[学习笔记] 类欧几里得算法

考虑递归进行处理

要不断凑出结构

为了防止n过大，对a>=c||b>=c与否进行讨论处理

 

#include<bits/stdc++.h>
#define reg register int
#define il inline
#define fi first
#define se second
#define mk(a,b) make_pair(a,b)
#define numb (ch^'0')
using namespace std;
typedef long long ll;
template<class T>il void rd(T &x){
    char ch;x=0;bool fl=false;
    while(!isdigit(ch=getchar()))(ch=='-')&&(fl=true);
    for(x=numb;isdigit(ch=getchar());x=x*10+numb);
    (fl==true)&&(x=-x);
}
template<class T>il void output(T x){if(x/10)output(x/10);putchar(x%10+'0');}
template<class T>il void ot(T x){if(x<0) putchar('-'),x=-x;output(x);putchar(' ');}
template<class T>il void prt(T a[],int st,int nd){for(reg i=st;i<=nd;++i) ot(a[i]);putchar('
');}

namespace Miracle{
const int mod=998244353;
const int iv2=499122177;
int t;
ll f(ll a,ll b,ll c,ll n){
    if(a==0){
        return (n+1)*(b/c)%mod;
    }
    if(a>=c||b>=c){
        return (f(a%c,b%c,c,n)+(a/c)*n%mod*(n+1)%mod*iv2%mod+(n+1)*(b/c)%mod)%mod;
    }
    ll m=(a*n+b)/c;
    return (n*m%mod-f(c,c-b-1,a,m-1)+mod)%mod;
}
int main(){
    int t;
    rd(t);
    ll n,a,b,c;
    while(t--){
        rd(n);rd(a);rd(b);rd(c);
        printf("%lld 233 233
",f(a,b,c,n));
    }
    return 0;
}

}
signed main(){
    Miracle::main();
    return 0;
}

/*
   Author: *Miracle*
   Date: 2019/4/13 19:58:12
*/

咕