Problem: Arc of Dream (matrix acceleration)

topic

Portal

Thinking

\(\begin{aligned}a_i*b_i&=(a_{i-1}*ax+ay)*(b_{i-1}*bx+by)\\&=a_{i-1}*ax*b_{i-1}*bx+a_{i-1}*ax*by+b_{i-1}*bx*ay+ay*by\end{aligned}\)

\(init=\begin{bmatrix}s_i\\a_{i-1}*b_{i-1}\\a_{i-1}\\b_{i-1}\\1\end{bmatrix}\)

\(acc=\begin{bmatrix}&1,&ax*bx,&ax*by,&bx*ay,&ay*by\\&0,&ax*bx,&ax*by,&bx*ay,&ay*by\\&0,&0,&ax,&0,&ay\\&0,&0,&0,&bx,&by\\&0,&0,&0,&0,&1\end{bmatrix}\)

Code

#include<iostream>
#include<cstring>
using namespace std;
long long n;
long long a,b;
const long long mod=2147493647;
struct node
{
    long long n,m;
    long long a[15][15];
    node operator * (const node &b)
    {
        node c;
        c.n=n;
        c.m=b.m;
        for(int i=1;i<=n;i++)
        {
            for(int j=1;j<=b.m;j++)
            {
                c.a[i][j]=0;
                for(int k=1;k<=m;k++)
                {
                    c.a[i][j]=(c.a[i][j]+a[i][k]*b.a[k][j]%mod)%mod;
                }
            }
        }
        return c;
    }
};
node qkpow(node a,long long b)
{
    if(b==1)
        return a;
    node t=qkpow(a,b/2);
    t=t*t;
    if(b%2==1)
        t=t*a;
    return t;
}
node init;
node acc;
void c_in()
{
    cin>>n>>a>>b;
}
int main()
{
    cin>>n;
    for(int i=1;i<=n;i++)
        c_in();
    return 0;
}