Problem p02660 (C++) — buggy submission, verdict: Time Limit Exceeded

#include <bits/stdc++.h>
using namespace std;
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 res = "{";
  for (int i = 0; i < static_cast<int>(v.size()); i++) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(v[i]);
  }
  res += "}";
  return res;
}

template <size_t N> string to_string(bitset<N> v) {
  string res = "";
  for (size_t i = 0; i < N; i++) {
    res += static_cast<char>('0' + v[i]);
  }
  return res;
}

template <typename A> string to_string(A v) {
  bool first = true;
  string res = "{";
  for (const auto &x : v) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(x);
  }
  res += "}";
  return res;
}

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 debug_out() { cerr << endl; }

template <typename Head, typename... Tail> void debug_out(Head H, Tail... T) {
  cerr << " " << to_string(H);
  debug_out(T...);
}

typedef long long ll;
typedef pair<int, int> pii;
#define mp make_pair
#define fst first
#define snd second
#define fr(i, a, b) for (int i = a; i < b; i++)
template <class T = int> using V = vector<T>;
template <class T = int> using VV = V<V<T>>;

int main() {
  cin.tie(nullptr);
  ios::sync_with_stdio(false);
  ll n;
  cin >> n;
  ll n2 = n;
  vector<pair<ll, ll>> vs;
  for (ll i = 2; i * i <= n2; i++) {
    int cnt = 0;
    while (n % i == 0) {
      n /= i;
      cnt++;
    }
    if (cnt) {
      vs.push_back({i, cnt});
    }
  }
  if (n != 1) {
    vs.push_back({n, 1});
  }
  ll res = 0;
  // debug_out(vs);
  for (int i = 0; i < vs.size(); i++) {
    if (vs[i].first != 1) {
      ll t = 1;
      while (t * (t + 1) <= 2 * vs[i].second)
        t++;
      t--;
      res += t;
    }
  }
  cout << res << endl;
}


Error: TLE

Fixed submission:

#include <bits/stdc++.h>
using namespace std;
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 res = "{";
  for (int i = 0; i < static_cast<int>(v.size()); i++) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(v[i]);
  }
  res += "}";
  return res;
}

template <size_t N> string to_string(bitset<N> v) {
  string res = "";
  for (size_t i = 0; i < N; i++) {
    res += static_cast<char>('0' + v[i]);
  }
  return res;
}

template <typename A> string to_string(A v) {
  bool first = true;
  string res = "{";
  for (const auto &x : v) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(x);
  }
  res += "}";
  return res;
}

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 debug_out() { cerr << endl; }

template <typename Head, typename... Tail> void debug_out(Head H, Tail... T) {
  cerr << " " << to_string(H);
  debug_out(T...);
}

typedef long long ll;
typedef pair<int, int> pii;
#define mp make_pair
#define fst first
#define snd second
#define fr(i, a, b) for (int i = a; i < b; i++)
template <class T = int> using V = vector<T>;
template <class T = int> using VV = V<V<T>>;

int main() {
  cin.tie(nullptr);
  ios::sync_with_stdio(false);
  ll n;
  cin >> n;
  vector<pair<ll, ll>> vs;
  for (int i = 2; i * i <= n; i++) {
    int cnt = 0;
    while (n % i == 0) {
      n /= i;
      cnt++;
    }
    if (cnt) {
      vs.push_back({i, cnt});
    }
  }
  if (n != 1) {
    vs.push_back({n, 1});
  }
  ll res = 0;
  // debug_out(vs);
  for (int i = 0; i < vs.size(); i++) {
    if (vs[i].first != 1) {
      ll t = 1;
      while (t * (t + 1) <= 2 * vs[i].second)
        t++;
      t--;
      res += t;
    }
  }
  cout << res << endl;
}