96.Unique-Binary-Search-Trees

96. Unique Binary Search Trees

题目地址

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

题目描述

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

Example:
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

代码

Approach #1 Dynamic Programming

class Solution {
  public int numTrees(int n) {
        int[] dp = new int[n + 1];
    dp[0] = 1;
    dp[1] = 1;

    for (int i = 2; i <= n; i++) {
      for (int j = 1; j <= i; j++) {
        dp[i] += dp[j - 1] * dp[i - j];
      }
    }

    return dp[n];
  }
}

Approach #2 Mathematical Deduction

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