模板扩展 BSGS/exBSGS

Posted 2021-11-07 thusloop

//#pragma GCC optimize(2)
//#pragma GCC optimize(3,"Ofast","inline")
#include<bits/stdc++.h>
#define int long long
#define fi first
#define se second
#define pb push_back
#define pii pair<int,int>
#define ios ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
using namespace std;
const int inf=(int)8e18+100;
const int maxn=2e5+100;
int bsgs(int a,int b,int p,int ad)
{
	map<int,int>mp;
	int m=ceill(sqrt(p));
	int tp=1;
	mp[b%p]=0;
	for(int i=1;i<=m;i++)
	{
		tp=tp*a%p;
		mp[tp*b%p]=i;
	}
	int res=tp;
	for(int i=1;i<=m;i++)
	{
		if(mp.find(ad*res%p)!=mp.end())
		{
			return i*m-mp[ad*res%p];
		}
		res=res*tp%p;
	}
	return -1;
}
int exbsgs(int a,int b,int p)
{
	a%=p;
	b%=p;
	if(b==1||p==1) return 0;
	int d=__gcd(a,p);
	int k=0;
	int ad=1;
	while(d!=1)
	{
		if(b%d!=0)return -1;
		k++;
		b/=d;
		p/=d;
		ad=ad*a/d%p;
		d=__gcd(a,p);
		if(ad==b)return k;
	}
	int ans=bsgs(a,b,p,ad);
	if(ans==-1)return ans;
	return ans+k;
}
signed main()
{
	IOS
	int a,b,p;
	while(cin>>a>>p>>b)
	{
		if(a==0&&b==0&&p==0)break;
		int ans=exbsgs(a,b,p);
		if(ans==-1)cout<<"No Solution\\n";
		else cout<<ans<<"\\n";
	}
}