Unique Binary Search Trees

Given n, how many structurally unique BST's (binary search trees) that store values 1...n?

难度：medium

Solution: Dynamic Programming

public class Solution {
    public int numTrees(int n) {
        int[] trees = new int[n + 1];
        trees[0] = 1;
        trees[1] = 1;
        for(int i = 2; i <= n; ++i) {
            for(int j = 1; j <= i; ++j) {
                trees[i] += trees[j - 1] * trees[i - j];
            }
        }
        return trees[n];
    }
}

Unique Binary Search Trees II

Given an integer n, generate all structurally unique BST's (binary search trees) that store values 1...n.

难度：medium

Solution: Recursive

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
public class Solution {
    public List<TreeNode> generateTrees(int n) {
        if(n < 1) {
            return new ArrayList<TreeNode>();
        }
        return generateTreesHelper(1, n);
    }
    private List<TreeNode> generateTreesHelper(int start, int end) {
        List<TreeNode> res = new ArrayList<>();
        if(start > end) {
            res.add(null);
            return res;
        }
        for(int i = start; i <= end; ++i) {
            List<TreeNode> lefts = generateTreesHelper(start, i - 1);
            List<TreeNode> rights = generateTreesHelper(i + 1, end);
            for(TreeNode left : lefts) {
                for(TreeNode right : rights) {
                    TreeNode root = new TreeNode(i);
                    root.left = left;
                    root.right = right;
                    res.add(root);
                }
            }
        }
        return res;
    }
}