Luogp1962 Fibonacci series, P1962 Fibonacci Series

Luogp1962 Fibonacci series, P1962 Fibonacci Series
Background

As we all know, the Fibonacci series is a series that meets the following characteristics:

• F (1) = 1

• F (2) = 1

• F (n) = f (n-1) + f (n-2) (n ≥ 2 and n is an integer)

Description

Find the value of f (n) mod 1000000007.

Input/Output Format

Input Format:

 

· Row 1st: an integer n

 

Output Format:

 

Row 3: f (n) mod 1st Value

 

Input and Output sample input sample #1: Copy

5

Output example #1: Copy

5

Input example #2: Copy

10

Output sample #2: Copy

55

Description

For 60% of data: n ≤ 92

For 100% of data, n is within the range of long (INT64.

 

 

Bare matrix Rapid power

We need to determine either of the following situations:

 1 #include<iostream> 2 #include<cstdio> 3 #include<cstring> 4 #include<cmath> 5 #define LL long long  6 using namespace std; 7 const int MAXN=200000001; 8 const int mod=1000000007; 9 inline LL read()10 {11     char c=getchar();LL flag=1,x=0;12     while(c<'0'||c>'9')    {if(c=='-')    flag=-1;c=getchar();}13     while(c>='0'&&c<='9')    x=x*10+c-48,c=getchar();    return x*flag;14 }15 LL n;16 struct Matrix17 {18     LL a[5][5];19     Matrix()20     {21         memset(a,0,sizeof(a));22     }23 };24 Matrix Matrix_Mul(Matrix a,Matrix b)25 {26     Matrix c;27     for(LL k=1;k<=2;k++)    28         for(LL i=1;i<=2;i++)29             for(LL j=1;j<=2;j++)30                 c.a[i][j]+=(a.a[i][k]*b.a[k][j])%mod;31     return c;32 }33 inline void WORK()34 {35     Matrix bg,tmp;36     bg.a[1][1]=1;bg.a[1][2]=1;37     38     tmp.a[1][1]=0;tmp.a[1][2]=1;39     tmp.a[2][1]=1;tmp.a[2][2]=1;40     while(n) 41     { 42         if(n&1)    bg=Matrix_Mul(bg,tmp);43         tmp=Matrix_Mul(tmp,tmp);44         n>>=1;45     } 46     printf("%lld",bg.a[1][2]%mod);47 }48 int main()49 {50     n=read();n=n-2;51     if(n==-1||n==-2)    52     {53         printf("1");54         return 0;55     }56         57     58     WORK();59     return 0;60 }