mmrz's library

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:heavy_check_mark: verify/yosupo/discrete_logarithm.test.cpp

Depends on

Code

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

#include "./../../template/template.hpp"
#include "./../../math/discrete_logarithm.hpp"

using namespace mmrz;

void SOLVE(){
	int x, y, m;
	cin >> x >> y >> m;
	cout << discrete_logarithm(x, y, m) << '\n';
}

void mmrz::solve(){
	int t = 1;
	cin >> t;
	while(t--)SOLVE();
}
#line 1 "verify/yosupo/discrete_logarithm.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/discrete_logarithm_mod"

#line 1 "template/template.hpp"
# include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ull = unsigned long long;
const double pi = acos(-1);
template<class T>constexpr T inf() { return ::std::numeric_limits<T>::max(); }
template<class T>constexpr T hinf() { return inf<T>() / 2; }
template <typename T_char>T_char TL(T_char cX) { return tolower(cX); }
template <typename T_char>T_char TU(T_char cX) { return toupper(cX); }
template<class T> bool chmin(T& a,T b) { if(a > b){a = b; return true;} return false; }
template<class T> bool chmax(T& a,T b) { if(a < b){a = b; return true;} return false; }
int popcnt(unsigned long long n) { int cnt = 0; for (int i = 0; i < 64; i++)if ((n >> i) & 1)cnt++; return cnt; }
int d_sum(ll n) { int ret = 0; while (n > 0) { ret += n % 10; n /= 10; }return ret; }
int d_cnt(ll n) { int ret = 0; while (n > 0) { ret++; n /= 10; }return ret; }
ll gcd(ll a, ll b) { if (b == 0)return a; return gcd(b, a%b); };
ll lcm(ll a, ll b) { ll g = gcd(a, b); return a / g*b; };
ll MOD(ll x, ll m){return (x%m+m)%m; }
ll FLOOR(ll x, ll m) {ll r = (x%m+m)%m; return (x-r)/m; }
template<class T> using dijk = priority_queue<T, vector<T>, greater<T>>;
# define all(qpqpq)           (qpqpq).begin(),(qpqpq).end()
# define UNIQUE(wpwpw)        (wpwpw).erase(unique(all((wpwpw))),(wpwpw).end())
# define LOWER(epepe)         transform(all((epepe)),(epepe).begin(),TL<char>)
# define UPPER(rprpr)         transform(all((rprpr)),(rprpr).begin(),TU<char>)
# define rep(i,upupu)         for(ll i = 0, i##_len = (upupu);(i) < (i##_len);(i)++)
# define reps(i,opopo)        for(ll i = 1, i##_len = (opopo);(i) <= (i##_len);(i)++)
# define len(x)                ((ll)(x).size())
# define bit(n)               (1LL << (n))
# define pb push_back
# define eb emplace_back
# define exists(c, e)         ((c).find(e) != (c).end())

struct INIT{
	INIT(){
		std::ios::sync_with_stdio(false);
		std::cin.tie(0);
		cout << fixed << setprecision(20);
	}
}INIT;

namespace mmrz {
	void solve();
}

int main(){
	mmrz::solve();
}
#line 2 "math/discrete_logarithm.hpp"

#line 2 "math/iroot.hpp"

#line 5 "math/iroot.hpp"

unsigned long long iroot(unsigned long long n, int k=2){
	constexpr unsigned long long LIM = std::numeric_limits<unsigned long long>::max();
	if(n <= 1 || k == 1){
		return n;
	}
	if(k >= 64){
		return 1;
	}
	if(k == 2){
		return sqrtl(n);
	}

	if(n == LIM)n--;

	auto safe_mul = [&](unsigned long long &x, unsigned long long &y) -> void {
		if(x <= LIM / y){
			x *= y;
		}else{
			x = LIM;
		}
	};

	auto power = [&](unsigned long long a, int b) -> unsigned long long {
		unsigned long long ret = 1;
		while(b){
			if(b & 1)safe_mul(ret, a);
			safe_mul(a, a);
			b >>= 1;
		}
		return ret;
	};

	unsigned long long ret = (k == 3 ? cbrt(n)-1 : std::pow(n, std::nextafter(1.0/double(k), 0.0)));
	while(power(ret+1, k) <= n)ret++;
	return ret;
}
#line 2 "math/power.hpp"

#include <type_traits>

template<typename T>
concept NotPrimitiveInt =
	!(std::is_same_v<T, int> ||
		std::is_same_v<T, long> ||
		std::is_same_v<T, long long> ||
		std::is_same_v<T, unsigned> ||
		std::is_same_v<T, unsigned long> ||
		std::is_same_v<T, unsigned long long>);

template<NotPrimitiveInt T>
T power(T n, long long k) {
	T ret = 1;
	while(k > 0) {
		if(k & 1)ret *= n;
		n = n*n;
		k >>= 1;
	}
	return ret;
}

long long power(long long n, long long k, long long p) {
	long long ret = 1;
	while(k > 0){
		if(k & 1)ret = ret*n % p;
		n = n*n % p;
		k >>= 1;
	}
	return ret;
}
#line 5 "math/discrete_logarithm.hpp"

#line 12 "math/discrete_logarithm.hpp"

long long __modinv(long long a, long long m){
	long long b=m, u=1, v=0;
	while(b){
		long long t = a/b;
		a -= t*b; std::swap(a, b);
		u -= t*v; std::swap(u, v);
	}
	u %= m;
	if(u < 0)u += m;
	return u;
}

long long discrete_logarithm(long long x, long long y, long long m) {
	assert(x < m && y < m);
	if(m == 1)return 0;
	if(y == 1)return 0;
	if(x == 0){
		if(y == 1)return 0;
		else if(y == 0)return 1;
		else return -1;
	}

	if(std::gcd(x, m) != 1){
		long long d = std::gcd(x, m);
		if(y%d)return -1;
		y /= d;
		m /= d;
		long long ret = discrete_logarithm(x%m, (y*__modinv(x/d, m))%m, m);
		if(ret == -1)return -1;
		else return ret+1;
	}

	long long sq = iroot(m);
	if(sq < 3)sq = 3;
	std::vector<long long> _b(sq);
	for(int i = 0;i < sq;i++)_b[i] = (i == 0 ? 1 : (_b[i-1]*x)%m);

	std::map<long long, long long> b;
	for(int i = sq-1;i >= 0;i--)b[_b[i]] = i;

	long long inv = __modinv((_b.back()*x)%m, m);

	for(int i = 0;i < sq;i++){
		long long num = (y*power(inv, i, m))%m;
		if(b.contains(num)){
			return i*sq + b[num];
		}
	}
	return -1;
};
#line 5 "verify/yosupo/discrete_logarithm.test.cpp"

using namespace mmrz;

void SOLVE(){
	int x, y, m;
	cin >> x >> y >> m;
	cout << discrete_logarithm(x, y, m) << '\n';
}

void mmrz::solve(){
	int t = 1;
	cin >> t;
	while(t--)SOLVE();
}
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