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

// C++ program to count number of factors
// of an array of integers
#include <bits/stdc++.h>
using namespace std;

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;
}

// Driver program to test above function
int main() {
  // generate prime factors of number
  // upto 10^6
  generatePrimeFactors();
  int n;
  cin >> n;
  int sum = 0;
  for (int i = 1; i <= n - 1; i++)
    sum += calculateNoOFactors(i);
  cout << sum;

  return 0;
}


Error: TLE

Fixed submission:

#include <algorithm>
#include <assert.h>
#include <cmath>
#include <cstring>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <stdio.h>
#include <stdlib.h>
#include <string>
#include <utility>
#include <vector>

#define int long long int
using namespace std;
#define max(a, b) (a > b ? a : b)
#define min(a, b) (a < b ? a : b)
int mod(int x) { return (((x) % 1000000007) + 1000000007) % 1000000007; }
int check(int a) {
  int count = 0;
  for (int i = 1; i <= sqrt(a); i++) {
    if (a % i == 0) {
      count++;
    }
  }
  int l = sqrt(a);

  if (l * l == a)
    count = count * 2 - 1;
  else
    count = count * 2;
  return count;
}
int solve() {
  int n;
  cin >> n;
  int sum = 0;
  for (int i = 1; i <= n - 1; i++) {
    sum += check(i);
  }
  cout << sum;
  return 0;
}

signed main() {
  ios::sync_with_stdio(0);
  cin.tie(NULL);
  cout.tie(NULL);
  int t;
  // cin >> t;
  t = 1;
  while (t--) {
    solve();
  }
  return 0;
}