题解 | 有多少个不同的二叉搜索树

#include <iostream>
#include <vector>
using namespace std;

int numTrees(int n) {
    vector<long long> dp(n + 1, 0);
    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];
}

int main() {
    int n;
    cin >> n;
    cout << numTrees(n) << endl;
    return 0;
}

import java.util.Scanner;

public class Main {
    public static int numTrees(int n) {
        long[] dp = new long[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 (int)dp[n];
    }
    
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        System.out.println(numTrees(n));
        sc.close();
    }
}

def num_trees(n):
    dp = [0] * (n + 1)
    dp[0] = dp[1] = 1
    
    for i in range(2, n + 1):
        for j in range(1, i + 1):
            dp[i] += dp[j-1] * dp[i-j]
    
    return dp[n]

n = int(input())
print(num_trees(n))