Problem p02624 (C++) — buggy submission, verdict: Time Limit Exceeded

#include <algorithm>
#include <bitset>
#include <cassert>
#include <cmath>
#include <cstdint>
#include <cstdlib>
#include <functional>
#include <iomanip>
#include <iostream>
#include <limits>
#include <map>
#include <math.h>
#include <numeric>
#include <queue>
#include <set>
#include <stack>
#include <string.h>
#include <string>
#include <utility>
#include <vector>

using namespace std;

/* template */

using ll = long long;

void debug_out() { std::cout << std::endl; }

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

#ifdef LOCAL
#define debug(...)                                                             \\
  cout << "debug: ";                                                           \\
  debug_out(__VA_ARGS__)
#else
#define debug(...)
#endif

#define rep(i, a, n) for (int i = (int)(a); i < (int)(n); i++)
#define rrep(i, a, n) for (int i = ((int)(n - 1)); i >= (int)(a); i--)
#define Rep(i, a, n) for (long long i = (long long)(a); i < (long long)(n); i++)
#define RRep(i, a, n)                                                          \\
  for (long long i = ((long long)(n - 1ll)); i >= (long long)(a); i--)
#define all(v) (v).begin(), (v).end()
#define rall(v) (v).rbegin(), (v).rend()

template <typename T>
std::ostream &operator<<(std::ostream &os, std::vector<T> vec) {
  for (std::size_t i = 0; i < vec.size(); i++)
    os << vec[i] << (i + 1 == vec.size() ? "" : " ");
  return os;
}

struct Edge {
  int to;
  ll weight;
  Edge(int t, ll w) : to(t), weight(w) {}
};

struct edge {
  int from;
  int to;
  ll weight;
  edge(int f, int t, ll w) : from(f), to(t), weight(w) {}
};

using Graph = vector<vector<Edge>>;
using graph = vector<vector<int>>;
using edges = vector<edge>;

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

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

template <class T> T lcm(T a, T b) { return (a * b) / gcd(a, b); }

ll ctoi(char c) {
  switch (c) {
  case '0':
    return 0;
  case '1':
    return 1;
  case '2':
    return 2;
  case '3':
    return 3;
  case '4':
    return 4;
  case '5':
    return 5;
  case '6':
    return 6;
  case '7':
    return 7;
  case '8':
    return 8;
  case '9':
    return 9;
  default:
    return 0;
  }
}

constexpr ll LNF = 1LL << 50;

constexpr int INF = 1e9 + 7;

const long double PI = 3.14159265358979323846;

vector<int> dx = {1, 0, -1, 1, -1, 0};
vector<int> dy = {1, 1, 1, 0, 0, -1};

/* template */

int main() {
  cin.tie(nullptr);
  ios::sync_with_stdio(false);
  ll n;
  cin >> n;
  ll ans = 0;
  Rep(i, 1, n + 1) {
    ll res = n / i;
    ans += i * res * (res + 1) / 2;
  }
  cout << ans << endl;
}

Error: TLE

Fixed submission:

#include <algorithm>
#include <bitset>
#include <cassert>
#include <cmath>
#include <cstdint>
#include <cstdlib>
#include <functional>
#include <iomanip>
#include <iostream>
#include <limits>
#include <map>
#include <math.h>
#include <numeric>
#include <queue>
#include <set>
#include <stack>
#include <string.h>
#include <string>
#include <utility>
#include <vector>

using namespace std;

/* template */

using ll = long long;

void debug_out() { std::cout << std::endl; }

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

#ifdef LOCAL
#define debug(...)                                                             \\
  cout << "debug: ";                                                           \\
  debug_out(__VA_ARGS__)
#else
#define debug(...)
#endif

#define rep(i, a, n) for (int i = (int)(a); i < (int)(n); i++)
#define rrep(i, a, n) for (int i = ((int)(n - 1)); i >= (int)(a); i--)
#define Rep(i, a, n) for (long long i = (long long)(a); i < (long long)(n); i++)
#define RRep(i, a, n)                                                          \\
  for (long long i = ((long long)(n - 1ll)); i >= (long long)(a); i--)
#define all(v) (v).begin(), (v).end()
#define rall(v) (v).rbegin(), (v).rend()

template <typename T>
std::ostream &operator<<(std::ostream &os, std::vector<T> vec) {
  for (std::size_t i = 0; i < vec.size(); i++)
    os << vec[i] << (i + 1 == vec.size() ? "" : " ");
  return os;
}

struct Edge {
  int to;
  ll weight;
  Edge(int t, ll w) : to(t), weight(w) {}
};

struct edge {
  int from;
  int to;
  ll weight;
  edge(int f, int t, ll w) : from(f), to(t), weight(w) {}
};

using Graph = vector<vector<Edge>>;
using graph = vector<vector<int>>;
using edges = vector<edge>;

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

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

template <class T> T lcm(T a, T b) { return (a * b) / gcd(a, b); }

ll ctoi(char c) {
  switch (c) {
  case '0':
    return 0;
  case '1':
    return 1;
  case '2':
    return 2;
  case '3':
    return 3;
  case '4':
    return 4;
  case '5':
    return 5;
  case '6':
    return 6;
  case '7':
    return 7;
  case '8':
    return 8;
  case '9':
    return 9;
  default:
    return 0;
  }
}

constexpr ll LNF = 1LL << 50;

constexpr int INF = 1e9 + 7;

const long double PI = 3.14159265358979323846;

vector<int> dx = {1, 0, -1, 1, -1, 0};
vector<int> dy = {1, 1, 1, 0, 0, -1};

/* template */

int main() {
  cin.tie(nullptr);
  ios::sync_with_stdio(false);
  ll n;
  cin >> n;
  vector<ll> a(n + 1);
  vector<map<ll, ll>> b(n + 1);
  vector<ll> p(n + 1, -1);
  rep(i, 2, n + 1) {
    if (p[i] == -1) {
      for (int j = 2 * i; j <= n; j += i) {
        p[j] = i;
      }
    }
  }
  a[1] = 1;
  ll ans = 1ll;
  rep(i, 2, n + 1) {
    ll x = 0;
    if (p[i] == -1) {
      x = 2;
      b[i][i]++;
    } else {
      ll y = i / p[i];
      ll t = b[y][p[i]];
      x = a[y] / (t + 1ll);
      x *= t + 2ll;
      b[i] = b[y];
      b[i][p[i]]++;
    }
    a[i] = x;
    ans += x * i;
  }
  cout << ans << endl;
}