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
/*直接套快速幂模板,求矩阵的n次幂
int ans=1;
while(n){
if(n&1)
ans*=x;
x*=x;
n>>=1;
就是此模板啦,将相应的ans 和x换成矩阵就行*/
#include<stdio.h>
#include<string.h>
#include<iostream>
#include<algorithm>
using namespace std;
int n,a[2][2],ans[2][2];
void mul(int a[2][2],int b[2][2]){
int temp[2][2];
memset(temp,0,sizeof temp);
for(int i=0;i<2;i++){
for(int j=0;j<2;j++){
for(int k=0;k<2;k++){
temp[i][j]=(temp[i][j]+a[i][k]*b[k][j])%10000;
}
}
}
for(int i=0;i<2;i++){
for(int j=0;j<2;j++){
b[i][j]=temp[i][j];
}
}
}
int main()
{
while(scanf("%d",&n)!=EOF){
if(n==-1)
return 0;
a[0][0]=a[0][1]=a[1][0]=1;
a[1][1]=0;
ans[0][0]=ans[1][1]=1;
ans[0][1]=ans[1][0]=0;//相当于ans=1,初始化为单位矩阵
while(n){
if(n&1)
mul(a,ans);//此过程相当于求ans=ans*a;
mul(a,a);//相当于求a=a*a;
n>>=1;
}
printf("%d\n",ans[0][1]);
}
}