test/yosupo_DiscreteLog.test.cpp

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Last update: 2023-04-05 23:10:22+09:00
Problem: https://judge.yosupo.jp/problem/discrete_logarithm_mod

Depends on

Code

#define PROBLEM "https://judge.yosupo.jp/problem/discrete_logarithm_mod"

#include "./template.hpp"

#include "../Math/log_mod.hpp"

void solve(){
    ll a,b,m;cin>>a>>b>>m;
    ll k=log_mod(a,b,m);
    cout<<k<<endl;
    // cout<<"a^res "<<pow_mod(a,k,m)<<" =? "<<b<<endl;
}

signed main(){
    int q;cin>>q;
    while(q--) solve();
    return 0;
}

#line 1 "test/yosupo_DiscreteLog.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/discrete_logarithm_mod"

#line 1 "template.hpp"
#include<bits/stdc++.h>
using namespace std;
#define ALL(x) begin(x),end(x)
#define rep(i,n) for(int i=0;i<(n);i++)
#define debug(v) cout<<#v<<":";for(auto x:v){cout<<x<<' ';}cout<<endl;
#define mod 1000000007
using ll=long long;
const int INF=1000000000;
const ll LINF=1001002003004005006ll;
int dx[]={1,0,-1,0},dy[]={0,1,0,-1};
// ll gcd(ll a,ll b){return b?gcd(b,a%b):a;}
template<class T>bool chmax(T &a,const T &b){if(a<b){a=b;return true;}return false;}
template<class T>bool chmin(T &a,const T &b){if(b<a){a=b;return true;}return false;}

struct IOSetup{
    IOSetup(){
        cin.tie(0);
        ios::sync_with_stdio(0);
        cout<<fixed<<setprecision(12);
    }
} iosetup;
 
template<typename T>
ostream &operator<<(ostream &os,const vector<T>&v){
    for(int i=0;i<(int)v.size();i++) os<<v[i]<<(i+1==(int)v.size()?"":" ");
    return os;
}
template<typename T>
istream &operator>>(istream &is,vector<T>&v){
    for(T &x:v)is>>x;
    return is;
}

#line 4 "test/yosupo_DiscreteLog.test.cpp"

#line 1 "Math/inv_mod.hpp"
ll inv_mod(ll a,ll m){
    ll b=m,u=1,v=0,t;
    while(b){
        t=a/b;
        swap(a-=t*b,b);swap(u-=t*v,v);
    }
    u%=m;
    if(u<0) u+=m;
    return u;
}
#line 1 "Math/pow_mod.hpp"
// a^n (mod m)
ll pow_mod(ll a,ll n,ll m){
    ll ret=1;
    while(n){
        if(n&1) ret=ret*a%m;
        a=(a*a)%m;
        n/=2;
    }
    return ret;
}
#line 3 "Math/log_mod.hpp"

// https://qiita.com/suisen_cp/items/d597c8ec576ae32ee2d7
// 最小の非負整数xを返す
// a ^ x = b mod m
ll log_mod(ll a,ll b,ll m){
    auto BSGS=[](ll a,ll b,ll m){
        ll sq_m=sqrt(m)+1;

        // baby-step
        unordered_map<ll,ll> bs;
        ll bab=1;
        for(int i=0;i<sq_m;i++,bab=bab*a%m)if(!bs.count(bab)) bs[bab]=i;

        // giant-step
        ll a_m=pow_mod(inv_mod(a,m),sq_m,m);
        ll gia=b;
        for(int i=0;i<=sq_m;i++,gia=gia*a_m%m)if(bs.count(gia)) return sq_m*i+bs[gia];
        return -1ll;
    };

    function<ll(ll,ll,ll)> decomp_BSGS=[&decomp_BSGS, &BSGS](ll a,ll b,ll m){
        a%=m,b%=m;
        
        if(m==1) return 0ll;
        if(b==1) return 0ll;

        ll g=gcd(a,m);
        if(g==1) return BSGS(a,b,m);

        if(b%g) return -1ll;
        m/=g;
        b=(b/g)*inv_mod(a/g,m);
        ll res=decomp_BSGS(a,b,m);
        if(res<0) return -1ll;
        return res+1;
    };
    return decomp_BSGS(a,b,m);
}
#line 6 "test/yosupo_DiscreteLog.test.cpp"

void solve(){
    ll a,b,m;cin>>a>>b>>m;
    ll k=log_mod(a,b,m);
    cout<<k<<endl;
    // cout<<"a^res "<<pow_mod(a,k,m)<<" =? "<<b<<endl;
}

signed main(){
    int q;cin>>q;
    while(q--) solve();
    return 0;
}