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.
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.
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).
0 9 999999999 1000000000
-1
0 34 626 6875
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:
.
#include<iostream> #include<cstring> #include<algorithm> using namespace std; void mul(int a[2][2],int b[2][2]){ int c[2][2]; memset(c,0,sizeof(c)); for (int i=0;i<2;i++) for (int j=0;j<2;j++) for (int k=0;k<2;k++){ c[i][j]=(c[i][j]+a[i][k]*b[k][j])%10000; } memcpy(a,c,sizeof(c)); } int main(){ int n; while (cin>>n && n!=-1){ int a[2][2]={{0,1},{1,1}}; int f[2][2]={{0,1},{0,0}}; while (n>0){ if (n&1) mul(f,a); mul(a,a); n>>=1; } cout<<f[0][0]<<endl; } return 0; }
原文：http://www.cnblogs.com/liumengyue/p/5172034.html