HDU 4686 Arc of Dream

矩阵快速幂

#include<cstdio>

#include<cstring>

#include<cmath>

#include<algorithm>

using namespace std;



struct Matrix

{

    long long A[10][10];

    Matrix operator*(Matrix b);

};

const long long MOD=1000000007;

long long R,C;

long long N,A0,AX,AY,B0,BX,BY;



Matrix Matrix::operator*(Matrix b)

{

    Matrix c;

    int i,j,k;

    memset(c.A,0,sizeof(c.A));

    for(i=1; i<=R; i++)

        for(j=1; j<=C; j++)

            for(k=1; k<=5; k++)

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

    return c;

}



int main()

{

    int i,j;

    while(~scanf("%lld",&N))

    {



        scanf("%lld%lld%lld",&A0,&AX,&AY);

        scanf("%lld%lld%lld",&B0,&BX,&BY);



        A0=A0%MOD;

        AX=AX%MOD;

        AY=AY%MOD;



        B0=B0%MOD;

        BX=BX%MOD;

        BY=BY%MOD;



        if(N==0)

        {

            printf("0\n");

            continue;

        }



        Matrix JZ;

        JZ.A[1][1]=1;JZ.A[1][2]=0;JZ.A[1][3]=0;JZ.A[1][4]=0;JZ.A[1][5]=0;

        JZ.A[2][1]=1;JZ.A[2][2]=(AX*BX)%MOD;JZ.A[2][3]=0;JZ.A[2][4]=0;JZ.A[2][5]=0;

        JZ.A[3][1]=0;JZ.A[3][2]=(AX*BY)%MOD;JZ.A[3][3]=AX%MOD;JZ.A[3][4]=0;JZ.A[3][5]=0;

        JZ.A[4][1]=0;JZ.A[4][2]=(AY*BX)%MOD;JZ.A[4][3]=0;JZ.A[4][4]=BX%MOD;JZ.A[4][5]=0;

        JZ.A[5][1]=0;JZ.A[5][2]=(AY*BY)%MOD;JZ.A[5][3]=AY%MOD;JZ.A[5][4]=BY%MOD;JZ.A[5][5]=1;



        Matrix c;

        for(i=1; i<=9; i++)

        {

            for(j=1; j<=9; j++)

            {

                if(i==j) c.A[i][j]=1;

                else c.A[i][j]=0;

            }

        }



        long long b=N-1;

        R=5;

        C=5;

        while(b>0)

        {

            if(b%2==1) c=c*JZ,b--;

            else JZ=JZ*JZ,b=b/2;

        }

        Matrix CS;

        CS.A[1][1]=(A0*B0)%MOD;

        CS.A[1][4]=((B0*BX)%MOD+BY)%MOD;

        CS.A[1][3]=((A0*AX)%MOD+AY)%MOD;

        CS.A[1][2]=(CS.A[1][3]*CS.A[1][4])%MOD;

        CS.A[1][5]=1;



        R=1;

        C=5;

        if(N!=1) CS=CS*c;



        printf("%lld\n",CS.A[1][1]);

    }

    return 0;

}