bzoj2242(BSGS)

题目链接

https://www.lydsy.com/JudgeOnline/problem.php?id=3239

题解

$BSGS$ 板子题,这个板子要求 $a$ 和 $inf$ 互质,所以在这题,需要特判 $a%inf=0$ ,给了个比较强的数据来测试,应该很快就能发现有没有写挂。。




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;
}





ll _x,_y,inf;
int p;

ll qpow(ll x,ll t){return t?qpow(sqr(x)%inf,t>>1)*(t&1?x:1ll)%inf:1ll;}

ll exgcd(ll a,ll b,ll&x,ll&y){
if(b==0){x=1;y=0;return a;}
ll t=exgcd(b,a%b,y,x);y-=a/b*x;return t;
}

//a^x=b(mod inf)
//try a=2 b=1111111 inf=12345701 output=9584351
ll bsgs(ll a,ll b){
map<int,int>v;int n=sqrt(inf)+1,ans=inf;
ll inv=qpow(a,inf-2),t=qpow(a,n);
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);
return ans;
}

int main(){
int _=read();p=read();while(_--){
_x=read();_y=read();inf=read();
if(p==1){
printf("%lld\n",qpow(_x,_y));
}else if(p==2){
_x%=inf;_y%=inf;
ll x,y;
ll t=exgcd(_x,inf,x,y);x%=inf;if(x<0)x+=inf;
if(_y%t){printf("Orz, I cannot find x!\n");continue;}
x*=_y/t;x%=inf;
printf("%lld\n",x);
}else{
_x%=inf;_y%=inf;
if(_x==0){if(_y==1)printf("0\n");else if(_y==0)printf("1\n");else printf("Orz, I cannot find x!\n");continue;}
int t=bsgs(_x,_y);if(t<inf)printf("%d\n",t);else printf("Orz, I cannot find x!\n");
}
}
return 0;
}