Problem p02574 (C++) — buggy submission, verdict: Time Limit Exceeded

#include <algorithm>
#include <cassert>
#include <cmath>
#include <cstdio>
#include <deque>
#include <functional>
#include <iomanip>
#include <iostream>
#include <iterator>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

using namespace std;
using namespace placeholders;

using LL = long long;
using ULL = unsigned long long;
using VI = vector<int>;
using VVI = vector<vector<int>>;
using VS = vector<string>;
using ISS = istringstream;
using OSS = ostringstream;
using PII = pair<int, int>;
using VPII = vector<pair<int, int>>;
template <typename T = int> using VT = vector<T>;
template <typename T = int> using VVT = vector<vector<T>>;
template <typename T = int> using LIM = numeric_limits<T>;
template <typename T = int> using OSI = ostream_iterator<T>;

template <typename T> inline istream &operator>>(istream &s, vector<T> &v) {
  for (T &t : v) {
    s >> t;
  }
  return s;
}
template <typename T>
inline ostream &operator<<(ostream &s, const vector<T> &v) {
  for (int i = 0; i < int(v.size()); ++i) {
    s << (" " + !i) << v[i];
  }
  return s;
}

void in_impl(){};
template <typename T, typename... TS> void in_impl(T &head, TS &...tail) {
  cin >> head;
  in_impl(tail...);
}
#define IN(T, ...)                                                             \\
  T __VA_ARGS__;                                                               \\
  in_impl(__VA_ARGS__);

template <typename T> inline T fromString(const string &s) {
  T res;
  istringstream iss(s);
  iss >> res;
  return res;
}
template <typename T> inline string toString(const T &a) {
  ostringstream oss;
  oss << a;
  return oss.str();
}

#define NUMBERED(name, number) NUMBERED2(name, number)
#define NUMBERED2(name, number) name##_##number
#define REP1(n) REP2(NUMBERED(REP_COUNTER, __LINE__), n)
#define REP2(i, n) REP3(i, 0, n)
#define REP3(i, m, n) for (int i = (int)(m); i < (int)(n); ++i)
#define GET_REP(a, b, c, F, ...) F
#define REP(...) GET_REP(__VA_ARGS__, REP3, REP2, REP1)(__VA_ARGS__)
#define FOR(e, c) for (auto &&e : c)
#define ALL(c) begin(c), end(c)
#define AALL(a)                                                                \\
  (remove_all_extents<decltype(a)>::type *)a,                                  \\
      (remove_all_extents<decltype(a)>::type *)a +                             \\
          sizeof(a) / sizeof(remove_all_extents<decltype(a)>::type)

#define SZ(v) ((int)(v).size())
#define EXISTS(c, e) ((c).find(e) != (c).end())

template <typename T> inline bool chmin(T &a, const T &b) {
  if (b < a) {
    a = b;
    return true;
  }
  return false;
}
template <typename T> inline bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}

#define PB push_back
#define EM emplace
#define EB emplace_back
#define BI back_inserter

#define MP make_pair
#define fst first
#define snd second

#define DUMP(x) cerr << #x << " = " << (x) << endl

//     Λ   Λ＿_
//  ／(*ﾟーﾟ)／＼
// ／| ￣U U￣|＼／
//   |      |／

// N 項素因数分解
std::vector<vector<long long>> primeFactorization(std::vector<int> A) {
  const int M = *max_element(std::begin(A), std::end(A));

  std::vector<int> is_prime(M + 1, true);
  std::vector<int> min_divisor(M + 1);
  std::iota(std::begin(min_divisor), std::end(min_divisor), 0);
  for (int i = 2; i <= M; ++i) {
    if (!is_prime[i]) {
      continue;
    }
    for (int j = 2; i * j <= M; ++j) {
      is_prime[i * j] = false;
      min_divisor[i * j] = i;
    }
  }

  std::vector<std::vector<long long>> result(A.size());
  for (auto &a : A) {
    if (a == 1) {
      result.back().push_back(1);
      continue;
    }
    while (1 < a) {
      result.back().push_back(min_divisor[a]);
      a /= min_divisor[a];
    }
  }
  return std::move(result);
}

bool pairwise_coprime(const VI &A) {
  VVT<LL> pss = primeFactorization(A);

  map<int, int> factors;
  FOR(ps, pss) {
    reverse(ALL(ps));
    ps.erase(unique(ALL(ps)), end(ps));
    FOR(p, ps) {
      if (++factors[p] == 2) {
        return false;
      }
    }
  }
  return true;
}

bool setwise_coprime(const VI &A) {
  int g = A[0];
  for_each(ALL(A), [&](const int a) { g = __gcd(g, a); });
  return g == 1;
}

int main() {
  cin.tie(nullptr);
  ios::sync_with_stdio(false);
  cout << setprecision(12) << fixed;

  IN(int, N);
  VI A(N);
  cin >> A;

  if (pairwise_coprime(A)) {
    cout << "pairwise coprime" << endl;
  } else if (setwise_coprime(A)) {
    cout << "setwise coprime" << endl;
  } else {
    cout << "not coprime" << endl;
  }

  return 0;
}

Error: TLE

Fixed submission:

#include <algorithm>
#include <cassert>
#include <cmath>
#include <cstdio>
#include <deque>
#include <functional>
#include <iomanip>
#include <iostream>
#include <iterator>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

using namespace std;
using namespace placeholders;

using LL = long long;
using ULL = unsigned long long;
using VI = vector<int>;
using VVI = vector<vector<int>>;
using VS = vector<string>;
using ISS = istringstream;
using OSS = ostringstream;
using PII = pair<int, int>;
using VPII = vector<pair<int, int>>;
template <typename T = int> using VT = vector<T>;
template <typename T = int> using VVT = vector<vector<T>>;
template <typename T = int> using LIM = numeric_limits<T>;
template <typename T = int> using OSI = ostream_iterator<T>;

template <typename T> inline istream &operator>>(istream &s, vector<T> &v) {
  for (T &t : v) {
    s >> t;
  }
  return s;
}
template <typename T>
inline ostream &operator<<(ostream &s, const vector<T> &v) {
  for (int i = 0; i < int(v.size()); ++i) {
    s << (" " + !i) << v[i];
  }
  return s;
}

void in_impl(){};
template <typename T, typename... TS> void in_impl(T &head, TS &...tail) {
  cin >> head;
  in_impl(tail...);
}
#define IN(T, ...)                                                             \\
  T __VA_ARGS__;                                                               \\
  in_impl(__VA_ARGS__);

template <typename T> inline T fromString(const string &s) {
  T res;
  istringstream iss(s);
  iss >> res;
  return res;
}
template <typename T> inline string toString(const T &a) {
  ostringstream oss;
  oss << a;
  return oss.str();
}

#define NUMBERED(name, number) NUMBERED2(name, number)
#define NUMBERED2(name, number) name##_##number
#define REP1(n) REP2(NUMBERED(REP_COUNTER, __LINE__), n)
#define REP2(i, n) REP3(i, 0, n)
#define REP3(i, m, n) for (int i = (int)(m); i < (int)(n); ++i)
#define GET_REP(a, b, c, F, ...) F
#define REP(...) GET_REP(__VA_ARGS__, REP3, REP2, REP1)(__VA_ARGS__)
#define FOR(e, c) for (auto &&e : c)
#define ALL(c) begin(c), end(c)
#define AALL(a)                                                                \\
  (remove_all_extents<decltype(a)>::type *)a,                                  \\
      (remove_all_extents<decltype(a)>::type *)a +                             \\
          sizeof(a) / sizeof(remove_all_extents<decltype(a)>::type)

#define SZ(v) ((int)(v).size())
#define EXISTS(c, e) ((c).find(e) != (c).end())

template <typename T> inline bool chmin(T &a, const T &b) {
  if (b < a) {
    a = b;
    return true;
  }
  return false;
}
template <typename T> inline bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}

#define PB push_back
#define EM emplace
#define EB emplace_back
#define BI back_inserter

#define MP make_pair
#define fst first
#define snd second

#define DUMP(x) cerr << #x << " = " << (x) << endl

//     Λ   Λ＿_
//  ／(*ﾟーﾟ)／＼
// ／| ￣U U￣|＼／
//   |      |／

// 素因数分解 O( √N )
vector<long long> primeFactorization(long long N) {
  if (N == 1) {
    return vector<long long>();
  }

  std::vector<bool> is_prime(N + 1, true);
  std::vector<int> min_divisor(N + 1);
  std::iota(std::begin(min_divisor), std::end(min_divisor), 0);
  for (int i = 2; i <= N; ++i) {
    if (!is_prime[i]) {
      continue;
    }
    for (int j = 2; i * j <= N; ++j) {
      is_prime[i * j] = false;
      min_divisor[i * j] = i;
    }
  }

  std::vector<long long> result;
  while (1 < N) {
    result.push_back(min_divisor[N]);
    N /= min_divisor[N];
  }
  return std::move(result);
}

bool pairwise_coprime(const VI &A) {
  VVT<LL> pss;
  for_each(ALL(A), [&](const int a) { pss.PB(primeFactorization(a)); });

  map<int, int> factors;
  FOR(ps, pss) {
    reverse(ALL(ps));
    ps.erase(unique(ALL(ps)), end(ps));
    FOR(p, ps) {
      if (++factors[p] == 2) {
        return false;
      }
    }
  }
  return true;
}

bool setwise_coprime(const VI &A) {
  int g = A[0];
  for_each(ALL(A), [&](const int a) { g = __gcd(g, a); });
  return g == 1;
}

int main() {
  cin.tie(nullptr);
  ios::sync_with_stdio(false);
  cout << setprecision(12) << fixed;

  IN(int, N);
  VI A(N);
  cin >> A;

  if (pairwise_coprime(A)) {
    cout << "pairwise coprime" << endl;
  } else if (setwise_coprime(A)) {
    cout << "setwise coprime" << endl;
  } else {
    cout << "not coprime" << endl;
  }

  return 0;
}