LeetCode95 Unique Binary Search Trees II

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

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：

这个题比前一道难在要构造出具体的树。但基本思路还是一样，枚举根节点，递归调用生成左右子树，然后左右子树结果组合在一个得到所有结果。

代码：

/**
 * 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 {
private:
    vector<TreeNode*> helper(int start, int end) {
        if (start > end) {
            return vector<TreeNode*>{nullptr};
        }
        if (start == end) {
            TreeNode* root = new TreeNode(start);
            return vector<TreeNode*>{root};
        }
        vector<TreeNode*> result;
        for (int i = start; i <= end; ++i) {
            vector<TreeNode*> leftV = helper(start, i - 1);
            vector<TreeNode*> rightV = helper(i + 1, end);
            for (int j = 0; j < leftV.size(); ++j) {
                for (int k = 0; k < rightV.size(); ++k) {
                    TreeNode* root = new TreeNode(i);
                    root -> left = leftV[j];
                    root -> right = rightV[k];
                    result.push_back(root);
                }
            }
        }
        return result;
    }
public:
    vector<TreeNode*> generateTrees(int n) {
        vector<TreeNode*> result;
        if (n == 0) {
            return result;
        }
        result = helper(1, n);
        return result;
    }
};