Xn数列（codevs 1281）

Posted 2020-08-19 Cola

题目描述 Description

给你6个数，m, a, c, x0, n, g

Xn+1 = ( aXn + c ) mod m，求Xn

m, a, c, x0, n, g<=10^18

输入描述 Input Description

一行六个数 m, a, c, x0, n, g

输出描述 Output Description

输出一个数 Xn mod g

样例输入 Sample Input

11 8 7 1 5 3

样例输出 Sample Output

2

/*
  这个题显然用矩阵乘法，公式也很好推。
*/
#include<cstdio>
#include<iostream>
#define lon long long
using namespace std;
lon m,a,c,x,n,g;
struct node{
    lon v[2][2];
};
lon Mul(lon s1,lon s2){//快速乘
    lon r=0,base=s1;
    while(s2){
        if(s2&1)r+=base;
        base+=base;
        r%=m;
        base%=m;
        s2>>=1;
    }
    return r;
}
node cheng(node s1,node s2){
    node s3;s3.v[0][0]=s3.v[0][1]=s3.v[1][0]=s3.v[1][1]=0;
    for(int i=0;i<=1;i++)
        for(int j=0;j<=1;j++)
            for(int k=0;k<=1;k++){
                s3.v[i][j]+=Mul(s1.v[i][k],s2.v[k][j]);//s1.v[i][k]*s2.v[k][j];
                s3.v[i][j]%=m;
            }
    return s3;
}
node poww(node aa,lon bb){
    node base=aa,r;
    r.v[0][0]=r.v[1][1]=1;
    r.v[0][1]=r.v[1][0]=0;
    while(bb){
        if(bb&1)r=cheng(r,base);
        base=cheng(base,base);
        bb>>=1;
    }
    return r;
}
int main(){
    cin>>m>>a>>c>>x>>n>>g;
    node s1,s2;
    s1.v[0][0]=x;s1.v[0][1]=1;
    s1.v[1][0]=0;s1.v[1][1]=0;
    s2.v[0][0]=a;s2.v[0][1]=0;
    s2.v[1][0]=c;s2.v[1][1]=1;
    node ans=poww(s2,n);
    ans=cheng(s1,ans);
    cout<<ans.v[0][0]%g;
    return 0;
}