Problem p02548 (C++) — buggy submission, verdict: Time Limit Exceeded

#pragma GCC optimize("Ofast")
#include "bits/stdc++.h"

// Begin Header {{{
using namespace std;

#ifndef DEBUG
#define dump(...)
#endif

#define all(x) begin(x), end(x)
#define rall(x) rbegin(x), rend(x)
#define rep(i, b, e) for (intmax_t i = (b), i##_limit = (e); i < i##_limit; ++i)
#define repc(i, b, e)                                                          \\
  for (intmax_t i = (b), i##_limit = (e); i <= i##_limit; ++i)
#define repr(i, b, e)                                                          \\
  for (intmax_t i = (b), i##_limit = (e); i >= i##_limit; --i)
#define var(Type, ...)                                                         \\
  Type __VA_ARGS__;                                                            \\
  input(__VA_ARGS__)

constexpr size_t operator""_zu(unsigned long long value) { return value; };
constexpr intmax_t operator""_jd(unsigned long long value) { return value; };
constexpr uintmax_t operator""_ju(unsigned long long value) { return value; };

constexpr int INF = 0x3f3f3f3f;
constexpr intmax_t LINF = 0x3f3f3f3f3f3f3f3f_jd;

template <class T, class Compare = less<>>
using MaxHeap = priority_queue<T, vector<T>, Compare>;
template <class T, class Compare = greater<>>
using MinHeap = priority_queue<T, vector<T>, Compare>;

inline void input() {}
template <class Head, class... Tail>
inline void input(Head &&head, Tail &&...tail) {
  cin >> head;
  input(forward<Tail>(tail)...);
}

template <class Container, class Value = typename Container::value_type,
          enable_if_t<!is_same<Container, string>::value, nullptr_t> = nullptr>
inline istream &operator>>(istream &is, Container &vs) {
  for (auto &v : vs)
    is >> v;
  return is;
}

inline void output() { cout << "\\n"; }
template <class Head, class... Tail>
inline void output(Head &&head, Tail &&...tail) {
  cout << head;
  if (sizeof...(tail))
    cout << " ";
  output(forward<Tail>(tail)...);
}

template <class Container, class Value = typename Container::value_type,
          enable_if_t<!is_same<Container, string>::value, nullptr_t> = nullptr>
inline ostream &operator<<(ostream &os, const Container &vs) {
  static constexpr const char *delim[] = {" ", ""};
  for (auto it = begin(vs); it != end(vs); ++it) {
    os << delim[it == begin(vs)] << *it;
  }
  return os;
}

template <class Iterator>
inline void join(const Iterator &Begin, const Iterator &End,
                 const string &delim = "\\n", const string &last = "\\n") {
  for (auto it = Begin; it != End; ++it) {
    cout << ((it == Begin) ? "" : delim) << *it;
  }
  cout << last;
}

template <class T> inline vector<T> makeVector(const T &initValue, size_t sz) {
  return vector<T>(sz, initValue);
}

template <class T, class... Args>
inline auto makeVector(const T &initValue, size_t sz, Args... args) {
  return vector<decltype(makeVector<T>(initValue, args...))>(
      sz, makeVector<T>(initValue, args...));
}

template <class Func> class FixPoint : Func {
public:
  explicit constexpr FixPoint(Func &&f) noexcept : Func(forward<Func>(f)) {}

  template <class... Args>
  constexpr decltype(auto) operator()(Args &&...args) const {
    return Func::operator()(*this, std::forward<Args>(args)...);
  }
};

template <class Func>
static inline constexpr decltype(auto) makeFixPoint(Func &&f) noexcept {
  return FixPoint<Func>{forward<Func>(f)};
}

template <class Container> struct reverse_t {
  Container &c;
  reverse_t(Container &c) : c(c) {}
  auto begin() { return c.rbegin(); }
  auto end() { return c.rend(); }
};

template <class Container> auto reversed(Container &c) {
  return reverse_t<Container>(c);
}

template <class T> inline bool chmax(T &a, const T &b) noexcept {
  return b > a && (a = b, true);
}

template <class T> inline bool chmin(T &a, const T &b) noexcept {
  return b < a && (a = b, true);
}

template <class T> inline T diff(const T &a, const T &b) noexcept {
  return a < b ? b - a : a - b;
}

void ioinit() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  cout << fixed << setprecision(10);
  clog << fixed << setprecision(10);
}
// }}} End Header

// SmartSieve {{{
class SmartSieve {
  intmax_t L, R, M;
  vector<intmax_t> small;         // 小さい篩 [2, sqrt(R))
  vector<vector<intmax_t>> large; // 大きい篩 [L, R)
  vector<intmax_t> aux;           // aux[i] := large[i] の素因数の積

public:
  SmartSieve(intmax_t L, intmax_t R) : L(L), R(R), M(sqrt(R) + 1) {
    small.resize(M);
    iota(small.begin(), small.end(), 0);
    large.resize(R - L);
    aux.assign(R - L, 1);

    for (intmax_t i = 2; i * i < R; ++i) {
      if (small[i] < i)
        continue;

      for (intmax_t j = i * i; j < M; j += i) {
        if (small[j] == j)
          small[j] = i;
      }

      for (intmax_t j = (L + i - 1) / i * i; j < R; j += i) {
        intmax_t k = j;
        do {
          if (aux[j - L] * aux[j - L] > R)
            break;

          large[j - L].emplace_back(i);
          aux[j - L] *= i;
          k /= i;
        } while (k % i == 0);
      }
    }
  }

  bool isPrime(intmax_t n) const {
    assert(L <= n && n < R);
    if (n < M)
      return (2 <= n && small[n] == n);
    return (aux[n - L] == 1);
  }

  vector<intmax_t> primeFactorize(intmax_t n) {
    assert(L <= n && n < R);
    vector<intmax_t> ret = large[n - L];
    n /= aux[n - L];
    if (n >= M) {
      ret.emplace_back(n);
      return ret;
    }
    while (n > 1) {
      ret.emplace_back(small[n]);
      n /= small[n];
    }
    return ret;
  }
};
// }}}

signed main() {
  ioinit();

  var(intmax_t, N);

  SmartSieve sieve(1, intmax_t(1e6) + 1);

  intmax_t res = 0;
  rep(c, 1, N) {
    const auto ps = sieve.primeFactorize(N - c);
    intmax_t m = 1;
    unordered_map<intmax_t, intmax_t> cs;
    for (const auto p : ps)
      cs[p]++;
    for (const auto c : cs)
      m *= (c.second + 1);
    res += m;
  }
  output(res);

  return 0;
}


Error: TLE

Fixed submission:

#pragma GCC optimize("Ofast")
#include "bits/stdc++.h"

// Begin Header {{{
using namespace std;

#ifndef DEBUG
#define dump(...)
#endif

#define all(x) begin(x), end(x)
#define rall(x) rbegin(x), rend(x)
#define rep(i, b, e) for (intmax_t i = (b), i##_limit = (e); i < i##_limit; ++i)
#define repc(i, b, e)                                                          \\
  for (intmax_t i = (b), i##_limit = (e); i <= i##_limit; ++i)
#define repr(i, b, e)                                                          \\
  for (intmax_t i = (b), i##_limit = (e); i >= i##_limit; --i)
#define var(Type, ...)                                                         \\
  Type __VA_ARGS__;                                                            \\
  input(__VA_ARGS__)

constexpr size_t operator""_zu(unsigned long long value) { return value; };
constexpr intmax_t operator""_jd(unsigned long long value) { return value; };
constexpr uintmax_t operator""_ju(unsigned long long value) { return value; };

constexpr int INF = 0x3f3f3f3f;
constexpr intmax_t LINF = 0x3f3f3f3f3f3f3f3f_jd;

template <class T, class Compare = less<>>
using MaxHeap = priority_queue<T, vector<T>, Compare>;
template <class T, class Compare = greater<>>
using MinHeap = priority_queue<T, vector<T>, Compare>;

inline void input() {}
template <class Head, class... Tail>
inline void input(Head &&head, Tail &&...tail) {
  cin >> head;
  input(forward<Tail>(tail)...);
}

template <class Container, class Value = typename Container::value_type,
          enable_if_t<!is_same<Container, string>::value, nullptr_t> = nullptr>
inline istream &operator>>(istream &is, Container &vs) {
  for (auto &v : vs)
    is >> v;
  return is;
}

inline void output() { cout << "\\n"; }
template <class Head, class... Tail>
inline void output(Head &&head, Tail &&...tail) {
  cout << head;
  if (sizeof...(tail))
    cout << " ";
  output(forward<Tail>(tail)...);
}

template <class Container, class Value = typename Container::value_type,
          enable_if_t<!is_same<Container, string>::value, nullptr_t> = nullptr>
inline ostream &operator<<(ostream &os, const Container &vs) {
  static constexpr const char *delim[] = {" ", ""};
  for (auto it = begin(vs); it != end(vs); ++it) {
    os << delim[it == begin(vs)] << *it;
  }
  return os;
}

template <class Iterator>
inline void join(const Iterator &Begin, const Iterator &End,
                 const string &delim = "\\n", const string &last = "\\n") {
  for (auto it = Begin; it != End; ++it) {
    cout << ((it == Begin) ? "" : delim) << *it;
  }
  cout << last;
}

template <class T> inline vector<T> makeVector(const T &initValue, size_t sz) {
  return vector<T>(sz, initValue);
}

template <class T, class... Args>
inline auto makeVector(const T &initValue, size_t sz, Args... args) {
  return vector<decltype(makeVector<T>(initValue, args...))>(
      sz, makeVector<T>(initValue, args...));
}

template <class Func> class FixPoint : Func {
public:
  explicit constexpr FixPoint(Func &&f) noexcept : Func(forward<Func>(f)) {}

  template <class... Args>
  constexpr decltype(auto) operator()(Args &&...args) const {
    return Func::operator()(*this, std::forward<Args>(args)...);
  }
};

template <class Func>
static inline constexpr decltype(auto) makeFixPoint(Func &&f) noexcept {
  return FixPoint<Func>{forward<Func>(f)};
}

template <class Container> struct reverse_t {
  Container &c;
  reverse_t(Container &c) : c(c) {}
  auto begin() { return c.rbegin(); }
  auto end() { return c.rend(); }
};

template <class Container> auto reversed(Container &c) {
  return reverse_t<Container>(c);
}

template <class T> inline bool chmax(T &a, const T &b) noexcept {
  return b > a && (a = b, true);
}

template <class T> inline bool chmin(T &a, const T &b) noexcept {
  return b < a && (a = b, true);
}

template <class T> inline T diff(const T &a, const T &b) noexcept {
  return a < b ? b - a : a - b;
}

void ioinit() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  cout << fixed << setprecision(10);
  clog << fixed << setprecision(10);
}
// }}} End Header

vector<intmax_t> divisor(intmax_t n) {
  vector<intmax_t> ret;

  for (intmax_t i = 1; i * i <= n; ++i) {
    if (n % i == 0) {
      ret.emplace_back(i);
      if (i * i != n) {
        ret.emplace_back(n / i);
      }
    }
  }

  sort(ret.begin(), ret.end());
  return ret;
}

signed main() {
  ioinit();

  var(intmax_t, N);

  intmax_t res = 0;
  repc(c, 1, N) { res += divisor(N - c).size(); }
  output(res);

  return 0;
}