(M)Dynamic Programming:95. Unique Binary Search Trees II

递归方法：找到一个数作为根结点，剩余的数分别划入左子树或者右子树。

class Solution {
public:
vector<TreeNode *> generateTrees(int n) {
if(n == 0)
{
vector<TreeNode*> v;
return v;
}
return createTree(1,n);
}

vector<TreeNode *> createTree(int start, int end)
{
vector<TreeNode *> results;
if(start>end)
{
results.push_back(NULL);
return results;
}

for(int k=start;k<=end;k++)
{
vector<TreeNode *> left = createTree(start,k-1);
vector<TreeNode *> right = createTree(k+1,end);
for(int i=0;i<left.size();i++)
{
for(int j=0;j<right.size();j++)
{
TreeNode * root = new TreeNode(k);
root->left = left[i];
root->right = right[j];
results.push_back(root);
}
}
}
return results;
}
}; 动态规划方法：
class Solution {
public:
TreeNode* clone(TreeNode* root){
if(root == nullptr)
return nullptr;
TreeNode* newroot = new TreeNode(root->val);
newroot->left = clone(root->left);
newroot->right = clone(root->right);
return newroot;
}
vector<TreeNode *> generateTrees(int n) {
if(n == 0)
{
vector<TreeNode*> res;
return res;
}
vector<TreeNode *> res(1,nullptr);
for(int i = 1; i <= n; i++){
vector<TreeNode *> tmp;
for(int j = 0; j<res.size();j++){
TreeNode* oldroot = res[j];
TreeNode* root = new TreeNode(i);
TreeNode* target = clone(oldroot);
root->left = target;
tmp.push_back(root);

if(oldroot!=nullptr){
TreeNode* tmpold = oldroot;
while(tmpold->right!=nullptr){
TreeNode* nonroot = new TreeNode(i);
TreeNode *tright = tmpold->right;
tmpold->right = nonroot;
nonroot->left = tright;
TreeNode *target = clone(oldroot);
tmp.push_back(target);
tmpold->right = tright;
tmpold = tmpold->right;
}
tmpold->right = new TreeNode(i);
TreeNode *target = clone(oldroot);
tmp.push_back(target);
tmpold->right = nullptr;
}
}
res=tmp;
}
return res;
}
};