BSGS（Baby Steps,Giant Steps）

Posted 2022-06-03 accpted

#include<bits/stdc++.h>

using namespace std;
typedef long long ll;
ll n,m,y,z,p,x,ans,block;
map<ll,int>mp;

ll quick(ll a,ll b,ll p)

    ll res=1%p;
    while (b)
    
        if (b&1)
        
            res=res*a%p;
        
        a=a*a%p;
        b=b>>1;
    
    return res;


void solve1()

    for (int i=1; i<=n; i++)
    
        scanf("%lld%lld%lld",&y,&z,&p);
        y=y%p;
        printf("%lld\\n",quick(y,z,p));
    


void solve2()

    for (int i=1; i<=n; i++)
    
        scanf("%lld%lld%lld",&y,&z,&p);
        y%=p;
        z%=p;
        if (y==0&&z!=0)
        
            printf("Orz, I cannot find x!\\n");
        
        else
        
            printf("%lld\\n",z*quick(y,p-2,p)%p);
        
    


void solve3()


    for (int i=1; i<=n; i++)
    
        scanf("%lld%lld%lld",&y,&z,&p);
        ans=-1;
        mp.clear();
        y=y%p;
        if (y==0&&z==0)
        
            printf("1\\n");
            continue;
        
        if (y==0)
        
            printf("Orz, I cannot find x!\\n");
            continue;
        
        block=ceil(sqrt(p));
        ll num=z;
        for (int j=0; j<=block; j++)
        
            mp[num]=j+1;
            num=num*y%p;
        
        ll sum=quick(y,block,p);
        num=sum;
        for (int j=1; j<=block; j++)
        
            if (mp[num%p])
            
                if (mp[num%p]==-1) ans=0;
                else
                
                    ans=j*block-mp[num]+1;
                
                break;
            
            num=num*sum%p;
        
        if (ans==-1)
        
            printf("Orz, I cannot find x!\\n");
        
        else
        
            printf("%lld\\n",ans);
        
    


int main()

    scanf("%lld%lld",&n,&m);
    if (m==1)
    
        solve1();
    
    if (m==2)
    
        solve2();
    
    if (m==3)
    
        solve3();