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 Fn = Fn − 1 + Fn − 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 Fn.
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
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
posted on 2012-11-14 21:38 LinuxPanda 阅读(151) 评论(0) 编辑 收藏 举报