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

分析：

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<TreeNode *> generateTrees(int n) {
        vector<TreeNode*> res;
        if(n == 0){
            res.push_back(NULL);
            return res;
        }
        return generateTrees(1, n);
    }
private:
    vector<TreeNode *> generateTrees(int left, int right)
    {
        TreeNode *node(NULL);
        vector<TreeNode*> 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;
    }
};