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1. Catalan number problem

Description

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

Question Link

https://leetcode.com/problems/unique-binary-search-trees/description/

Example I

Input: 3
Output: 5
Explanation:
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

Questions

• LeetCode - 96. Unique Binary Search Trees

Analysis

Transform Function

Solution I

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

Solution II

class Solution {
    public int numTrees(int n) {
        long res = 1;
        for(int i = 0; i < n; i++) {
            res = res * 2 * (2 * i + 1) / (i + 2);
        }
        return (int)res;
    }
}