扩展BSGS

Posted 2021-01-12 xiuwenli

#include <iostream>
#include <cstdio>
#include <cmath>
using namespace std;
typedef long long LL;
const int maxn=65535;
struct Hash
{
    int a,b,next;
}hash[maxn<<1];
int flg[maxn+66];
int top,idx;
void ins(int a,int b)
{
    int k=b&maxn;
    if(flg[k]!=idx) {
        flg[k]=idx;
        hash[k] = (Hash){a,b,-1};
        return ;
    }
    while(hash[k].next!=-1)  {
        if(hash[k].b==b) return ;
        k=hash[k].next;
    }
    hash[k].next=++top;
    hash[top] = (Hash){a,b,-1};
}
int find(int b)
{
    int k=b&maxn;
    if(flg[k]!=idx) return -1;
    while(k!=-1)    {
        if(hash[k].b==b) return hash[k].a;
        k=hash[k].next;
    }
    return -1;
}
int gcd(int a,int b)
{
    return b==0?a:gcd(b,a%b);
}
int exgcd(int a,int b,int &x,int &y)
{
    int t,ret;
    if(!b)  {
        x=1,y=0;
        return a;
    }
    ret=exgcd(b,a%b,x,y);
    t=x,x=y,y=t-a/b*y;
    return ret;
}
int Inval(int a,int b,int n)
{
    int x,y,e;
    exgcd(a,n,x,y);
    e=(LL)x*b%n;
    return e<0?e+n:e;
}
int pow_mod(LL a,int b,int mod)
{
    LL ret=1;
    a%=mod;
    while(b)  {
        if(b&1) ret = ret * a % mod;
        a = a * a % mod;
        b >>= 1;
    }
    return ret;
}
int BabyStep(int A,int B,int C)
{
    top=maxn;
    ++idx;
    LL buf=1%C,D=buf,K;
    int i,d=0,tmp;
    for(i=0;i<=100;buf=buf*A%C,i++)
      if(buf==B) return i;
    while((tmp=gcd(A,C))!=1)     {
        if(B%tmp) return -1; //无解
        ++d;
        C/=tmp;
        B/=tmp;
        D=D*A/tmp%C;
    }
    int M=(int)ceil(sqrt((double)C));
    for(buf=1%C,i=0;i<=M;buf=buf*A%C,i++) ins(i,buf);
    for(i=0,K=pow_mod((LL)A,M,C);i<=M;D=D*K%C,i++)  {
        tmp=Inval((int)D,B,C);
        int w;
        if(tmp>=0&&(w=find(tmp))!=-1)
          return i*M+w+d;
    }
    return -1;
}
int main()
{
    int A,B,C;
    while(scanf("%d%d%d",&A,&C,&B)!=EOF,A||B||C)  {
        B%=C;
        int tmp=BabyStep(A,B,C);
        if(tmp<0) puts("No Solution");
        else printf("%d
",tmp);
    }
    return 0;
}