Accessing an uninitialized value, most probably in a vector - c++

Question

I am doing an exercise where I need to find a positive integers p and q which are factors of another natural number n.
Following the formula n=pq*q where p is a squarefree number.
However, for some instances of the program my compiler detects a memory error saying that I am accessing an uninitialized value.
The logic I tried is as follows. Firstly, I took the number that needs to be factored (name it n). Next I found all factors of the number n and placed them in a vector. After that, check if every element of that vector is squarefree. If true, put the element in another vector(a vector of squarefree factors of the number n). After that, go through every element of the vector of squarefree factors and solve the equation q=sqrt(n/p) where p is the squarefree factor from the vector. Additionally, I check the condition if(int(sqrt(n/p))==sqrt(n/p)) because the square root needs to be a positive integer.
#include <iostream>
#include <vector>
#include <cmath>
using namespace std;
// Function that checks if the number is squarefree
bool isSquareFree(int n)
{
if (n % 2 == 0)
n = n / 2;
if (n % 2 == 0)
return false;
for (int i = 3; i <= sqrt(n); i += 2)
{
if (n % i == 0)
{
n = n / i;
if (n % i == 0)
return false;
}
}
return true;
}
void Factorise_the_number(int n, int &p, int &q)
{
if (n <= 0)
return 0;
vector<int> factors(0); // vector of factors
vector<int> sqfree_factors(0); // vector of squarefree factors
int sqfree_number; // the number "p"
int squared; // is essentially the number "q"
for (int i = 1; i <= n / 2; i++)
{
if (n % i == 0)
factors.push_back(i); // takes all factors of the number "n"
}
for (int i = 0; i < factors.size(); i++)
{
if (isSquareFree(factors.at(i)))
sqfree_factors.push_back(factors.at(i));
} // checks if each factor is squarefree. if yes, put it in a separate vector
for (auto x : sqfree_factors)
{
if (int(sqrt(n / x)) == sqrt(n / x))
{ // if true, we found the numbers
squared = sqrt(n / x);
sqfree_number = x;
break;
}
}
p = sqfree_number;
q = squared;
}
int main()
{
int n, p = 0, q = 0;
cin >> n;
Factorise_the_number(n, p, q);
cout << p << " " << q;
return 0;
}
For example, my program works if I enter the number 99, but doesn't work if I enter 39. Can anyone give any insight?
Thanks!

Answer 1

As you said, for 39 it doesn't work. Have you checked what it's doing with 39? You should do it, as it is the best way to debug your program.
Let's have a look at it together. First it tries to find all the factors, and it finds 1, 3 and 13: this looks fine.
Then, it checks whether each of those numbers is squarefree, and they all are: this also looks correct.
Then, it checks whether any of the squarefree factors satisfy the equality you are looking for. None of them does (39 is 3 x 13, there's no way it can contain a squared factor). This means that if (int(sqrt(n / x)) == sqrt(n / x)) is never true, and that block is never run. What's the value of sqfree_number and squared at that point? It is never initialised. Using uninitialised values leads to "undefined behaviour", that is, your program can do anything. In this case, p and q end up containing random values.
How can you fix it? Consider this: if n doesn't satisfy your equation, that is, it can't be expressed as pq*q, what, exactly, should the program output? Would your output, as it is now, ever make sense? No. This means you have to modify your program so that it covers a case you hadn't considered.
A way is to add a bool found = false; just before your final for loop. When you find the factors, before breaking, set that variable to true. Then, outside the loop, check it: is it true? Then you can return the correct values. But if it's still false, it means the equality doesn't hold, and you can't return correct values. You have to find a way to signal this to the caller (which is your main function), so that it can print an appropriate message.
And how can you signal it? In general, you could change your Factorise_the_number (by the way, the name of functions should start with a lowercase letter; uppercase letters are usually used for classes) to return a bool. Or you could use a trick: return a special value for p and q that cannot be the result of the calculation. Like -1. Then, before printing, check: if the values are -1, it means the number can't be expressed as pq*q.