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

#include <bits/stdc++.h>
using namespace std;
typedef long long int ll;
#define mod 1000000007

ll gcd(ll a, ll b) {
  if (a == 0)
    return b;
  else
    return gcd(b % a, a);
}

ll lcm(ll a, ll b) { return (a * b) / gcd(a, b); }

ll fact(ll n) {
  if (n == 0)
    return 1;
  else
    return n * fact(n - 1);
}

const int MAX = 1000001;

// array to store prime factors
int factor[MAX] = {0};

// function to generate all prime factors
// of numbers from 1 to 10^6
void generatePrimeFactors() {
  factor[1] = 1;

  // Initializes all the positions with their value.
  for (int i = 2; i < MAX; i++)
    factor[i] = i;

  // Initializes all multiples of 2 with 2
  for (int i = 4; i < MAX; i += 2)
    factor[i] = 2;

  // A modified version of Sieve of Eratosthenes to
  // store the smallest prime factor that divides
  // every number.
  for (int i = 3; i * i < MAX; i++) {
    // check if it has no prime factor.
    if (factor[i] == i) {
      // Initializes of j starting from i*i
      for (int j = i * i; j < MAX; j += i) {
        // if it has no prime factor before, then
        // stores the smallest prime divisor
        if (factor[j] == j)
          factor[j] = i;
      }
    }
  }
}

// function to calculate number of factors
int calculateNoOFactors(int n) {
  if (n == 1)
    return 1;

  int ans = 1;

  // stores the smallest prime number
  // that divides n
  int dup = factor[n];

  // stores the count of number of times
  // a prime number divides n.
  int c = 1;

  // reduces to the next number after prime
  // factorization of n
  int j = n / factor[n];

  // false when prime factorization is done
  while (j != 1) {
    // if the same prime number is dividing n,
    // then we increase the count
    if (factor[j] == dup)
      c += 1;

    /* if its a new prime factor that is factorizing n,
       then we again set c=1 and change dup to the new
       prime factor, and apply the formula explained
       above. */
    else {
      dup = factor[j];
      ans = ans * (c + 1);
      c = 1;
    }

    // prime factorizes a number
    j = j / factor[j];
  }

  // for the last prime factor
  ans = ans * (c + 1);

  return ans;
}

void solve() {

  ll N;
  cin >> N;
  generatePrimeFactors();
  ll i, c = 0;
  for (i = 1; i < N; i++) {
    ll x = calculateNoOFactors(i);
    // cout<<x<<"\\n";
    c += x;
  }
  cout << c;
}

int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  // freopen("D:\\\\codes\\\\1input.txt","r",stdin);
  // freopen("D:\\\\codes\\\\1output.txt","w",stdout);
  ll T = 1;
  // cin>>T;
  for (ll t = 1; t <= T; t++) {
    // cout<<"Case #"<<t<<": ";
    solve();
    // cout<<"\\n";
  }
}


Error: TLE

Fixed submission:

#include <bits/stdc++.h>
using namespace std;
typedef long long int ll;
#define mod 1000000007

ll gcd(ll a, ll b) {
  if (a == 0)
    return b;
  else
    return gcd(b % a, a);
}

ll lcm(ll a, ll b) { return (a * b) / gcd(a, b); }

ll fact(ll n) {
  if (n == 0)
    return 1;
  else
    return n * fact(n - 1);
}

ll nCr(ll n, ll r) { return fact(n) / (fact(r) * fact(n - r)); }

void SieveOfEratosthenes(ll n) {
  bool prime[n + 1];
  memset(prime, true, sizeof(prime));
  for (ll p = 2; p * p <= n; p++) {
    if (prime[p] == true) {
      for (ll i = p * p; i <= n; i += p)
        prime[i] = false;
    }
  }

  for (int p = 2; p <= n; p++)
    if (prime[p])
      cout << p << " ";
}

ll countDivisors(ll n) {
  ll cnt = 0, i = 0;
  for (i = 1; i <= sqrt(n); i++) {
    if (n % i == 0) {
      if (n / i == i)
        cnt++;
      else
        cnt = cnt + 2;
    }
  }
  return cnt;
}

void solve() {

  ll N;
  cin >> N;
  ll i, c = 0;
  for (i = 1; i < N; i++) {
    c += countDivisors(i);
  }
  cout << c;
}

int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  // freopen("D:\\\\codes\\\\1input.txt","r",stdin);
  // freopen("D:\\\\codes\\\\1output.txt","w",stdout);
  ll T = 1;
  // cin>>T;
  for (ll t = 1; t <= T; t++) {
    // cout<<"Case #"<<t<<": ";
    solve();
    // cout<<"\\n";
  }
}