Problem p02722 (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...);
}
#define debug(...) cerr << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)

#define rep(i, n) for (int i = 0; i < n; ++i)
#define reps(i, s, n) for (int i = s; i < n; ++i)
#define rep1(i, n) for (int i = 1; i <= n; ++i)
#define per(i, n) for (int i = n - 1; i >= 0; --i)
#define per1(i, n) for (int i = n; i >= 1; --i)
#define all(c) begin(c), end(c)
template <typename T> inline bool chmin(T &a, T b) {
  if (a > b) {
    a = b;
    return 1;
  }
  return 0;
}
template <typename T> inline bool chmax(T &a, T b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <typename T> inline T intceil(T a, T b) { return (a + (b - 1)) / b; }
typedef long long ll;
typedef long double ld;
typedef pair<int, int> P;
typedef pair<ll, ll> PL;
const long long MOD = 1e9 + 7;
#define precout() cout << std::fixed << std::setprecision(20);
const string alphabet = "abcdefghijklmnopqrstuvwxyz";
const int dy[4] = {0, 1, 0, -1};
const int dx[4] = {1, 0, -1, 0};
// if(nextY >= 0 && nextY < H && nextX >= 0 && nextX < W)
static const long double pi = acos(-1.0);
typedef complex<ld> cd;

template <typename T> vector<T> enum_divisors(T N) {
  vector<T> res;
  for (T i = 2; i * i <= N; ++i) {
    if (N % i == 0) {
      res.push_back(i);
      if (N / i != i)
        res.push_back(N / i);
    }
  }
  sort(res.begin(), res.end());
  return res;
}

int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);

  ll N;
  cin >> N;
  if (N == 2) {
    cout << 1 << endl;
    return 0;
  }

  auto nums = enum_divisors(N);
  auto nums2 = enum_divisors(N - 1);

  int ans = 2 + nums2.size();
  for (auto &a : nums) {
    // debug(a);
    ll n = N;
    while (n % a == 0) {
      n /= a;
    }
    if (n % a == 1LL) {
      // debug(a);
      ++ans;
    }
  }

  cout << ans << 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...);
}
#define debug(...) cerr << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)

#define rep(i, n) for (int i = 0; i < n; ++i)
#define reps(i, s, n) for (int i = s; i < n; ++i)
#define rep1(i, n) for (int i = 1; i <= n; ++i)
#define per(i, n) for (int i = n - 1; i >= 0; --i)
#define per1(i, n) for (int i = n; i >= 1; --i)
#define all(c) begin(c), end(c)
template <typename T> inline bool chmin(T &a, T b) {
  if (a > b) {
    a = b;
    return 1;
  }
  return 0;
}
template <typename T> inline bool chmax(T &a, T b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
template <typename T> inline T intceil(T a, T b) { return (a + (b - 1)) / b; }
typedef long long ll;
typedef long double ld;
typedef pair<int, int> P;
typedef pair<ll, ll> PL;
const long long MOD = 1e9 + 7;
#define precout() cout << std::fixed << std::setprecision(20);
const string alphabet = "abcdefghijklmnopqrstuvwxyz";
const int dy[4] = {0, 1, 0, -1};
const int dx[4] = {1, 0, -1, 0};
// if(nextY >= 0 && nextY < H && nextX >= 0 && nextX < W)
static const long double pi = acos(-1.0);
typedef complex<ld> cd;

template <typename T> vector<T> enum_divisors(T N) {
  vector<T> res;
  for (T i = 2; i * i <= N; ++i) {
    if (N % i == 0) {
      res.push_back(i);
      if (N / i != i)
        res.push_back(N / i);
    }
  }
  sort(res.begin(), res.end());
  return res;
}

int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);

  ll N;
  cin >> N;
  if (N == 2) {
    cout << 1 << endl;
    return 0;
  }

  auto nums = enum_divisors(N);
  auto nums2 = enum_divisors(N - 1);

  int ans = 2 + nums2.size();
  for (auto &a : nums) {
    debug(a);
    ll n = N;
    while (n >= a) {
      if (n % a == 0) {
        n /= a;
      } else {
        n -= a;
      }
    }
    if (n == 1LL) {
      // debug(a);
      ++ans;
    }
  }

  cout << ans << endl;
}