Leetcode 95. Unique Binary Search Trees II

Given an integer 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

s思路：

1. 列举所有可能，那还是backtracking. 但又和普通的backtrack不一样。不一样的地方是，这回是构建BST,以前都是枚举所有的vector。for循环里，对每个数遍历，把这个数的左侧和右侧的数分别recursive得到所有左子树和右子树的根节点，然后在用双重for来组装即可！

//
class Solution {
public:

vector<TreeNode*> helper(int start,int end){

if(start>end) return {NULL};//
vector<TreeNode*> res;
for(int i=start;i<=end;i++){
vector<TreeNode*> l=helper(start,i-1);
vector<TreeNode*> r=helper(i+1,end);
for(int j=0;j<l.size();j++){
for(int k=0;k<r.size();k++){
TreeNode* root=new TreeNode(i);
root->left=l[j];
root->right=r[k];
res.push_back(root);
}
}
}
return res;

}
vector<TreeNode*> generateTrees(int n) {
//
vector<TreeNode*> res;
if(n==0) return res;
return helper(1,n);
}
};