HDOJ 2802 F(N)

Problem Description

Giving the N, can you tell me the answer of F(N)?

Input
Each test case contains a single integer N(1<=N<=10^9). The input is terminated by a set starting with N = 0. This set should not be processed.

Output
For each test case, output on a line the value of the F(N)%2009.

Sample Input
1
2
3
0

Sample Output
1
7
20

一般这种让根据公式求出对应项的值得题都有规律 （有一个循环，此题的循环为4018（注意 这种有循环规律的是让你输出对应项对某个数取余后的题））可以先打表写出有限个数的结果，再观察规律，或者直接写代码判断是否进入了循环。

import java.math.BigDecimal;
import java.util.Scanner;

public class Main {
    static int[] f = new int[10000];
    public static void main(String[] args) {
        f[1]=1;
        f[2]=7;
        for(int i=3;i<=4018;i++){
            f[i] = (f[i-2]-((i-1)*(i-1)*(i-1))+(i*i*i))%2009;
            //System.out.println(i+" "+f[i]);
        }
        Scanner sc = new Scanner(System.in);
        while(sc.hasNext()){
            int n = sc.nextInt();
            if(n==0)
                return ;
//          for(int i=3;i<100000;i+=2){
//              if(f[i]==1&&f[i+1]==7){
//                  System.out.println(i-1);
//                  break;
//              }
//          }
            //判断多久开始循环
            System.out.println(f[n%4018]);
        }

    }

}