TheAlgorithms-C-Plus-Plus/Math/Prime_Factorization/primefactorization.cpp

#include <bits/stdc++.h>
#include <algorithm>
using namespace std;

// Declaring variables for maintaing prime numbers and to check whether a number is prime or not
bool isprime[1000006];
vector<int> prime_numbers;
vector<pair<int,int> > factors;

// Calculating prime number upto a given range
void SieveOfEratosthenes(int N)
{
    // initializes the array isprime
    memset(isprime, true, sizeof isprime);

    for(int i=2; i<=N ; i++)
    {
        if(isprime[i])
        {
            for(int j=2*i; j<=N; j+=i)
                isprime[j]=false;
        }
    }

    for(int i=2; i<=N; i++)
    {
        if(isprime[i])
            prime_numbers.push_back(i);
    }

}

// Prime factorization of a number
void prime_factorization(int num)
{

    vector<int>::iterator it;

    // make sure num is not a prime number
    it = find (prime_numbers.begin(), prime_numbers.end(), num);
    if (it == prime_numbers.end())
    {
        for(int i=0; prime_numbers[i]<=num; i++)
        {
            int count=0;

            while(num%prime_numbers[i] == 0)
            {
                count++;
                num = num/prime_numbers[i];
            }

            if(count)
                factors.push_back(make_pair(prime_numbers[i],count));
        }
    }
    else
    {
        factors.push_back(make_pair(num,1));
    }

}

int main()
{
    int num;
    cout << "\t\tComputes the prime factorization\n\n";
    cout << "Type in a number: ";
    cin>>num;

    SieveOfEratosthenes(num);

    prime_factorization(num);

    // Prime factors with their powers in the given number in new line
    for(auto it: factors)
    {
        cout<<it.first<<" "<<it.second<<endl;
    }

    return 0;
}