C++: Could someone help me optimize my solution? [closed] - c++

Question

Closed. This question needs details or clarity. It is not currently accepting answers.
Want to improve this question? Add details and clarify the problem by editing this post.
Closed 1 year ago.
Improve this question
Program adds 2 fractions and displays their sum in a reduced form (n times). Could someone help me optimize my solution (According to SPOJ, the time limit has been exceeded)
My solution:
#include <iostream>
using namespace std;
int main()
{
int n, a, b, c, d, gcd;
long long num, den;
cin >> n;
for(int i = 0; i < n; i++)
{
cin >> a >> b >> c >> d;
num = (a*d)+(b*c);
den = b*d;
for(int j = 1; j <= num && j <= den; ++j)
{
if(num % j == 0 && den % j == 0)
{
gcd = j;
}
}
cout << num/gcd << " " << den/gcd << endl;
}
}

Answer 1

The key step in your code is computing the greatest common divisor of num and den. The code does this by testing every number less than or equal to either of them to find the largest that divides both. While this is a correct algorithm, it is very slow, requiring time proportional to whichever is smaller.
To make this faster, use the Euclidean algorithm, which takes time proportional to the logarithm of the smaller number, which means it is much faster. The essence of this algorithm is to divide one number by the other and replace the larger with the resulting remainder until that remainder is zero. Concretely, copying and slightly reformatting the code from tutorialspoint.com:
int gcd(int a, int b)
{
if (b == 0)
return a;
return gcd(b, a % b);
}
Alternatively, as noted in a comment by #badfilms, C++17 contains std::gcd in the library.