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【LeetCode】Unique Binary Search Trees II

Unique Binary Search Trees II

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

 

由于1~n是升序列,因此建起来的树天然就是BST。

递归思想,依次选择根节点,对左右子序列再分别建树。

由于左右子序列建树的结果也可能不止一种,需要考虑所有搭配情况。

/** * 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;        }        else         {            return Helper(1, n);        }    }    vector<TreeNode*> Helper(int begin, int end)    {        vector<TreeNode*> res;        if(begin > end)        {            res.push_back(NULL);            return res;        }        else if(begin == end)        {            TreeNode* root = new TreeNode(begin);            res.push_back(root);            return res;        }        else        {            for(int i = begin; i <= end; i ++)            {                //tag                vector<TreeNode*> left = Helper(begin, i-1);                vector<TreeNode*> right = Helper(i+1, end);                for(int l = 0; l < left.size(); l ++)                {//all BST in left                    for(int r = 0; r < right.size(); r ++)                    {//all BST in right                        //new root here! not the tag position.                        TreeNode* root = new TreeNode(i);                        root->left = left[l];                        root->right = right[r];                        res.push_back(root);                    }                }                            }            return res;        }    }};

【LeetCode】Unique Binary Search Trees II