95. Unique Binary Search Trees II

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

Example:

Input: 3
Output:
[
  [1,null,3,2],
  [3,2,null,1],
  [3,1,null,null,2],
  [2,1,3],
  [1,null,2,null,3]
]
Explanation:
The above output corresponds to the 5 unique BST's shown below:

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

 

Approach #1: C++.

/**
 * Definition for a binary tree node.
 * 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) {
        if (n == 0) {
            return vector<TreeNode*>();
        } else {
            return generate_trees(1, n);
        }
    }
    
    vector<TreeNode*> generate_trees(int start, int end) {
        vector<TreeNode*> all_trees;
        if (start > end) {
            all_trees.push_back(NULL);
            return all_trees;
        }
        
        for (int i = start; i <= end; ++i) {
            vector<TreeNode*> left_trees = generate_trees(start, i - 1);
            vector<TreeNode*> right_trees = generate_trees(i + 1, end);
            
            for (TreeNode* l : left_trees) {
                for (TreeNode* r : right_trees) {
                    TreeNode* curr_tree = new TreeNode(i);
                    curr_tree->left = l;
                    curr_tree->right = r;
                    all_trees.push_back(curr_tree);
                }
            }
        }
        return all_trees;
    }
    
};