95,Unique Binary Search Trees II
Given an integer n, return all the structurally unique BST’s (binary search trees), which has exactly n nodes of unique values from 1 to n. Return the answer in any order.
Example 1:
Input: n = 3
Output: [[1,null,2,null,3],[1,null,3,2],[2,1,3],[3,1,null,null,2],[3,2,null,1]]
Example 2:
Input: n = 1
Output: [[1]]
Constraints:
1 <= n <= 8
class Solution {
public LinkedList<TreeNode> generate_trees(int start, int end) {
LinkedList<TreeNode> all_trees = new LinkedList<TreeNode>();
if (start > end) {
all_trees.add(null);
return all_trees;
}
// pick up a root
for (int i = start; i <= end; i++) {
// all possible left subtrees if i is choosen to be a root
LinkedList<TreeNode> left_trees = generate_trees(start, i - 1);
// all possible right subtrees if i is choosen to be a root
LinkedList<TreeNode> right_trees = generate_trees(i + 1, end);
// connect left and right trees to the root i
for (TreeNode l : left_trees) {
for (TreeNode r : right_trees) {
TreeNode current_tree = new TreeNode(i);
current_tree.left = l;
current_tree.right = r;
all_trees.add(current_tree);
}
}
}
return all_trees;
}
public List<TreeNode> generateTrees(int n) {
if (n == 0) {
return new LinkedList<TreeNode>();
}
return generate_trees(1, n);
}
}
96,Unique Binary Search Trees
Given an integer n, return the number of structurally unique BST’s (binary search trees) which has exactly n nodes of unique values from 1 to n.
Example 1:
Input: n = 3
Output: 5
Example 2:
Input: n = 1
Output: 1
public class Solution {
public int numTrees(int n) {
int[] G = new int[n + 1];
G[0] = 1;
G[1] = 1;
for (int i = 2; i <= n; ++i) {
for (int j = 1; j <= i; ++j) {
G[i] += G[j - 1] * G[i - j];
}
}
return G[n];
}
}
