## Unique Binary Search Trees II

### 描述

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


### 代码

// Unique Binary Search Trees II
// 时间复杂度TODO，空间复杂度TODO
class Solution {
public:
vector<TreeNode *> generateTrees(int n) {
if (n == 0) return vector<TreeNode*>();
return generate(1, n);
}
private:
vector<TreeNode *> generate(int start, int end) {
vector<TreeNode*> subTree;
if (start > end) {
subTree.push_back(nullptr);
return subTree;
}
for (int k = start; k <= end; k++) {
vector<TreeNode*> leftSubs = generate(start, k - 1);
vector<TreeNode*> rightSubs = generate(k + 1, end);
for (auto i : leftSubs) {
for (auto j : rightSubs) {
TreeNode *node = new TreeNode(k);
node->left = i;
node->right = j;
subTree.push_back(node);
}
}
}
return subTree;
}
};