LeetCode----Unique Binary Search Trees 2

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

递归即可。枚举所有的 root 节点，root 的左子树和右子树就是两个子问题，递归求解。

但是有一点要注意，容易出错。

如果子树的节点个数为零，这时候返回的应该是一个包含 NULL 的 vector;

/**
 * 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
  
    generateTrees(int n) {
        vector
   
     res; if(n == 0){ res.push_back(NULL); return res; } return generateTrees(1, n); } private: vector
    
      generateTrees(int left, int right) { TreeNode *node(NULL); vector
     
       trees, left_tree, right_tree; if(left > right) { trees.push_back(NULL); return trees; } for(int i=left; i<=right; ++i) { left_tree = generateTrees(left, i-1); right_tree = generateTrees(i+1, right); for(auto j : left_tree) for(auto k : right_tree) { node = new TreeNode(i); node->left = j; node->right = k; trees.push_back(node); } } return trees; } };