2022.03.22 87日目

白駿13699号(点火式)

質問する

t(0)=1
t(n)=t(0)*t(n-1)+t(1)*t(n-2)+...+t(n-1)*t(0)

t(1)=t(0)*t(0)=1
t(2)=t(0)*t(1)+t(1)*t(0)=2
t(3)=t(0)*t(2)+t(1)*t(1)+t(2)*t(0)=5
...

私の答え

import java.io.*;
import java.util.*;

public class Main {
    static long[] dp;
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

        int n = Integer.parseInt(br.readLine());

        dp = new long[n + 1];
        dp[0] = 1;

        for (int i = 1; i <= n; i++) {
            long temp = 0;
            for (int j = i; j >= 1; j--) {
                temp += dp[i - j] * dp[j - 1];
            }
            dp[i] = temp;
        }

        System.out.println(dp[n]);
    }
}

考える