萌新求助ExBSGS
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萌新求助ExBSGS
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jiangby楼主2021/4/2 15:14

自己瞎搞了一个 ExBSGS ,求卡

思路如下

AxB (mod p)AilimjB (mod p)AilimBAj (mod p)\begin{aligned} A^x &\equiv B \ (mod\ p) \\ A^{ilim-j}&\equiv B\ (mod\ p)\\ A^{ilim}&\equiv BA^j\ (mod\ p)\\ \end{aligned}

预处理AilimA^{ilim},枚举 jj 来做,但是由于可能没有逆元,所以一组 iijj ,不一定能找到一个合法的 xx,所以特判一下是否合法

#include<bits/stdc++.h>
#define ll long long
#define ull unsigned ll
#define uint unsigned int
#define db double
#define ld long double
#define pint pair<int,int>
#define fi first
#define se second
#define mk make_pair
#define pb push_back
#define eb emplace_back
#define ins insert
#define Rep(x,y,z) for(int x=(y);x<=(z);x++)
#define Red(x,y,z) for(int x=(y);x>=(z);x--)
using namespace std;
const int Mod=998244353,Mod1=Mod-1;
const int MAXN=1e4+5;
inline int read(){
	int x;scanf("%d",&x);return x;
}
char n[MAXN];int x,m,len,tmp;
unordered_map<int,int>vis;
inline int Fp(int x,int k){int ans=1;for(;k;k>>=1,x=1ll*x*x%Mod)if(k&1)ans=1ll*ans*x%Mod;return ans;}
inline int Fpow(int x,int k,int Mod){int ans=1;for(;k;k>>=1,x=1ll*x*x%Mod)if(k&1)ans=1ll*ans*x%Mod;return ans;}
namespace Task2{
	inline int Solve(){
		int lim=sqrt(m),tmpp=1;vis.clear();
		for(int i=0;i<lim;i++)tmpp=1ll*tmpp*tmp%m;
		int tmppp=tmpp;
		for(int i=1;i<=lim;i++){
			if(!vis.count(tmppp))vis[tmppp]=i;
			tmppp=1ll*tmppp*tmpp%m;
		}
		int ans=-1,s=x;
		if(x==1)ans=0;
		for(int i=0;i<lim;i++){
			if(vis.count(x)){
				if(Fpow(tmp,vis[x]*lim-i,m)==s){
					if(ans==-1)ans=vis[x]*lim-i;
					else ans=min(ans,vis[x]*lim-i);
				}
			}x=1ll*x*tmp%m;
		}return ans;
	}
}
int main(){
//	freopen("problem.in","r",stdin);
//	freopen("problem.out","w",stdout); 
	for(;scanf("%d%d%d",&tmp,&m,&x)!=EOF;){
		if(m==0&&tmp==0&&x==0)break;
		int ans=Task2::Solve();
		if(ans==-1)puts("No Solution");
		else cout<<ans<<"\n";
	}	
	return 0;
}
2021/4/2 15:14
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