prime_factorization.cpp

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#include <algorithm>
#include <cstring>
#include <iostream>
#include <vector>

bool isprime[1000006];

std::vector<int> prime_numbers;

std::vector<std::pair<int, int>> factors;

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);
    }
}

void prime_factorization(int num) {
    int number = num;
 
    for (int i = 0; prime_numbers[i] <= num; i++) {
        int count = 0;
 
        // termination condition
        if (number == 1) {
            break;
        }
 
        while (number % prime_numbers[i] == 0) {
            count++;
            number = number / prime_numbers[i];
        }
 
        if (count)
            factors.push_back(std::make_pair(prime_numbers[i], count));
    }
}

int main() {
    int num;
    std::cout << "\t\tComputes the prime factorization\n\n";
    std::cout << "Type in a number: ";
    std::cin >> num;
 
    SieveOfEratosthenes(num);
 
    prime_factorization(num);
 
    // Prime factors with their powers in the given number in new line
    for (auto it : factors) {
        std::cout << it.first << " " << it.second << std::endl;
    }
 
    return 0;
}