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A Problem With Fibonacci Sequence

2014-03-13 14:14 162 查看

A Problem With Fibonacci Sequence

TimeLimit: 1000ms, SpecialTime Limit:2500ms, MemoryLimit:65536KB

Total submitusers: 47, Acceptedusers: 38

Problem 11448 : Nospecial judgement

Problem description

Fibonacci sequenceis well-known in the world. We define Fibonacci sequence asfollows: F(0) = 0, F(1) = 1. F(n) = F(n-1) + F(n-2),n>=2. It’s easy for us to calculate F(n) mod m. Butthis time we want to make the problem
more difficult. We want tocalculate the formula:

is the combinationnumber.

Input

First line is thetestcase T. Following T lines, each line is two integers n, m ( 0 ≤n ≤ 109, 1 ≤ m ≤ 30000 )

Output

Output the answermod m

Sample Input

2
1 30000
2 30000

Sample Output

1
3

Problem Source

reason@sword

#include <stdio.h>

using namespace std;
struct Mat{
int num[3][3];
};
Mat mult(Mat a,Mat b,int mod){
Mat c;
for(inti=1;i<=2;i++)
for(intj=1;j<=2;j++){
c.num[i][j]=0;
for(int k=1;k<=2;k++)
c.num[i][j]=(c.num[i][j]+a.num[i][k]*b.num[k][j])%mod;
}
return c;
}
Mat my_pow(Mat x,int y,int mod){
Mat ans;
for(inti=1;i<=2;i++)
for(intj=1;j<=2;j++){
if(i==j)
ans.num[i][j]=1;
else
ans.num[i][j]=0;
}
for(;y;y>>=1){
if(y&1)
ans=mult(ans,x,mod);
x=mult(x,x,mod);
}
return ans;
}
int main(){
int t,n,m;
Mat A;
scanf("%d",&t);
for(inti=0;i<t;i++){
scanf("%d%d",&n,&m);
A.num[1][1]=2;
A.num[1][2]=1;
A.num[2][1]=1;
A.num[2][2]=1;
A=my_pow(A,n,m);
printf("%d\n",A.num[2][1]);
}

return 0;
}

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