NYOJ148fibonacci数列(二)

fibonacci数列(二)

时间限制：1000 ms  |  内存限制：65535 KB

难度：3

 

描述

In the Fibonacci integer sequence, F₀ = 0, F₁ = 1, and F_n = F_{n − 1} + F_{n − 2} for n ≥ 2. For example, the first ten terms of the Fibonacci sequence are:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, …

An alternative formula for the Fibonacci sequence is

.

Given an integer n, your goal is to compute the last 4 digits of F_n.

 

Hint

As a reminder, matrix multiplication is associative, and the product of two 2 × 2 matrices is given by

.

Also, note that raising any 2 × 2 matrix to the 0th power gives the identity matrix:

.

 

 

输入

The input test file will contain multiple test cases. Each test case consists of a single line containing n (where 0 ≤ n ≤ 1,000,000,000). The end-of-file is denoted by a single line containing the number −1.

输出

For each test case, print the last four digits of Fn. If the last four digits of Fn are all zeros, print ‘0’; otherwise, omit any leading zeros (i.e., print Fn mod 10000).

样例输入

0
9
1000000000
-1

样例输出

0
34
6875

 
#include<stdio.h>
#define N 20000
int f[N]={0,1};
int findT()
{
    int i,j,k;
    for(i=2;i<N;i++)
       {
          f[i]=(f[i-1]+f[i-2])%10000;
          if(f[i]==1&&f[i-1]==0)break;
       }
      
       return i-1;
}
int main()
{
    int i,j,k,n;
    int t=findT();
    while(scanf("%d",&n),n!=-1)
    {
       printf("%d\n",f[n%t]);
    }
    return 0;
}