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| Time Limit: 1000MS | Memory Limit: 65536K | |
| Total Submissions: 12833 | Accepted: 9124 |
Description
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.
Input
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.
Output
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).
Sample Input
0 9 999999999 1000000000 -1
Sample Output
0 34 626 6875
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:
.
Source
一个矩阵乘法就砸了上去
代码是偷来的2333
from：http://blog.csdn.net/orion_rigel/article/details/51926671
1 #include <cstdio> 2 #include <iostream> 3 #include <cstring> 4 using namespace std; 5 int n; 6 void cheng (int a[2][2],int b[2][2]) 7 { 8 int c[2][2]; 9 memset(c,0,sizeof(c)); 10 for (int i=0;i<2;i++) 11 for (int j=0;j<2;j++) 12 for (int k=0;k<2;k++) 13 c[i][j]=(c[i][j]+a[i][k]*b[k][j])%10000; 14 memcpy(a,c,sizeof(c)); 15 } 16 int main() 17 { 18 while (cin>>n && n!=-1) 19 { 20 int f[2][2]={{0,1},{0,0}}; 21 int a[2][2]={{0,1},{1,1}}; 22 while (n>0) 23 { 24 if(n&1) cheng(f,a); 25 cheng (a,a); 26 n>>=1; 27 } 28 printf("%d\n",f[0][0]); 29 } 30 }
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原文地址：http://www.cnblogs.com/SilverNebula/p/5684286.html
