the head of the sequence is the root of the tree, and the rest numbers greater than the head are its right children, when we insert a new number, such as 4, we only need to insert it before its right children, or as a new head. you can imagine how to add a greater number in the real BST.`enter code here`

the first sequence is "1",

and for each number i from 2 to n, we insert this i into each sequence to generate a new sequence, the insert position is before a number that greater or equal to the head of this sequence.

such as insert 2 to "1", because the the first number 1 >=1, so the new sequence is "21", we create this new sequence and append to the end, we also modify the original sequence by append the i at the end, as "12", so the result is "12","21"

we continue insert the 3 to "12","21", to insert 3 to "12", because 1>=1, so "312",because 2 >1, so "132", and then append the 3 at the end so "123", so we get "312","132","123"

to insert 3 to "21", we get "321", because 1<2, so we don't insert 3 between 2 and 1. then we append the 3 at the end to get "213". the final result is "312","132","123","321","213".

I test my program can get the correct result, but I don't know why it cannot pass the test.

```
void InsertTreeNode(TreeNode* root, int num)
{
if (root->val > num)
{
if (root->left == NULL)
{
root->left = new TreeNode(num);
}
else {
InsertTreeNode(root->left, num);
}
}
else {
if (root->right == NULL)
{
root->right = new TreeNode(num);
}
else {
InsertTreeNode(root->right, num);
}
}
}
vector<TreeNode *> generateTrees(int n) {
vector<TreeNode *> trees;
if (n < 1)
{
return trees;
}
vector<vector<int>*> seqnumbers;
int seqSize = 1;
seqnumbers.push_back(new vector<int>);
seqnumbers[0]->push_back(1);
for (int i = 2; i <= n; i++)
{
unsigned int size = seqnumbers.size();
for (unsigned int j = 0; j < size; j++)
{
vector<int> *pSeq = seqnumbers[j];
int rightChildnum = 0;
for (unsigned int k = 0; k < pSeq->size(); k++)
{
if (pSeq->at(k) > rightChildnum)
{
vector<int> *pNew = new vector<int>(*pSeq);
pNew->insert(pNew->begin() + k, i);
seqnumbers.push_back(pNew);
rightChildnum = pSeq->at(k);
}
}
pSeq->push_back(i);
}
}
for (unsigned int i = 0; i < seqnumbers.size(); i++)
{
vector<int> * pSeq = seqnumbers[i];
printNumbers(*pSeq);
TreeNode *root = new TreeNode(pSeq->at(0));
for (unsigned int j = 1; j < pSeq->size(); j++)
{
InsertTreeNode(root, pSeq->at(j));
}
trees.push_back(root);
}
for (unsigned int i = 0; i < seqnumbers.size(); i++)
{
delete seqnumbers[i];
}
return trees;
}
```

]]>the head of the sequence is the root of the tree, and the rest numbers greater than the head are its right children, when we insert a new number, such as 4, we only need to insert it before its right children, or as a new head. you can imagine how to add a greater number in the real BST.`enter code here`

the first sequence is "1",

and for each number i from 2 to n, we insert this i into each sequence to generate a new sequence, the insert position is before a number that greater or equal to the head of this sequence.

such as insert 2 to "1", because the the first number 1 >=1, so the new sequence is "21", we create this new sequence and append to the end, we also modify the original sequence by append the i at the end, as "12", so the result is "12","21"

we continue insert the 3 to "12","21", to insert 3 to "12", because 1>=1, so "312",because 2 >1, so "132", and then append the 3 at the end so "123", so we get "312","132","123"

to insert 3 to "21", we get "321", because 1<2, so we don't insert 3 between 2 and 1. then we append the 3 at the end to get "213". the final result is "312","132","123","321","213".

I test my program can get the correct result, but I don't know why it cannot pass the test.

```
void InsertTreeNode(TreeNode* root, int num)
{
if (root->val > num)
{
if (root->left == NULL)
{
root->left = new TreeNode(num);
}
else {
InsertTreeNode(root->left, num);
}
}
else {
if (root->right == NULL)
{
root->right = new TreeNode(num);
}
else {
InsertTreeNode(root->right, num);
}
}
}
vector<TreeNode *> generateTrees(int n) {
vector<TreeNode *> trees;
if (n < 1)
{
return trees;
}
vector<vector<int>*> seqnumbers;
int seqSize = 1;
seqnumbers.push_back(new vector<int>);
seqnumbers[0]->push_back(1);
for (int i = 2; i <= n; i++)
{
unsigned int size = seqnumbers.size();
for (unsigned int j = 0; j < size; j++)
{
vector<int> *pSeq = seqnumbers[j];
int rightChildnum = 0;
for (unsigned int k = 0; k < pSeq->size(); k++)
{
if (pSeq->at(k) > rightChildnum)
{
vector<int> *pNew = new vector<int>(*pSeq);
pNew->insert(pNew->begin() + k, i);
seqnumbers.push_back(pNew);
rightChildnum = pSeq->at(k);
}
}
pSeq->push_back(i);
}
}
for (unsigned int i = 0; i < seqnumbers.size(); i++)
{
vector<int> * pSeq = seqnumbers[i];
printNumbers(*pSeq);
TreeNode *root = new TreeNode(pSeq->at(0));
for (unsigned int j = 1; j < pSeq->size(); j++)
{
InsertTreeNode(root, pSeq->at(j));
}
trees.push_back(root);
}
for (unsigned int i = 0; i < seqnumbers.size(); i++)
{
delete seqnumbers[i];
}
return trees;
}
```

]]>