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

/**
 * @brief  : c++ code for AtCoder
 * @author : rk222
 * @created: 2020.08.29 20:48:20
 */

#define _CRT_SECURE_NO_WARNINGS
#include <algorithm>
#include <bitset>
#include <cmath>
#include <cstdio>
#include <iostream>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <vector>
using namespace std;

// #define int long long

typedef long long ll;
typedef long double ld;
typedef pair<int, int> P;
typedef pair<int, P> P1;
typedef tuple<int, int, int> T;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<ll> vl;
typedef vector<P> vp;
typedef vector<tuple<int, int, int>> vt;

#define fr first
#define sc second
#define mp make_pair
#define pb push_back
#define rep(i, x) for (int i = 0; i < x; i++)
#define rep1(i, x) for (int i = 1; i <= x; i++)
#define srep(i, s, x) for (int i = s; i < x; i++)
#define rrep(i, x) for (int i = x - 1; i >= 0; i--)
#define rrep1(i, x) for (int i = x; i > 0; i--)
#define rsrep(i, s, x) for (int i = x - 1; i >= s; i--)
#define maxs(x, y) (x = max(x, y))
#define mins(x, y) (x = min(x, y))
#define limit(x, l, r) max(l, min(x, r))
#define lims(x, l, r) (x = max(l, min(x, r)))
#define sor(v) sort(v.begin(), v.end())
#define rev(s) reverse(s.begin(), s.end())
#define lb(vec, a) lower_bound(vec.begin(), vec.end(), a)
#define ub(vec, a) upper_bound(vec.begin(), vec.end(), a)
#define uniq(vec) vec.erase(unique(vec.begin(), vec.end()), vec.end())
#define mp1(a, b, c) P1(a, P(b, c))
#define dame                                                                   \\
  {                                                                            \\
    puts("-1");                                                                \\
    return 0;                                                                  \\
  }
#define yn                                                                     \\
  puts("Yes");                                                                 \\
  else puts("No")
#define YN                                                                     \\
  puts("YES");                                                                 \\
  else puts("NO")

template <typename A, typename B> string to_string(pair<A, B> p);
template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p);
template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p);
string to_string(const string &s) { return '"' + s + '"'; }
string to_string(const char *s) { return to_string((string)s); }
string to_string(bool b) { return (b ? "true" : "false"); }
string to_string(vector<bool> v) {
  bool first = true;
  string ret = "{";
  for (int i = 0; i < static_cast<int>(v.size()); i++) {
    if (!first) {
      ret += ", ";
    }
    first = false;
    ret += to_string(v[i]);
  }
  ret += "}";
  return ret;
}
template <size_t N> string to_string(bitset<N> v) {
  string ret = "";
  for (size_t i = 0; i < N; i++) {
    ret += static_cast<char>('0' + v[i]);
  }
  return ret;
}
template <typename A> string to_string(A v) {
  bool first = true;
  string ret = "{";
  for (const auto &x : v) {
    string s = to_string(x);
    if (!first) {
      ret += ", ";
    }
    if (s[0] == '{') {
      s = "\\n" + s;
    }
    first = false;
    ret += s;
  }
  if (ret[ret.size() - 1] == '}') {
    ret += "\\n}";
  } else {
    ret += "}";
  }
  return ret;
}
template <typename A, typename... Lest>
string to_string(A *v, int n, Lest... L) {
  bool first = true;
  string ret = "{";
  rep(i, n) {
    auto x = v[i];
    string s = to_string(x, L...);
    if (!first) {
      ret += ", ";
    }
    if (s[0] == '{') {
      s = "\\n" + s;
    }
    first = false;
    ret += s;
  }
  if (ret[ret.size() - 1] == '}') {
    ret += "\\n}";
  } else {
    ret += "}";
  }
  return ret;
}
template <typename A, typename B> string to_string(pair<A, B> p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}
template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p) {
  return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " +
         to_string(get<2>(p)) + ")";
}
template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p) {
  return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " +
         to_string(get<2>(p)) + ", " + to_string(get<3>(p)) + ")";
}
void name_disp(string s) {
  cerr << "-------" << endl;
  cerr << s << ": " << endl;
}
void val_disp() { cerr << endl; }
template <typename First, typename... Lest> void val_disp(First F, Lest... L) {
  cerr << to_string(F) << endl;
  val_disp(L...);
}
template <typename A, typename... Lest> void val_disp(A *v, Lest... L) {
  cerr << to_string(v, L...) << endl;
  val_disp();
}
#define disp(...)                                                              \\
  name_disp(#__VA_ARGS__);                                                     \\
  val_disp(__VA_ARGS__)
#define adisp(a, ...)                                                          \\
  name_disp(#a);                                                               \\
  val_disp(a, __VA_ARGS__)

#ifdef int
const ll INF = 1002003004005006007ll;
#else
const int INF = 1002003004;
#endif

const int M = 100000000;
const int dir_4[4][2] = {{1, 0}, {0, 1}, {-1, 0}, {0, -1}};
const int dir_8[8][2] = {{1, 0},  {1, 1},   {0, 1},  {-1, 1},
                         {-1, 0}, {-1, -1}, {0, -1}, {1, -1}};

/* ------------------------------------- */
int gcd(int a, int b) {
  if (a % b == 0) {
    return b;
  } else {
    return gcd(b, a % b);
  }
}

const int MAX_N = 1000010;
bool primeDp[MAX_N];
// n以下の素数を取得する
// だいたいO(n)
vi getPrimes(int n) {
  int u = n + 32;
  double lu = log(u);
  vi ret((int)(u / lu + u / lu / lu * 1.5));

  for (int i = 2; i <= n; i++)
    primeDp[i] = true;
  int sqn = sqrt(n);
  for (int i = 2; i <= sqn; i++) {
    if (!primeDp[i])
      continue;
    for (int j = i * i; j <= n; j += i)
      primeDp[j] = false;
  }
  int idx = 0;
  for (int i = 2; i <= n; i++) {
    if (primeDp[i]) {
      ret[idx] = i;
      idx++;
    }
  }
  return vi(ret.begin(), ret.begin() + idx);
}

// (素数, その個数)というpair<int, int>を配列にまとめたものを返す
vp primeFact(vi primes, int a) {
  if (a == 1) {
    return vp({mp(1, 1)});
  }

  vp ret;
  rep(i, primes.size()) {
    int num = 0;
    int p = primes[i];
    while (a % p == 0) {
      a /= p;
      num++;
    }
    if (num > 0) {
      ret.pb(mp(p, num));
    }
  }
  if (a > 1) {
    ret.pb(mp(a, 1));
  }
  return ret;
}

int n, a[1000100];
int num[1000100];
signed main() {
  scanf("%d", &n);
  rep(i, n) { scanf("%d", &a[i]); }
  vi primes = getPrimes(1000000);
  bool pairwise = true;
  rep(i, n) { num[a[i]]++; }
  rep(i, primes.size()) {
    int p = primes[i];
    int nu = 0;
    for (int j = 1; p * j < 1000001; j++) {
      nu += num[p * j];
    }
    if (nu > 1) {
      pairwise = false;
      break;
    }
  }

  if (pairwise) {
    printf("pairwise coprime\\n");
  } else {
    int c = a[0];
    rep(i, n - 1) { c = gcd(c, a[i + 1]); }
    if (c == 1) {
      printf("setwise coprime\\n");
    } else {
      printf("not coprime\\n");
    }
  }

  /* --------------------------------- */
  return 0;
};

Error: TLE

Fixed submission:

/**
 * @brief  : c++ code for AtCoder
 * @author : rk222
 * @created: 2020.08.29 20:48:20
 */

#define _CRT_SECURE_NO_WARNINGS
#include <algorithm>
#include <bitset>
#include <cmath>
#include <cstdio>
#include <iostream>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <vector>
using namespace std;

// #define int long long

typedef long long ll;
typedef long double ld;
typedef pair<int, int> P;
typedef pair<int, P> P1;
typedef tuple<int, int, int> T;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<ll> vl;
typedef vector<P> vp;
typedef vector<tuple<int, int, int>> vt;

#define fr first
#define sc second
#define mp make_pair
#define pb push_back
#define rep(i, x) for (int i = 0; i < x; i++)
#define rep1(i, x) for (int i = 1; i <= x; i++)
#define srep(i, s, x) for (int i = s; i < x; i++)
#define rrep(i, x) for (int i = x - 1; i >= 0; i--)
#define rrep1(i, x) for (int i = x; i > 0; i--)
#define rsrep(i, s, x) for (int i = x - 1; i >= s; i--)
#define maxs(x, y) (x = max(x, y))
#define mins(x, y) (x = min(x, y))
#define limit(x, l, r) max(l, min(x, r))
#define lims(x, l, r) (x = max(l, min(x, r)))
#define sor(v) sort(v.begin(), v.end())
#define rev(s) reverse(s.begin(), s.end())
#define lb(vec, a) lower_bound(vec.begin(), vec.end(), a)
#define ub(vec, a) upper_bound(vec.begin(), vec.end(), a)
#define uniq(vec) vec.erase(unique(vec.begin(), vec.end()), vec.end())
#define mp1(a, b, c) P1(a, P(b, c))
#define dame                                                                   \\
  {                                                                            \\
    puts("-1");                                                                \\
    return 0;                                                                  \\
  }
#define yn                                                                     \\
  puts("Yes");                                                                 \\
  else puts("No")
#define YN                                                                     \\
  puts("YES");                                                                 \\
  else puts("NO")

template <typename A, typename B> string to_string(pair<A, B> p);
template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p);
template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p);
string to_string(const string &s) { return '"' + s + '"'; }
string to_string(const char *s) { return to_string((string)s); }
string to_string(bool b) { return (b ? "true" : "false"); }
string to_string(vector<bool> v) {
  bool first = true;
  string ret = "{";
  for (int i = 0; i < static_cast<int>(v.size()); i++) {
    if (!first) {
      ret += ", ";
    }
    first = false;
    ret += to_string(v[i]);
  }
  ret += "}";
  return ret;
}
template <size_t N> string to_string(bitset<N> v) {
  string ret = "";
  for (size_t i = 0; i < N; i++) {
    ret += static_cast<char>('0' + v[i]);
  }
  return ret;
}
template <typename A> string to_string(A v) {
  bool first = true;
  string ret = "{";
  for (const auto &x : v) {
    string s = to_string(x);
    if (!first) {
      ret += ", ";
    }
    if (s[0] == '{') {
      s = "\\n" + s;
    }
    first = false;
    ret += s;
  }
  if (ret[ret.size() - 1] == '}') {
    ret += "\\n}";
  } else {
    ret += "}";
  }
  return ret;
}
template <typename A, typename... Lest>
string to_string(A *v, int n, Lest... L) {
  bool first = true;
  string ret = "{";
  rep(i, n) {
    auto x = v[i];
    string s = to_string(x, L...);
    if (!first) {
      ret += ", ";
    }
    if (s[0] == '{') {
      s = "\\n" + s;
    }
    first = false;
    ret += s;
  }
  if (ret[ret.size() - 1] == '}') {
    ret += "\\n}";
  } else {
    ret += "}";
  }
  return ret;
}
template <typename A, typename B> string to_string(pair<A, B> p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}
template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p) {
  return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " +
         to_string(get<2>(p)) + ")";
}
template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p) {
  return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " +
         to_string(get<2>(p)) + ", " + to_string(get<3>(p)) + ")";
}
void name_disp(string s) {
  cerr << "-------" << endl;
  cerr << s << ": " << endl;
}
void val_disp() { cerr << endl; }
template <typename First, typename... Lest> void val_disp(First F, Lest... L) {
  cerr << to_string(F) << endl;
  val_disp(L...);
}
template <typename A, typename... Lest> void val_disp(A *v, Lest... L) {
  cerr << to_string(v, L...) << endl;
  val_disp();
}
#define disp(...)                                                              \\
  name_disp(#__VA_ARGS__);                                                     \\
  val_disp(__VA_ARGS__)
#define adisp(a, ...)                                                          \\
  name_disp(#a);                                                               \\
  val_disp(a, __VA_ARGS__)

#ifdef int
const ll INF = 1002003004005006007ll;
#else
const int INF = 1002003004;
#endif

const int M = 100000000;
const int dir_4[4][2] = {{1, 0}, {0, 1}, {-1, 0}, {0, -1}};
const int dir_8[8][2] = {{1, 0},  {1, 1},   {0, 1},  {-1, 1},
                         {-1, 0}, {-1, -1}, {0, -1}, {1, -1}};

/* ------------------------------------- */
int gcd(int a, int b) {
  if (a % b == 0) {
    return b;
  } else {
    return gcd(b, a % b);
  }
}

const int MAX_N = 1000010;
bool primeDp[MAX_N];
// n以下の素数を取得する
// だいたいO(n)
vi getPrimes(int n) {
  int u = n + 32;
  double lu = log(u);
  vi ret((int)(u / lu + u / lu / lu * 1.5));

  for (int i = 2; i <= n; i++)
    primeDp[i] = true;
  int sqn = sqrt(n);
  for (int i = 2; i <= sqn; i++) {
    if (!primeDp[i])
      continue;
    for (int j = i * i; j <= n; j += i)
      primeDp[j] = false;
  }
  int idx = 0;
  for (int i = 2; i <= n; i++) {
    if (primeDp[i]) {
      ret[idx] = i;
      idx++;
    }
  }
  return vi(ret.begin(), ret.begin() + idx);
}

// (素数, その個数)というpair<int, int>を配列にまとめたものを返す
vp primeFact(vi primes, int a) {
  if (a == 1) {
    return vp({mp(1, 1)});
  }

  vp ret;
  rep(i, primes.size()) {
    int num = 0;
    int p = primes[i];
    while (a % p == 0) {
      a /= p;
      num++;
    }
    if (num > 0) {
      ret.pb(mp(p, num));
    }
  }
  if (a > 1) {
    ret.pb(mp(a, 1));
  }
  return ret;
}

int n, a[1000100];
int num[1000100];
signed main() {
  scanf("%d", &n);
  rep(i, n) { scanf("%d", &a[i]); }
  vi primes = getPrimes(1000000);
  bool pairwise = true;
  rep(i, n) {
    vp vec = primeFact(primes, a[i]);
    rep(j, vec.size()) {
      int p = vec[j].fr;
      if (num[p] > 0 && p > 1) {
        pairwise = false;
        break;
      } else {
        num[p]++;
      }
    }
    if (!pairwise) {
      break;
    }
  }
  if (pairwise) {
    printf("pairwise coprime\\n");
  } else {
    int c = a[0];
    rep(i, n - 1) { c = gcd(c, a[i + 1]); }
    if (c == 1) {
      printf("setwise coprime\\n");
    } else {
      printf("not coprime\\n");
    }
  }

  /* --------------------------------- */
  return 0;
};