HDU 4686 Arc of Dream （矩阵快速幂）

Arc of Dream

Time Limit: 2000/2000 MS (Java/Others)    Memory Limit: 65535/65535 K (Java/Others)
Total Submission(s): 419    Accepted Submission(s): 148

Problem Description

An Arc of Dream is a curve defined by following function:

where
a₀ = A0
a_i = a_i-1*AX+AY
b₀ = B0
b_i = b_i-1*BX+BY
What is the value of AoD(N) modulo 1,000,000,007?

Input

There are multiple test cases. Process to the End of File.
Each test case contains 7 nonnegative integers as follows:
N
A0 AX AY
B0 BX BY
N is no more than 10¹⁸, and all the other integers are no more than 2×10⁹.

Output

For each test case, output AoD(N) modulo 1,000,000,007.

Sample Input

1
1 2 3
4 5 6
2
1 2 3
4 5 6
3
1 2 3
4 5 6

Sample Output

4
134
1902

Author

Zejun Wu (watashi)

Source

2013 Multi-University Training Contest 9

Recommend

zhuyuanchen520

http://www.cnblogs.com/liuxueyang/archive/2013/08/20/3270893.html

#include<iostream>
#include<cstdio>
#include<cstring>

using namespace std;

const int mod=;

struct Matrix{
    long long arr[][];
};

Matrix init,unit;
long long n,a0,ax,ay,b0,bx,by;  //注意用long long，否则会溢出

Matrix Mul(Matrix a,Matrix b){
    Matrix c;
    for(int i=;i<;i++)
        for(int j=;j<;j++){
            c.arr[i][j]=;
            for(int k=;k<;k++)
                c.arr[i][j]=(c.arr[i][j]+a.arr[i][k]*b.arr[k][j]%mod)%mod;
            c.arr[i][j]%=mod;
        }
    return c;
}

Matrix Pow(Matrix a,Matrix b,long long k){
    while(k){
        if(k&){
            b=Mul(b,a);
        }
        a=Mul(a,a);
        k>>=;
    }
    return b;
}

void Init(){
    for(int i=;i<;i++)
        for(int j=;j<;j++){
            init.arr[i][j]=;
            unit.arr[i][j]=;
        }
    unit.arr[][]=,   unit.arr[][]=a0%mod,    unit.arr[][]=b0%mod,    unit.arr[][]=a0*b0%mod,
    unit.arr[][]=a0*b0%mod;

    init.arr[][]=,   init.arr[][]=ay%mod,    init.arr[][]=by%mod,    init.arr[][]=ay*by%mod,
    init.arr[][]=ay*by%mod,   init.arr[][]=ax%mod,  init.arr[][]=ax*by%mod,   init.arr[][]=ax*by%mod,
    init.arr[][]=bx%mod,  init.arr[][]=ay*bx%mod,   init.arr[][]=ay*bx%mod,   init.arr[][]=ax*bx%mod,
    init.arr[][]=ax*bx%mod,   init.arr[][]=;
}

int main(){

    //freopen("input.txt","r",stdin);

    while(cin>>n){
        //scanf("%d%d%d%d%d%d",&a0,&ax,&ay,&b0,&bx,&by);
        cin>>a0>>ax>>ay>>b0>>bx>>by;
        if(n==){
            puts("");
            continue;
        }
        Init();
        Matrix ans=Pow(init,unit,n-);
        cout<<ans.arr[][]<<endl;
    }
    return ;
}