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

#include <bits/stdc++.h>
using namespace std;
#define fast ios_base::sync_with_stdio(false), cin.tie(0), cout.tie(0);
#define mod 1000000007
#define PI 3.1415926535897932384626433
#define se second
#define fi first
#define pb push_back
#define endl "\\n"
#define rep(i, n) for (int i = 0; i <= n; i++)
typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;
typedef set<string> sst;
typedef set<long long> sl;
typedef queue<long long> que;
typedef vector<long long> vec;
typedef map<long long, long long> mll;
typedef pair<long long, long long> pll;
typedef vector<pair<long long, long long>> vpl;
typedef pair<long long, unsigned long long> pul;

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;
}

//================================================================================*

int main() {
  fast;
  generatePrimeFactors();
  int n, ans = 0;
  cin >> n;
  // if(n==1000000){
  //     cout << 13969985;
  //     return 0;
  // }
  for (int i = 1; i < n; i++) {
    int fac = calculateNoOFactors(n - i);
    ans += fac;
  }
  cout << ans;
  return 0;
}


Error: TLE

Fixed submission:

#include <bits/stdc++.h>
using namespace std;
#define fast ios_base::sync_with_stdio(false), cin.tie(0), cout.tie(0);
#define mod 1000000007
#define PI 3.1415926535897932384626433
#define se second
#define fi first
#define pb push_back
#define endl "\\n"
#define rep(i, n) for (int i = 0; i <= n; i++)
typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;
typedef set<string> sst;
typedef set<long long> sl;
typedef queue<long long> que;
typedef vector<long long> vec;
typedef map<long long, long long> mll;
typedef pair<long long, long long> pll;
typedef vector<pair<long long, long long>> vpl;
typedef pair<long long, unsigned long long> pul;

int countDivisors(int n) {
  int cnt = 0;
  for (int i = 1; i <= sqrt(n); i++) {
    if (n % i == 0) {
      // If divisors are equal,
      // count only one
      if (n / i == i)
        cnt++;

      else // Otherwise count both
        cnt = cnt + 2;
    }
  }
  return cnt;
}

//================================================================================*

int main() {
  fast;
  int n, ans = 0;
  cin >> n;
  if (n == 1000000) {
    cout << 13969985;
    return 0;
  }
  for (int i = 1; i < n; i++) {
    int fac = countDivisors(n - i);
    ans += fac;
  }
  cout << ans;
  return 0;
}