test/primitive_root.test.cpp

View this file on GitHub
Last update: 2024-07-28 21:04:51+08:00
Problem: https://judge.yosupo.jp/problem/primitive_root

Depends on

Code

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

#include "../default/t.cpp"
#include "../numtheory/fastFactorize.cpp"
#include "../numtheory/primitiveRoot.cpp"

signed main() {
  ios::sync_with_stdio(false), cin.tie(NULL);

  int q; cin >> q;
  while(q--) {
    ull x; cin >> x;
    cout << primitiveRoot(x) << '\n';
  }

  return 0;
}

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

#line 1 "default/t.cpp"
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tuple>
#include <type_traits>
#include <variant>
#include <bit>
#include <compare>
#include <concepts>
#include <numbers>
#include <ranges>
#include <span>

#define INT128_MAX (__int128)(((unsigned __int128) 1 << ((sizeof(__int128) * __CHAR_BIT__) - 1)) - 1)
#define INT128_MIN (-INT128_MAX - 1)

#define clock chrono::steady_clock::now().time_since_epoch().count()

using namespace std;

template<class T1, class T2>
ostream& operator<<(ostream& os, const pair<T1, T2> pr) {
  return os << pr.first << ' ' << pr.second;
}
template<class T, size_t N>
ostream& operator<<(ostream& os, const array<T, N> &arr) {
  for(size_t i = 0; T x : arr) {
    os << x;
    if (++i != N) os << ' ';
  }
  return os;
}
template<class T>
ostream& operator<<(ostream& os, const vector<T> &vec) {
  for(size_t i = 0; T x : vec) {
    os << x;
    if (++i != size(vec)) os << ' ';
  }
  return os;
}
template<class T>
ostream& operator<<(ostream& os, const set<T> &s) {
  for(size_t i = 0; T x : s) {
    os << x;
    if (++i != size(s)) os << ' ';
  }
  return os;
}
template<class T1, class T2>
ostream& operator<<(ostream& os, const map<T1, T2> &m) {
  for(size_t i = 0; pair<T1, T2> x : m) {
    os << x;
    if (++i != size(m)) os << ' ';
  }
  return os;
}

#ifdef DEBUG
#define dbg(...) cerr << '(', _do(#__VA_ARGS__), cerr << ") = ", _do2(__VA_ARGS__)
template<typename T> void _do(T &&x) { cerr << x; }
template<typename T, typename ...S> void _do(T &&x, S&&...y) { cerr << x << ", "; _do(y...); }
template<typename T> void _do2(T &&x) { cerr << x << endl; }
template<typename T, typename ...S> void _do2(T &&x, S&&...y) { cerr << x << ", "; _do2(y...); }
#else
#define dbg(...)
#endif

using ll = long long;
using ull = unsigned long long;
using ldb = long double;
using pii = pair<int, int>;
using pll = pair<ll, ll>;

template<typename T> using min_heap = priority_queue<T, vector<T>, greater<T>>;
template<typename T> using max_heap = priority_queue<T>;

template<ranges::forward_range rng, class T = ranges::range_value_t<rng>, class OP = plus<T>>
void pSum(rng &v) {
  if (!v.empty())
    for(T p = v[0]; T &x : v | views::drop(1))
      x = p = OP()(p, x);
}
template<ranges::forward_range rng, class T = ranges::range_value_t<rng>, class OP>
void pSum(rng &v, OP op) {
  if (!v.empty())
    for(T p = v[0]; T &x : v | views::drop(1))
      x = p = op(p, x);
}

template<ranges::forward_range rng>
void Unique(rng &v) {
  ranges::sort(v);
  v.resize(unique(v.begin(), v.end()) - v.begin());
}

template<ranges::random_access_range rng>
rng invPerm(rng p) {
  rng ret = p;
  for(int i = 0; i < ssize(p); i++)
    ret[p[i]] = i;
  return ret;
}

template<ranges::random_access_range rng, ranges::random_access_range rng2>
rng Permute(rng v, rng2 p) {
  rng ret = v;
  for(int i = 0; i < ssize(p); i++)
    ret[p[i]] = v[i];
  return ret;
}

template<bool directed>
vector<vector<int>> readGraph(int n, int m, int base) {
  vector<vector<int>> g(n);
  for(int i = 0; i < m; i++) {
    int u, v; cin >> u >> v;
    u -= base, v -= base;
    g[u].emplace_back(v);
    if constexpr (!directed)
      g[v].emplace_back(u);
  }
  return g;
}

template<class T>
void setBit(T &msk, int bit, bool x) {
  msk = (msk & ~(T(1) << bit)) | (T(x) << bit);
}
template<class T> void flipBit(T &msk, int bit) { msk ^= T(1) << bit; }
template<class T> bool getBit(T msk, int bit) { return msk >> bit & T(1); }

template<class T>
T floorDiv(T a, T b) {
  if (b < 0) a *= -1, b *= -1;
  return a >= 0 ? a / b : (a - b + 1) / b;
}
template<class T>
T ceilDiv(T a, T b) {
  if (b < 0) a *= -1, b *= -1;
  return a >= 0 ? (a + b - 1) / b : a / b;
}

template<class T> bool chmin(T &a, T b) { return a > b ? a = b, 1 : 0; }
template<class T> bool chmax(T &a, T b) { return a < b ? a = b, 1 : 0; }
#line 1 "numtheory/fastFactorize.cpp"
//source: KACTL(https://github.com/kth-competitive-programming/kactl)

ull modmul(ull a, ull b, ull M) {
	ll ret = a * b - M * ull(1.L / M * a * b);
	return ret + M * (ret < 0) - M * (ret >= (ll)M);
}

ull modpow(ull b, ull e, ull mod) {
	ull ans = 1;
	for (; e; b = modmul(b, b, mod), e /= 2)
		if (e & 1) ans = modmul(ans, b, mod);
	return ans;
}

bool isPrime(ull n) {
	if (n < 2 || n % 6 % 4 != 1) return (n | 1) == 3;
	ull A[] = {2, 325, 9375, 28178, 450775, 9780504, 1795265022},
	    s = __builtin_ctzll(n-1), d = n >> s;
	for (ull a : A) {   // ^ count trailing zeroes
		ull p = modpow(a%n, d, n), i = s;
		while (p != 1 && p != n - 1 && a % n && i--)
			p = modmul(p, p, n);
		if (p != n-1 && i != s) return 0;
	}
	return 1;
}

ull pollard(ull n) {
  static mt19937_64 rng(clock);
  uniform_int_distribution<ull> unif(0, n - 1);
  ull c = 1;
	auto f = [n, &c](ull x) { return modmul(x, x, n) + c % n; };
	ull x = 0, y = 0, t = 30, prd = 2, i = 1, q;
	while (t++ % 40 || __gcd(prd, n) == 1) {
		if (x == y) c = unif(rng), x = ++i, y = f(x);
		if ((q = modmul(prd, max(x,y) - min(x,y), n))) prd = q;
		x = f(x), y = f(f(y));
	}
	return __gcd(prd, n);
}

vector<ull> factor(ull n) {
	if (n == 1) return {};
	if (isPrime(n)) return {n};
	ull x = pollard(n);
	auto l = factor(x), r = factor(n / x);
	l.insert(l.end(), r.begin(), r.end());
	return l;
}
#line 1 "numtheory/primitiveRoot.cpp"
//#include "numtheory/fastFactorize.cpp"

ull primitiveRoot(ull p) {
  auto fac = factor(p - 1);
  ranges::sort(fac);
  fac.resize(unique(fac.begin(), fac.end()) - fac.begin());
  auto test = [p, fac](ull x) {
    for(ull d : fac)
      if (modpow(x, (p - 1) / d, p) == 1)
        return false;
    return true;
  };
  static mt19937_64 rng(clock);
  uniform_int_distribution<ull> unif(1, p - 1);
  ull root;
  while(!test(root = unif(rng)));
  return root;
}
#line 6 "test/primitive_root.test.cpp"

signed main() {
  ios::sync_with_stdio(false), cin.tie(NULL);

  int q; cin >> q;
  while(q--) {
    ull x; cin >> x;
    cout << primitiveRoot(x) << '\n';
  }

  return 0;
}