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;
}