Iterative equivalent a recursive algorithm - c++

Question

I'm trying to modify this program to their equivalent iterative but it becomes very difficult to me because as yet i'm still a newbie, it comes to an algorithm that decomposes a number into its prime factors, here the code:
#include <iostream>
#include <map>
#include <cmath>
std::map< int, std::pair<int, int> > decompositions;
void descompon_number(int num, int root, int i = 2 )
{
auto iterator = decompositions.find(num);
if (iterator == decompositions.end())
{
if (num > 1 && i <= root)
{
if (num % i == 0)
{
int n = num / i;
decompositions[num] = std::make_pair(i, n);
descompon_number(n, (int) std::sqrt(n));
}
else
descompon_number(num, root, i + 1);
}
else
decompositions[num] = std::make_pair(num, 1);
}
}
void show(int num, int factor, int exponent, int see)
{
auto pair = decompositions[num];
if (num <= 1 || factor != pair.first)
{
if (see)
std::cout << factor;
if (exponent > 1 && see)
std::cout << "^" << exponent;
if (pair.first > 1 && see)
std::cout << " * ";
exponent = 0;
}
if (num > 1)
show(pair.second, pair.first, exponent + 1, see);
}
void descompon(int a, int b, int see)
{
if (a <= b)
{
descompon_number(a, (int) std::sqrt(a));
if (see)
std::cout << a << " = ";
show(a, decompositions[a].first, 0, see);
if (see)
std::cout << std::endl;
descompon(a + 1, b, see);
}
}
int main()
{
descompon(2, 100, 1);
return 0;
}
Someone can help me out with this

Answer 1

Finding prime factors iteratively is not very complicated.
Here's the pseudocode how to do this.
Let P be a list of the first n prime numbers, such that Pn <= sqrt(m).
array findPrimeFactors(m)
answer = new array
for p in P
while m can be divided by p
m = m / p
answer.append(p)
if m == 1
break
return answer
Note: empty array is returned if m is prime.

Answer 2

You can use an erastotenes' sieve to compute prime numbers, and later you can use the algorithm posted by popovitsj.
The following code can be optimized, but its main purpose is to show you how to proceed.
Complete example:
#include <iostream>
#include <vector>
using namespace std;
// Returns a vector containing the first <number> prime numbers
vector<int> erastotenes_sieve(int number)
{
vector<int> result;
int *sieve = new int[number];
for (int i = 0; i < number; i++) sieve[i] = 0;
// Traverse the sieve marking multiples.
for (int i = 2; i < number / 2; i++)
for (int j = i + i; j < number; j += i)
sieve[j] = 1;
// Collect unaffected indexes, those are prime numbers.
for (int i = 2; i < number; i++)
if (!sieve[i])
result.push_back(i);
delete [] sieve;
return result;
}
vector<int> descompon_number(int number)
{
vector<int> result;
if (number == 1 || number == 0)
{
result.push_back(number);
return result;
}
for (int &prime : erastotenes_sieve(number))
{
while (number % prime == 0 && number != 1)
{
number /= prime;
result.push_back(prime);
}
}
return result;
}
int main()
{
for (auto &i : descompon_number(20))
{
cout << i << endl;
}
return 0;
}