bzoj1467(EXBSGS)

题目链接

https://www.lydsy.com/JudgeOnline/problem.php?id=1467

题解

$EXBSGS$ 板子题,就是在 $BSGS$ 基础上对模数疯狂约去 $gcd$




代码

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/**
*         ┏┓    ┏┓
*         ┏┛┗━━━━━━━┛┗━━━┓
*         ┃       ┃  
*         ┃   ━    ┃
*         ┃ >   < ┃
*         ┃       ┃
*         ┃... ⌒ ...  ┃
*         ┃ ┃
*         ┗━┓ ┏━┛
*          ┃ ┃ Code is far away from bug with the animal protecting          
*          ┃ ┃ 神兽保佑,代码无bug
*          ┃ ┃           
*          ┃ ┃       
*          ┃ ┃
*          ┃ ┃           
*          ┃ ┗━━━┓
*          ┃ ┣┓
*          ┃ ┏┛
*          ┗┓┓┏━━━━━━━━┳┓┏┛
*           ┃┫┫ ┃┫┫
*           ┗┻┛ ┗┻┛
*/

#include<cstdio>
#include<cstring>
#include<algorithm>
#include<iostream>
#include<queue>
#include<map>
#include<stack>
#include<cmath>
#include<set>
#include<bitset>
#include<complex>
#include<assert.h>
#define inc(i,l,r) for(int i=l;i<=r;i++)
#define dec(i,l,r) for(int i=l;i>=r;i--)
#define link(x) for(edge *j=h[x];j;j=j->next)
#define mem(a) memset(a,0,sizeof(a))
#define ll long long
#define eps 1e-8
#define succ(x) (1<<x)
#define lowbit(x) (x&(-x))
#define sqr(x) ((x)*(x))
#define mid (x+y)/2
#define NM 2100005
#define nm 105
using namespace std;
const double pi=acos(-1);
ll read(){
ll x=0,f=1;char ch=getchar();
while(!isdigit(ch)){if(ch=='-')f=-1;ch=getchar();}
while(isdigit(ch))x=x*10+ch-'0',ch=getchar();
return f*x;
}






int x,y;
ll inf;
ll qpow(ll x,ll t){return t?qpow(sqr(x)%inf,t>>1)*(t&1?x:1ll)%inf:1ll;}
void exgcd(ll a,ll b,ll&x,ll&y){if(b==0)x=1,y=0;else exgcd(b,a%b,y,x),y-=a/b*x;}


//try a=4560 b=848750 inf=1203550 ans=783
ll bsgs(ll a,ll b){
int s=0;ll x,y;
a%=inf;b%=inf;
for(int i=0,t=1%inf;succ(i)<=inf;i++,t=t*a%inf)if(t==b)return i;
for(int t=__gcd(a,inf);t>1;t=__gcd(a,inf)){
if(b%t)return -1;
s++;b/=t;inf/=t;
exgcd(a/t,inf,x,y);x%=inf;if(x<0)x+=inf;
b*=x;b%=inf;
}
map<int,int>v;int n=sqrt(inf)+1,ans=inf;a%=inf;
ll inv,t=qpow(a,n);exgcd(a,inf,inv,y);inv%=inf;if(inv<0)inv+=inf;
for(int i=0;i<n;i++,b=b*inv%inf)if(!v.count(b))v[b]=i;
for(int i=0,k=1;i<n;i++,k=k*t%inf)if(v.count(k))ans=min(ans,v[k]+i*n);
if(ans==inf)return -1;else return ans+s;
}

int main(){
while(~scanf("%d%lld%d",&x,&inf,&y)&&(x||y||inf)){
if(y>=inf){puts("No Solution");continue;}
int t=bsgs(x,y);
if(t==-1)puts("No Solution");else printf("%d\n",t);
}
return 0;
}