HDU 4549 M斐波那契数列 ( 矩阵快速幂 + 费马小定理 )

 

HDU 4549 M斐波那契数列 (  矩阵快速幂 + 费马小定理  )

题意：中文题，不解释

分析：最好的分析就是先推一推前几项，看看有什么规律

 

#include <cstdio>

#include <cstring>

#include <algorithm>

using namespace std;

typedef __int64 LL;

#define CLR( a, b )    memset( a, b, sizeof(a) )

#define MOD 1000000007



struct Mat

{

    LL mat[2][2];

    Mat()

    {

        CLR( mat, 0 );

    }

    void init()

    {

        for( int i = 0; i < 2; ++i )

            for( int j = 0; j < 2; ++j )

                mat[i][j] = ( i == j );

    }

    void zero()

    {

        CLR( mat, 0 );

    }

    Mat operator * ( const Mat &b ) const

    {

        Mat c;

        c.zero();

        for( int k = 0; k < 2; ++k )

            for( int i = 0; i < 2; ++i )    if( mat[i][k] )

                for( int j = 0; j < 2; ++j )

                    c.mat[i][j] = ( c.mat[i][j] + mat[i][k] * b.mat[k][j] ) % ( MOD - 1 );

        return c;

    }

};



Mat Mat_mod( Mat a, LL b )

{

    Mat c;

    c.init();

    while( b )

    {

        if( b & 1 )    c = c * a;

        a = a * a;

        b >>= 1;

    }

    return c;

}



LL fast_mod( LL a, LL b )

{

    LL ans = 1;

    while( b )

    {

        if( b & 1 )    ans = ans * a % MOD;

        a = a * a % MOD;

        b >>= 1;

    }

    return ans;

}



void Orz()

{

    Mat c;

    c.mat[0][1] = c.mat[1][0] = c.mat[1][1] = 1;

    LL a, b, n;

    while( ~scanf( "%I64d %I64d %I64d",&a, &b, &n ) )

    {

        if( n == 0 )    printf( "%I64d\n", a % MOD );

        else if( n == 1 )    printf( "%I64d\n", b % MOD );

        else if( n == 2 )    printf( "%I64d\n", a * b % MOD );

        else

        {

            //0 1 1 2 3 5 8 13

            Mat t = Mat_mod( c, n - 3 );

            LL n1 = ( t.mat[1][0] + t.mat[1][1] ) % ( MOD - 1 );

            t = t * c;

            LL n2 = ( t.mat[1][0] + t.mat[1][1] ) % ( MOD - 1 );

            LL ans = fast_mod( a, n1 ) * fast_mod( b, n2 ) % MOD;

            printf( "%I64d\n", ans );    

        }

    }

}



int main()

{

    Orz();    

    return 0;

}

代码君