Unique Binary Search Trees

Problem

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

Example

Given n = 3, there are a total of 5 unique BST's.

1           3    3       2      1 \         /    /       / \      \  3      2     1       1   3      2 /      /       \                  \2     1          2                  3

Note

DP

Solution

public class Solution {    public int numTrees(int n) {        int[] count = new int[n+1];        count[0] = 1;        for (int i = 1; i <= n; i++) {            for (int root = 1; root <= i; root++) {                int left = count[root-1];                int right = count[i-root];                count[i] += left*right;            }        }        return count[n];    }}

Unique Binary Search Trees II

Problem

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

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

Note

DFS

Solution

class Solution {    public List
    
      generateTrees(int n) {        if (n == 0) return new ArrayList<>();        return helper(1, n);    }    private List
     
       helper(int start, int end) {        List
      
        res = new ArrayList<>();        if (start > end) {            res.add(null);            return res;        }        for (int i = start; i <= end; i++) {            List
       
         left = helper(start, i-1);            List
        
          right = helper(i+1, end);            for (TreeNode leftNode: left) {                for (TreeNode rightNode: right) {                    TreeNode root = new TreeNode(i);                    root.left = leftNode;                    root.right = rightNode;                    res.add(root);                }            }        }        return res;    }}