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

样例输出

0
34
6875

View Code

 1  
 2 #include<stdio.h>
 3 #define N 20000
 4 int f[N]={0,1};
 5 int findT()
 6 {
 7     int i,j,k;
 8     for(i=2;i<N;i++)
 9        {
10           f[i]=(f[i-1]+f[i-2])%10000;
11           if(f[i]==1&&f[i-1]==0)break;
12        }
13       
14        return i-1;
15 }
16 int main()
17 {
18     int i,j,k,n;
19     int t=findT();
20     while(scanf("%d",&n),n!=-1)
21     {
22        printf("%d\n",f[n%t]);
23     }
24     return 0;
25 }
26