++i){
            vector<TreeNode*> left_tree = helper(left,i-1);
            vector<TreeNode*> right_tree = helper(i+1,right);
            for(int j = 0;j < left_tree.size();++j){
                for(int k = 0;k < right_tree.size();++k){
                    TreeNode* root = new TreeNode(i);
                    root->left = left_tree[j];
                    root->right = right_tree[k];
                    ret.push_back(root);
                }
            }
        }
        return ret;
    }
};