Fibonacci Sequence II
Time Limit:1000MS
Memory Limit:65536K
Description
A sequence of the form 1 1 2 3 5 8 13 21 34 55 89 144..., find the nth term of the Fibonacci sequence.
Input
n (1〈 n 〈 231）
Output
A number is the nth term mod 10000 of the Fibonacci sequence;
Sample Input
123456789
Sample Output
4514
Problem solving ideas
This question is P1962 Fibonacci number (fast matrix multiplication + power) of the original title
with only a change of a few%
AC code
#include<cstdio>
using namespace std;
long long n,k;
struct node
{
long long oo[5][5];
}a;
node operator*(node x,node y)//重新定义“*”，变为矩阵乘法
{
node z;
for(long long i=1;i<=2;i++)//都改为2
for(long long j=1;j<=2;j++)
z.oo[i][j]=0;
for(long long o=1;o<=2;o++)
for(long long i=1;i<=2;i++)
for(long long j=1;j<=2;j++)
z.oo[i][j]=(z.oo[i][j]+x.oo[i][o]*y.oo[o][j])%10000;
return z;
}
node ksm(node x,long long k)//快速幂
{
node y=x;
while(k)
{
if(k%2)y=x*y;
x=x*x;
k/=2;
}
return y;
}
int main()
{
scanf("%lld",&n);
a.oo[1][1]=0;//初始值
a.oo[1][2]=a.oo[2][1]=a.oo[2][2]=1;
a=ksm(a,n);
printf("%lld",a.oo[1][1]);
return 0;
}