Leetcode 96. Unique Binary Search Trees
Given n, how many structurally unique BST’s (binary search trees) that store values 1…n?
For example,
Given n = 3, there are a total of 5 unique BST’s.
class Solution {
public:
int numTrees(int n) {
int res[n+1] = {0};
res[0] = res[1] = 1;
for (int i=2; i<=n; i++)
for (int j=1; j<=i; j++)
res[i] += res[j-1] * res[i-j];
return res[n];
}
};
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
idea: 当数组为 1，2，3，4，.. i，.. n时，基于以下原则的BST建树具有唯一性 以i为根节点的树，其左子树由[1, i-1]构成， 其右子树由[i+1, n]构成。
class Solution {
public:
vector<TreeNode*> help_tree(int first, int last) {
vector<TreeNode*> res;
for (int root=first; root<last+1; root++) {
auto left = root==first ? vector<TreeNode*>{nullptr}:help_tree(first, root-1);
auto right = root==last ? vector<TreeNode*>{nullptr}:help_tree(root+1, last);
for (auto l:left)
for (auto r:right) {
TreeNode *node = new TreeNode(root);
node -> left = l;
node -> right = r;
res.push_back(node);
}
}
return res;
}
vector<TreeNode*> generateTrees(int n) {
return help_tree(1, n);
}
};