Codeforces 450B - Jzzhu and Sequences ( 矩阵快速幂 )

 

Codeforces 450B - Jzzhu and Sequences ( 矩阵快速幂 )

 

 

题意:

给定f1和f2，求fn

 

分析:



特判f1,f2



当n>=3时使用矩阵快速幂即可( 简单题 )



将公式转化一下 , 可以得到一个变换矩阵

 

 

#include <cstdio>

#include <cstring>

#include <algorithm>

using namespace std;

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

#define MAT_SIZE 2

#define MOD 1000000007

typedef long long LL;

struct Mat

{

    LL mat[MAT_SIZE][MAT_SIZE];

    void zero()

    {

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

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

                mat[i][j] = 0;

    }

    void init()

    {

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

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

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

    }    

    void setv( int v )

    {

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

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

                mat[i][j] = v;

    }

    Mat operator*( const Mat &b)const

    {

        Mat c;

        c.zero();

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

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

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

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

        return c;

    }    

};



Mat fast_mod( Mat a, int b )

{

    Mat res;

    res.init();

    while( b )

    {

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

        a = a * a;

        b >>= 1;

    }

    return res;

}



void Orz()

{

    int n;

    LL x, y;

    while( ~scanf( "%lld %lld %d", &x, &y, &n ) )

    {

        if( n == 1 )    printf( "%lld\n", ( x % MOD + MOD ) % MOD );

        else if( n == 2 )    printf( "%lld\n", ( y % MOD + MOD ) % MOD ); 

        else

        {

            Mat t;

            t.mat[0][0] = 0;

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

            t.mat[1][0] = -1;        

            t.mat[1][1] = 1;

            t = fast_mod( t, n-2 );

            LL res = ( ( t.mat[1][0] * x + t.mat[1][1] * y ) % MOD + MOD ) % MOD;

            printf( "%lld\n", res );

        }

    }

}



int main()

{

    Orz();

    return 0;

}

代码君