exbsgs

Posted 2020-11-21 miracevin

#include<cstdio>
#include<algorithm>
#include<cstdlib>
#include<iostream>
#include<cstring>
#include<cmath>
using namespace std;
typedef long long ll;
const int N=31630;//sqrt fai()
const int mod=100003;
ll C,A,B;
ll ni[N];
struct node{
    int nxt[mod],val[mod],id[mod],cnt;
    int hd[mod];
    void init(){
        memset(nxt,0,sizeof nxt),memset(val,0,sizeof val),memset(id,0,sizeof id);
        memset(hd,0,sizeof hd),cnt=0;
    }
    void insert(ll x,int d){
        int st=x%mod;
        for(int i=hd[st];i;i=nxt[i]){
            if(val[i]==x) return;
        }
        val[++cnt]=x,nxt[cnt]=hd[st],id[cnt]=d,hd[st]=cnt;
    }
    int find(ll x){
        int st=x%mod;
        for(int i=hd[st];i;i=nxt[i]){
            if(val[i]==x) return id[i];
        }    
        return -233;
    }
}ha;
ll qm(ll a,ll b,ll p){
    ll ret=1,base=a;
    while(b){
        if(b&1) ret=(base*ret)%p;
        base=(base*base)%p;
        b>>=1;
    }
    return ret;
}
int gcd(int a,int b){
    return (b==0)?a:gcd(b,a%b);
}
int BSGS(ll a,ll b,ll c){
    int up=(int)floor(sqrt(1.0*c-1));
    ni[0]=1;
    for(int i=1;i<=up;i++){
        ni[i]=qm(qm(a,i*up,c),c-2,c);
    }
    for(int i=0;i<=up-1;i++){
        ll kk=qm(a,i,c);
        ha.insert(kk,i);
    }
    for(int i=0;i<=up;i++){
        ll bb=b*ni[i]%c;
        int kk=ha.find(bb);
        if(kk>=0) return i*up+kk;
    }
    return -233;
}
int EXBSGS(){
    int num=0;
    int yC=C;
    ll ji=1;
    int ret=0x3f3f3f3f;
     bool flag=false;    
    while(1){
        int g=gcd(A,C);
        if(g==1) break;
        if(B%g) {
            flag=true;break;
        }
        B/=g,C/=g,ji=(ji*A/g)%C;
        num++;
    }
    if(!flag){
        ll ni=1;
        if(C!=1) ni=qm(ji,C-2,C);
        ll NB=B*ni;
        ret=BSGS(A,NB,C);
    }
    for(int i=0;i<=num;i++){
        ll kk=qm(A,i,yC);
        if(kk%yC==B) return i;
    }
    if(ret>=0) return ret+num;
    else return -233;
}
int main(){
    while(1){
        scanf("%lld%lld%lld",&A,&C,&B);
        if(A==0&&B==0&&C==0) break;
        ha.init();
        B%=C;
        int ret=EXBSGS();
        if(ret>=0){
            printf("%d
",ret);
        }
        else{
            puts("No Solution");
        }
    }
    return 0;
}

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