CP-templates

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:heavy_check_mark: test/mytest_factorize_sqrt.test.cpp

Depends on

Code

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

#include "../default/t.cpp"
#include "../numtheory/factorize_sqrt.cpp"
#include "../numtheory/factorize_pollard_rho.cpp"

void check(int64_t x) {
  vc<int64_t> pf;
  for(auto p : factor(x))
    pf.eb(p);
  ranges::sort(pf);
  vc<pair<int64_t, int64_t>> pf2;
  for(int i = 0, j = 0; i < ssize(pf); i = j) {
    while(j < ssize(pf) and pf[i] == pf[j]) j++;
    pf2.emplace_back(pf[i], j - i);
  }
  pf.resize(unique(pf.begin(), pf.end()) - pf.begin());
  vc<int64_t> divisor;
  auto dfs = [&](int i, int64_t prod, auto &self) -> void {
    if (i == ssize(pf)) {
      divisor.emplace_back(prod);
      return;
    }
    for(int j = 0; j <= pf2[i].second; j++) {
      if (j) prod *= pf2[i].first;
      self(i + 1, prod, self);
    }
  };
  dfs(0, 1, dfs);
  ranges::sort(divisor);
  
  assert(pf2 == prime_factorize_sqrt(x));
  assert(pf == prime_factor_sqrt(x));
  assert(divisor == divisor_sqrt(x));
}

void check_small() {
  for(int64_t x = 1; x < (1 << 10); x++)
    check(x);
}

void check_large() {
  mt19937_64 rng(clock);
  for(int64_t l = (1ll << 10); l < (1ll << 53); l <<= 1)
    for(int i = 0; i < 10; i++)
      check(rng() % l + l);
}

void a_plus_b() {
  int x, y; cin >> x >> y;
  cout << x + y << '\n';
}

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

  check_small();
  check_large();
  a_plus_b();

  return 0;
}
#line 1 "test/mytest_factorize_sqrt.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"

#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 pb push_back
#define eb emplace_back
#define clock chrono::steady_clock::now().time_since_epoch().count()

using namespace std;

template<size_t I = 0, typename... args>
ostream& print_tuple(ostream& os, const tuple<args...> tu) {
  os << get<I>(tu);
  if constexpr (I + 1 != sizeof...(args)) {
    os << ' ';
    print_tuple<I + 1>(os, tu);
  }
  return os;
}
template<typename... args>
ostream& operator<<(ostream& os, const tuple<args...> tu) {
  return print_tuple(os, tu);
}
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 T>
ostream& operator<<(ostream& os, const multiset<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.first << " : " << x.second;
    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 vc = vector<T>;
template<typename T> using vvc = vc<vc<T>>;
template<typename T> using vvvc = vc<vvc<T>>;

using vi = vc<int>;
using vll = vc<ll>;
using vvi = vvc<int>;
using vvll = vvc<ll>;

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

template<typename R, typename F, typename... Args>
concept R_invocable = requires(F&& f, Args&&... args) {
  { std::invoke(std::forward<F>(f), std::forward<Args>(args)...) } -> std::same_as<R>;
};
template<ranges::forward_range rng, class T = ranges::range_value_t<rng>, typename F>
requires R_invocable<T, F, T, T>
void pSum(rng &&v, F f) {
  if (!v.empty())
    for(T p = *v.begin(); T &x : v | views::drop(1))
      x = p = f(p, x);
}
template<ranges::forward_range rng, class T = ranges::range_value_t<rng>>
void pSum(rng &&v) {
  if (!v.empty())
    for(T p = *v.begin(); T &x : v | views::drop(1))
      x = p = 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>
vi argSort(rng p) {
  vi id(size(p));
  iota(id.begin(), id.end(), 0);
  ranges::sort(id, {}, [&](int i) { return pair(p[i], i); });
  return id;
}

template<ranges::random_access_range rng, class T = ranges::range_value_t<rng>, typename F>
requires invocable<F, T&>
vi argSort(rng p, F proj) {
  vi id(size(p));
  iota(id.begin(), id.end(), 0);
  ranges::sort(id, {}, [&](int i) { return pair(proj(p[i]), i); });
  return id;
}

template<bool directed>
vvi read_graph(int n, int m, int base) {
  vvi 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<bool directed>
vvi adjacency_list(int n, vc<pii> e, int base) {
  vvi g(n);
  for(auto [u, v] : e) {
    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 &= ~(T(1) << bit)) |= T(x) << bit; }
template<class T> void onBit(T &msk, int bit) { setBit(msk, bit, true); }
template<class T> void offBit(T &msk, int bit) { setBit(msk, bit, false); }
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/factorize_sqrt.cpp"
vc<pair<int64_t, int64_t>> prime_factorize_sqrt(int64_t x) {
  using i64 = int64_t;
  vc<pair<i64, i64>> res;
  for(i64 d = 2; d * d <= x; d++) {
    if (x % d != 0) continue;
    res.emplace_back(d, 0ll);
    while(x % d == 0)
      x /= d, res.back().second++;
  }
  if (x != 1) res.emplace_back(x, 1);
  return res;
}

vc<int64_t> prime_factor_sqrt(int64_t x) {
  using i64 = int64_t;
  vc<i64> res;
  for(i64 d = 2; d * d <= x; d++) {
    if (x % d != 0) continue;
    res.emplace_back(d);
    while(x % d == 0)
      x /= d;
  }
  if (x != 1) res.emplace_back(x);
  return res;
}

vc<int64_t> divisor_sqrt(int64_t x, bool sorted = true) {
  using i64 = int64_t;
  vc<i64> divisor = {1};
  for(auto [p, f] : prime_factorize_sqrt(x)) {
    vc<i64> nxt;
    nxt.reserve(ssize(divisor) * (f + 1));
    uint64_t q = 1;
    for(int i = 0; i <= f; i++, q *= p)
      for(i64 d : divisor)
        nxt.emplace_back(d * q);
    divisor.swap(nxt);
  }
  if (sorted)
    ranges::sort(divisor);
  return divisor;
}
#line 1 "numtheory/factorize_pollard_rho.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 6 "test/mytest_factorize_sqrt.test.cpp"

void check(int64_t x) {
  vc<int64_t> pf;
  for(auto p : factor(x))
    pf.eb(p);
  ranges::sort(pf);
  vc<pair<int64_t, int64_t>> pf2;
  for(int i = 0, j = 0; i < ssize(pf); i = j) {
    while(j < ssize(pf) and pf[i] == pf[j]) j++;
    pf2.emplace_back(pf[i], j - i);
  }
  pf.resize(unique(pf.begin(), pf.end()) - pf.begin());
  vc<int64_t> divisor;
  auto dfs = [&](int i, int64_t prod, auto &self) -> void {
    if (i == ssize(pf)) {
      divisor.emplace_back(prod);
      return;
    }
    for(int j = 0; j <= pf2[i].second; j++) {
      if (j) prod *= pf2[i].first;
      self(i + 1, prod, self);
    }
  };
  dfs(0, 1, dfs);
  ranges::sort(divisor);
  
  assert(pf2 == prime_factorize_sqrt(x));
  assert(pf == prime_factor_sqrt(x));
  assert(divisor == divisor_sqrt(x));
}

void check_small() {
  for(int64_t x = 1; x < (1 << 10); x++)
    check(x);
}

void check_large() {
  mt19937_64 rng(clock);
  for(int64_t l = (1ll << 10); l < (1ll << 53); l <<= 1)
    for(int i = 0; i < 10; i++)
      check(rng() % l + l);
}

void a_plus_b() {
  int x, y; cin >> x >> y;
  cout << x + y << '\n';
}

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

  check_small();
  check_large();
  a_plus_b();

  return 0;
}
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