51nod 算法马拉松17 解题报告

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cmath>
#include <vector>
#include <cstring>
#include <set>
#include <map>
using namespace std;
typedef long long ll;
inline void r(ll&num){
    num=0;ll f=1;char ch=getchar();
    while(ch<‘0‘||ch>‘9‘){if(ch==‘-‘)f=-1;ch=getchar();}
    while(ch>=‘0‘&&ch<=‘9‘)num=num*10+ch-‘0‘,ch=getchar();
    num*=f;
}
inline void r(int &num){
    num=0;int f=1;char ch=getchar();
    while(ch<‘0‘||ch>‘9‘){if(ch==‘-‘)f=-1;ch=getchar();}
    while(ch>=‘0‘&&ch<=‘9‘)num=num*10+ch-‘0‘,ch=getchar();
    num*=f;
}
const long long N = 2;
const long long M = 1e9+7;
struct Matr
{
    long long line;
    long long a[N+1][N+1];
    Matr(){
        line=2;
        a[0][0] = 1; a[0][1] = 2;
        a[1][0] = 1; a[1][1] = 1;
    }
};
Matr isit(Matr x,long long c)  //矩阵初始化
{
    for(long long i=0;i<N;i++)
        for(long long j=0;j<N;j++)
            x.a[i][j]=c;
    return x;
}

Matr Matlab(Matr x,Matr s)  //矩阵乘法
{
    Matr ans;
    ans.line = x.line;
    ans=isit(ans,0);
    for(long long i=0;i<x.line;i++)
    {
        for(long long j=0;j<x.line;j++)
        {
            for(long long k=0;k<s.line;k++)
            {
                ans.a[i][j] = (ans.a[i][j]+x.a[i][k]*s.a[k][j])%M;
                ans.a[i][j]=(ans.a[i][j]+M)%M;
            }
        }
    }
    return ans;
}
long long Fast_Matrix(Matr tmp,long long n)
{
    if(n==1)
        return 1;
    if(n==0)
        return 1;
    if(n==2)
        return 3;
    n--;
    Matr ans,ch;
    ans.line = 2;
    ans.a[0][0] = 1;
    ans.a[0][1] = 0;
    ans.a[1][0] = 1;
    ans.a[1][1] = 0;
    while(n>0)
    {
        if(n%2)
        {
            ans=Matlab(ans,tmp);
        }
        tmp=Matlab(tmp,tmp);
        n/=2;
    }
    return (ans.a[0][0]+ans.a[0][1])%M;
}
int main()
{
    Matr T;
    long long n;
    cin>>n;
    long long x = Fast_Matrix(T,n);
    cout<<(x*x+(n&1))%M<<endl;
    return 0;
}