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

// #pragma GCC optimize("Ofast")
// #pragma GCC optimize("unroll-loops")
// #pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ull = unsigned long long;
using db = double;
using ld = long double;
template <typename T> using V = vector<T>;
template <typename T> using VV = vector<vector<T>>;
#define fs first
#define sc second
#define pb push_back
#define mp make_pair
#define mt make_tuple
#define eb emplace_back
#define lb lower_bound
#define ub upper_bound
#define all(v) (v).begin(), (v).end()
#define siz(v) (ll)(v).size()
#define rep(i, a, n) for (ll i = a; i < (ll)(n); ++i)
#define repr(i, a, n) for (ll i = n - 1; (ll)a <= i; --i)
#define ENDL '\\n'
typedef pair<int, int> Pi;
typedef pair<ll, ll> PL;
constexpr ll mod = 1000000007; // 998244353;
constexpr ll INF = 1000000099;
constexpr ll LINF = (ll)(1e18 + 99);
const ld PI = acos((ld)-1);
const vector<ll> dx = {-1, 1, 0, 0}, dy = {0, 0, -1, 1};
template <typename T, typename U> inline bool chmin(T &t, const U &u) {
  if (t > u) {
    t = u;
    return 1;
  }
  return 0;
}
template <typename T, typename U> inline bool chmax(T &t, const U &u) {
  if (t < u) {
    t = u;
    return 1;
  }
  return 0;
}
template <typename T> inline T gcd(T a, T b) { return b ? gcd(b, a % b) : a; }

template <typename T, typename Y> inline T mpow(T a, Y n) {
  T res = 1;
  for (; n; n >>= 1) {
    if (n & 1)
      res = res * a;
    a = a * a;
  }
  return res;
}

template <typename T, typename Y>
ostream &operator<<(ostream &os, const pair<T, Y> &p) {
  return os << "{" << p.fs << "," << p.sc << "}";
}
template <typename T> ostream &operator<<(ostream &os, const V<T> &v) {
  os << "{";
  for (auto e : v)
    os << e << ",";
  return os << "}";
}
template <typename... Args> void debug(Args &...args) {
  for (auto const &x : {args...}) {
    cerr << x << ' ';
  }
  cerr << ENDL;
}

bool pc = true;
set<ll> prime;

template <typename T> vector<T> eratosthenes(T N) {
  vector<T> v(N + 1, 1);
  iota(all(v), 0);
  for (int i = 2; i * i < N + 1; i++) {
    for (int j = i * i; j < N + 1; j += i) // i^2からスタートしてよい
    {
      if (v.at(j) == j)
        v.at(j) = i;
    }
  }
  return v;
}
// その数を割り切る(最小の)素数を入れる
//  1以外、1が入っているならば素数
// →素因数分解が対数時間で可能
//  now→now/v[now]として1まで遷移していく

template <typename T> vector<T> factor(T n, const vector<T> &s) {
  V<T> ret(0);
  while (n > 1) {
    ret.eb(s.at(n));
    n /= s.at(n);
  }
  return ret;
}

signed main() {
  cin.tie(0);
  cerr.tie(0);
  ios::sync_with_stdio(false);
  cout << fixed << setprecision(20);
  ll n;
  cin >> n;

  V<ll> v(n), er = eratosthenes(1000010ll);
  rep(i, 0, n) cin >> v[i];
  ll g = v[0];
  rep(i, 1, n) g = gcd(g, v[i]);

  rep(i, 0, n) {
    V<ll> ps = factor(v[i], er);
    sort(all(ps));
    ps.erase(unique(all(ps)), ps.end());

    rep(j, 0, siz(ps)) {
      if (prime.count(ps[j]))
        pc = false;
      else
        prime.insert(ps[j]);
    }
  }

  if (pc)
    cout << "pairwise coprime" << ENDL;
  else if (g == 1)
    cout << "setwise coprime" << ENDL;
  else
    cout << "not coprime" << ENDL;
}
//! ( . _ . ) !
// CHECK overflow,vector_size,what to output?

Error: TLE

Fixed submission:

// #pragma GCC optimize("Ofast")
// #pragma GCC optimize("unroll-loops")
// #pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ull = unsigned long long;
using db = double;
using ld = long double;
template <typename T> using V = vector<T>;
template <typename T> using VV = vector<vector<T>>;
#define fs first
#define sc second
#define pb push_back
#define mp make_pair
#define mt make_tuple
#define eb emplace_back
#define lb lower_bound
#define ub upper_bound
#define all(v) (v).begin(), (v).end()
#define siz(v) (ll)(v).size()
#define rep(i, a, n) for (ll i = a; i < (ll)(n); ++i)
#define repr(i, a, n) for (ll i = n - 1; (ll)a <= i; --i)
#define ENDL '\\n'
typedef pair<int, int> Pi;
typedef pair<ll, ll> PL;
constexpr ll mod = 1000000007; // 998244353;
constexpr ll INF = 1000000099;
constexpr ll LINF = (ll)(1e18 + 99);
const ld PI = acos((ld)-1);
const vector<ll> dx = {-1, 1, 0, 0}, dy = {0, 0, -1, 1};
template <typename T, typename U> inline bool chmin(T &t, const U &u) {
  if (t > u) {
    t = u;
    return 1;
  }
  return 0;
}
template <typename T, typename U> inline bool chmax(T &t, const U &u) {
  if (t < u) {
    t = u;
    return 1;
  }
  return 0;
}
template <typename T> inline T gcd(T a, T b) { return b ? gcd(b, a % b) : a; }

template <typename T, typename Y> inline T mpow(T a, Y n) {
  T res = 1;
  for (; n; n >>= 1) {
    if (n & 1)
      res = res * a;
    a = a * a;
  }
  return res;
}

template <typename T, typename Y>
ostream &operator<<(ostream &os, const pair<T, Y> &p) {
  return os << "{" << p.fs << "," << p.sc << "}";
}
template <typename T> ostream &operator<<(ostream &os, const V<T> &v) {
  os << "{";
  for (auto e : v)
    os << e << ",";
  return os << "}";
}
template <typename... Args> void debug(Args &...args) {
  for (auto const &x : {args...}) {
    cerr << x << ' ';
  }
  cerr << ENDL;
}

bool pc = true;
set<ll> prime;

template <typename T> vector<T> eratosthenes(T N) {
  vector<T> v(N + 1, 1);
  v.at(1) = 1;
  for (int i = 2; i * i < N + 1; i++) {
    if (v.at(i) == 1) {
      for (int j = i * i; j < N + 1; j += i) // i^2からスタートしてよい
      {
        v.at(j) = i;
      }
    }
  }
  return v;
}
// その数を割り切る(最小の)素数を入れる
//  1以外、1が入っているならば素数
// →素因数分解が対数時間で可能
//  now→now/v[now]として1まで遷移していく

template <typename T> vector<T> factor(T n, vector<T> &p) {
  V<T> ret(0);
  while (n > 1) {
    ret.eb(p.at(n));
    n /= p.at(n);
  }
  return ret;
}

signed main() {
  cin.tie(0);
  cerr.tie(0);
  ios::sync_with_stdio(false);
  cout << fixed << setprecision(20);
  ll n;
  cin >> n;

  V<ll> v(n), er = eratosthenes(1000010ll);
  rep(i, 0, n) cin >> v[i];
  ll g = v[0];
  rep(i, 1, n) g = gcd(g, v[i]);

  rep(i, 0, n) {
    V<ll> ps = factor(v[i], er);
    sort(all(ps));
    ps.erase(unique(all(ps)), ps.end());

    rep(j, 0, siz(ps)) {
      if (prime.count(ps[j]))
        pc = false;
      else
        prime.insert(ps[j]);
    }
  }

  if (pc)
    cout << "pairwise coprime" << ENDL;
  else if (g == 1)
    cout << "setwise coprime" << ENDL;
  else
    cout << "not coprime" << ENDL;
}
//! ( . _ . ) !
// CHECK overflow,vector_size,what to output?