# Max count of unique ratio/fraction pairs in given arrays

Given two arrays num[] and den[] which denotes the numerator and denominator respectively, the task is to find the count of the unique fractions.

Examples:

Input: num[] = {1, 2, 3, 4, 5}, den[] = {2, 4, 6, 1, 11}
Output: 3
Explanation:
Simplest forms of the fractions
Frac => Frac => Frac => Frac => Frac => Count of Unique Fractions => 3

Input: num[] = {10, 20, 30, 50}, den[] = {10, 10, 10, 10}
Output: 4
Explanation:
Simplest forms of the fractions
Frac => Frac => Frac => Frac => Count of Unique Fractions => 4

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: The idea is to use hash-map to find the unique fractions. To store the fractions such that the duplicates are not there, we convert each fraction to its lowest form.

Below is the implementation of the above approach:

## C++

 // C++ implementation to find   // fractions in its lowest form     #include     using namespace std;     // Recursive function to   // find gcd of a and b  int gcd(int a, int b)  {      if (b == 0)          return a;      return gcd(b, a % b);  }     // Function to count the unique  // fractios in the given array  int countUniqueFractions(int num[],                     int den[], int N){             // Hash-map to store the fractions      // in its lowest form      map, int> mp;             // Loop to iterate over the       // fractions and store is lowest      // form in the hash-map      for (int i = 0; i < N; i++) {          int numer, denom;                     // To find the Lowest form          numer = num[i] / gcd(num[i], den[i]);          denom = den[i] / gcd(num[i], den[i]);          mp[make_pair(numer, denom)] += 1;      }             return mp.size();  }     // Driver code  int main()  {      int N = 6;             // Numerator Array      int num[] = { 1, 40, 20, 5, 6, 7 };             // Denominator Array      int den[] = { 10, 40, 2, 5, 12, 14 };             cout << countUniqueFractions(num, den, N);             return 0;  }

## Python3

 # Python3 implementation to find   # fractions in its lowest form  from collections import defaultdict      # Recursive function to   # find gcd of a and b  def gcd(a, b):         if (b == 0):          return a      return gcd(b, a % b)     # Function to count the unique  # fractios in the given array  def countUniqueFractions(num, den, N):             # Hash-map to store the fractions      # in its lowest form      mp = defaultdict(int)             # Loop to iterate over the       # fractions and store is lowest      # form in the hash-map      for i in range(N):                     # To find the Lowest form          numer = num[i] // gcd(num[i], den[i])          denom = den[i] // gcd(num[i], den[i])          mp[(numer, denom)] += 1            return len(mp)     # Driver code  if __name__ == "__main__":             N = 6            # Numerator Array      num = [ 1, 40, 20, 5, 6, 7 ]             # Denominator Array      den = [ 10, 40, 2, 5, 12, 14 ]             print(countUniqueFractions(num, den, N))     # This code is contributed by chitranayal

Output:

4


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Improved By : chitranayal, nidhi_biet