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

----------------------- thinking ----------------------------------

https://oj.leetcode.com/discuss/9790/java-solution-with-dp

------------------------- codes -----------------------------------
/**
 * 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 *> trees[n+1];
        trees[0].push_back(NULL);
        trees[1].push_back(new TreeNode(1));
        for (int i = 2; i <n+1; i++) {
            for (int j = 1; j <= i; j++) {
                for (int left = 0; left < trees[j-1].size(); left++) {
                    for (int right = 0; right < trees[i-j].size(); right++) {
                        TreeNode *newroot = new TreeNode(j);
                        //trick here, we don't need to clone the left side trees since they are kepted the same
                        newroot->left = trees[j-1][left];
                        newroot->right = cloneTree(trees[i-j][right], j);
                        trees[i].push_back(newroot);
                    }
                }
            }
        }
        return trees[n];
    }
    TreeNode * cloneTree(TreeNode* root, int offset) {
        if (root == NULL) {
            return NULL;
        }
        TreeNode *newroot = new TreeNode(root->val + offset);
        newroot->left = cloneTree(root->left, offset);
        newroot->right = cloneTree(root->right, offset);
        return newroot;
    }
};