[LeetCode] Unique Binary Search Trees II
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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[Analysis]
对于大小为n的BST,轮流让 i (0 <= i <= n)作为根,当i为根时,左子树由1~i-1这些数组成,右子树由i+1~n这些数组成。
[Solution]
class Solution {
public:
// generate trees between start and end
vector<TreeNode *> generateTrees(int start, int end) {
// Start typing your C/C++ solution below
// DO NOT write int main() function
vector<TreeNode *> res;
// null node
if(start > end){
res.push_back(NULL);
}
// root node
else if(start == end){
TreeNode *root = new TreeNode(start);
res.push_back(root);
}
else{
// root node could be 1~n
for(int i = start; i <= end; ++i){
// generate left brunch and right brunch
vector<TreeNode *> leftTrees = generateTrees(start, i-1);
vector<TreeNode *> rightTrees = generateTrees(i+1, end);
// both left brunch and right brunch are null
if(leftTrees.size() == 0 && rightTrees.size() == 0){
// create root node
TreeNode *root = new TreeNode(i);
res.push_back(root);
}
// left brunch is null
else if(leftTrees.size() == 0){
for(int j = 0; j < rightTrees.size(); ++j){
// create root node
TreeNode *root = new TreeNode(i);
root->right = rightTrees[j];
res.push_back(root);
}
}
// right brunch is null
else if(rightTrees.size() == 0){
for(int j = 0; j < leftTrees.size(); ++j){
// create root node
TreeNode *root = new TreeNode(i);
root->left = leftTrees[j];
res.push_back(root);
}
}
// both left brunch and right brunch are not null
else{
for(int j = 0; j < leftTrees.size(); ++j){
for(int k = 0; k < rightTrees.size(); ++k){
// create root node
TreeNode *root = new TreeNode(i);
root->left = leftTrees[j];
root->right = rightTrees[k];
res.push_back(root);
}
}
}
}
}
return res;
}
// generate trees
vector<TreeNode *> generateTrees(int n) {
// Start typing your C/C++ solution below
// DO NOT write int main() function
return generateTrees(1, n);
}
};
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