Uva 10655 - Contemplation! Algebra ( 矩阵快速幂 )

 

Uva 10655 - Contemplation! Algebra ( 矩阵快速幂 )

 

 

#include <cstdio>

#include <cstring>

#include <algorithm>

using namespace std;

typedef long long LL;

#define MAX_SIZE 2



LL p, q, n, t;

LL M[MAX_SIZE];



struct Mat

{

    LL mat[MAX_SIZE][MAX_SIZE];



    void init()

    {

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

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

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

    }

    void zero()

    {

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

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

                mat[i][j] = 0;

    }

    void setv( int v )

    {

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

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

                mat[i][j] = v;

    }

    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] );

        return c;

    }    

    void debug()

    {

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

        {

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

            {

                if( j != 0 )    putchar( ' ' );

                printf( "%lld", mat[i][j] );

            }

            putchar( '\n' );

        }

    }

};



Mat fast_mod( Mat a, LL b )

{

    Mat res;

    res.init();

    while( b )

    {

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

        a = a * a;

        b >>= 1;

    }

    return res;

}



void Orz()

{

    while( scanf( "%lld %lld %lld", &p, &q, &n) == 3 )

    {

        /******************************/

        M[0] = p, M[1] = p * p - 2 * q;

        Mat c;

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

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

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

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

        //c.debug();

        /******************************/

        if( n == 0 )    puts( "2" ); 

        else if( n == 1 )    printf( "%lld\n", M[0] );

        else if( n == 2 )    printf( "%lld\n", M[1] );

        else

        {

            //Mat res = fast_mod( c, n-1 );    

            Mat res = fast_mod( c, n-2 );    

            LL ans = res.mat[1][0] * M[0] + res.mat[1][1] * M[1];

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

        }        

    }

}



int main()

{

    Orz();    

    return 0;

}

代码君///特别注意输入的判定，，，狂WA N发不解释