LeetCode OJ ：Unique Binary Search Trees II（唯一二叉搜索树）

题目如下所示：返回的结果是一个Node的Vector：

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
　　
树节点的定义是下面这样的

 1 /**
 2  * Definition for a binary tree node.
 3  * struct TreeNode {
 4  *     int val;
 5  *     TreeNode *left;
 6  *     TreeNode *right;
 7  *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 8  * };
 9  */
10 class Solution {
11 public:
12     vector<TreeNode*> generateTrees(int n) {
13         return createNode(1, n);
14     }
15     
16     vector<TreeNode*> createNode(int start, int end)
17     {
18         vector<TreeNode*> result;
19         if(start > end){
20             result.push_back(NULL);
21             return result;
22         }
23         for(int i = start; i <= end; ++i){
24             vector<TreeNode*> leftNode = createNode(start, i - 1);
25             vector<TreeNode*> rightNode = createNode(i + 1, end);
26             for(int j = 0; j < leftNode.size(); ++j){
27                 for(int k = 0; k < rightNode.size(); ++k){
28                     TreeNode * tmpNode = new TreeNode(i);
29                     tmpNode->left = leftNode[j];　　
30                     tmpNode->right = rightNode[k];
31                     result.push_back(tmpNode);
32                 }
33             }
34         }
35         return result;
36     }
37 };

这一题实际上更另外一个叫做different ways to add parentheses的题目比较相似，这个详见上一篇博文。

java版本的代码如下：

 1 /**
 2  * Definition for a binary tree node.
 3  * public class TreeNode {
 4  *     int val;
 5  *     TreeNode left;
 6  *     TreeNode right;
 7  *     TreeNode(int x) { val = x; }
 8  * }
 9  */
10 public class Solution {
11     public List<TreeNode> generateTrees(int n) {
12         if(n == 0)//如果不加上这一条，当为0的时候会返回[[]]，不知道为什么，很奇怪
13             return new ArrayList<TreeNode>();
14         return createTree(1, n);
15     }
16 
17     public List<TreeNode> createTree(int start, int end){
18         ArrayList<TreeNode> result = new ArrayList<TreeNode>();
19         if(start > end){
20             result.add(null);
21             return result;
22         }
23         for(int i = start; i <= end; ++i){
24             for(TreeNode leftNode : createTree(start, i - 1)){
25                 for(TreeNode rightNode : createTree(i + 1, end)){
26                     TreeNode node = new TreeNode(i);
27                     node.left = leftNode;
28                     node.right = rightNode;
29                     result.add(node);
30                 }
31             }
32         }
33         return result;
34     }
35 }