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[0] =>Frac[1] =>
Frac[2] =>
Frac[3] =>
Frac[4] =>
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[0] =>Frac[1] =>
Frac[2] =>
Frac[3] =>
Count of Unique Fractions => 4
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 <bits/stdc++.h> 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<pair<int, int>, 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; } |
Java
// Java implementation to find // fractions in its lowest form import java.lang.*; import java.util.*; class GFG{ static class pair { int x, y; pair(int x,int y) { this.x = x; this.y = y; } @Override public int hashCode() { return this.x; } @Override public boolean equals(Object obj) { // If both the object references are // referring to the same object. if(this == obj) return true; // It checks if the argument is of the // type pair by comparing the classes // of the passed argument and this object. // if(!(obj instanceof pair)) return // false; ---> avoid. if(obj == null || obj.getClass() != this.getClass()) return false; // Type casting of the argument. pair geek = (pair) obj; // comparing the state of argument with // the state of 'this' Object. return (geek.x == this.x && geek.y == this.y); } } // Recursive function to // find gcd of a and b static 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 static int countUniqueFractions(int num[], int den[], int N) { // Hash-map to store the fractions // in its lowest form Map<pair, Integer> mp = new HashMap<>(); // Loop to iterate over the // fractions and store is lowest // form in the hash-map for(int i = 0; i < N; i++) { // To find the Lowest form int numer = num[i] / gcd(num[i], den[i]); int denom = den[i] / gcd(num[i], den[i]); pair tmp = new pair(numer, denom); mp.put(tmp, 1); } return mp.size(); } // Driver Code public static void main (String[] args) { int N = 6; // Numerator Array int num[] = { 1, 40, 20, 5, 6, 7 }; // Denominator Array int den[] = { 10, 40, 2, 5, 12, 14 }; System.out.print(countUniqueFractions(num, den, N)); } } // This code is contributed by offbeat |
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 |
4
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