给定结点数n,结点值为1,2,...,n,求由这些结点可以构成的所有二叉查找树。

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

思路:递归构造,分别构造出左,右子树,然后组合成来。

/**
* 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)
{
return generateTrees(1,n);
} vector<TreeNode *> generateTrees(int start, int end)
{
vector<TreeNode *> trees;
if (start > end)
{
trees.push_back(NULL);
return trees;
}
if (start==end)
{
trees.push_back(new TreeNode(start));
return trees;
} for (int i=start; i<=end; ++i)
{
vector<TreeNode *> treesleft = generateTrees(start,i-1);
vector<TreeNode *> treesright = generateTrees(i+1,end); for (size_t j=0; j<treesleft.size(); ++j)
{
for (size_t k=0; k<treesright.size(); ++k)
{
TreeNode *root = new TreeNode(i);
root->left = treesleft[j];
root->right = treesright[k];
trees.push_back(root);
}
}
} return trees;
}
};

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