Given rational numbers, the task is to find the maximum rational number.
Examples:
Input : ra_num = {{1, 2},
{2, 3},
{3, 4},
{4, 5}};
Output : 4 5
Input : ra_num = {{10, 12},
{12, 33},
{33, 14},
{14, 15}};
Output : 33 14
A simple solution is to find float values and compare the float values. The float computations may cause precision errors. We can avoid them using the below approach.
Say numbers are 1/2, 2/3, 3/4, 4/5
First take an LCM of (2, 3, 4, 5) which is the denominator of all rational numbers. So the LCM of this is 60, then divide with all denominator’s and multiple with all numerators, so the value of numerators are (30, 40, 45, 48)
Then find the max between these rational numbers. So here the last numerator is max then print the last rational number, which is 4/5.
C++
// CPP program to find the maximum rational// number in an array.#include <bits/stdc++.h>using namespace std;struct Rational { // numerator and Denominator int nume, deno;};// here we find the Denominator LCMint lcmOfDenominator(vector<Rational> ra_num){ // get the first Denominator as lcm int lcm = ra_num[0].deno; int i; // find the lcm of all relational // number Denominator for (i = 1; i < ra_num.size(); i++) lcm = (lcm * (ra_num[i].deno)) / __gcd(lcm, ra_num[i].deno); // return the lcm return lcm;}int maxRational(vector<Rational> ra_num){ // take a temp array for find // maximum numerator after multiple int temp[ra_num.size()] = { 0 }; // get here the lcm of all rational //number denominator int lcm = lcmOfDenominator(ra_num); // take maximum for get maximum index int maximum = 0; int maximumind = 0; // find the index which contain maximum value for (int i = 0; i < ra_num.size(); i++) { // divide lcm with denominator // and multiple with numerator temp[i] = (ra_num[i].nume) * (lcm / ra_num[i].deno); // get the maximum numerator if (maximum < temp[i]) { maximum = temp[i]; maximumind = i; } } // return index which contain // maximum rational number return maximumind;}int main(){ // given rational number vector<Rational> ra_num = { { 1, 2 }, { 2, 3 }, { 3, 4 }, { 4, 5 } }; // get the index which contain maximum value int index_max = maxRational(ra_num); // print numerator and denominator cout << ra_num[index_max].nume << " " << ra_num[index_max].deno << "\n";} |
Java
// Java program to find the maximum rational // number in an array. import java.util.*;class GFG {static class Rational{ // numerator and Denominator int nume, deno; public Rational(int nume, int deno) { this.nume = nume; this.deno = deno; } }; // here we find the Denominator LCM static int lcmOfDenominator(Vector<Rational> ra_num) { // get the first Denominator as lcm int lcm = ra_num.get(0).deno; int i; // find the lcm of all relational // number Denominator for (i = 1; i < ra_num.size(); i++) lcm = (lcm * (ra_num.get(i).deno)) / __gcd(lcm, ra_num.get(i).deno); // return the lcm return lcm; } static int maxRational(Vector<Rational> ra_num) { // take a temp array for find // maximum numerator after multiple int []temp = new int[ra_num.size()]; // get here the lcm of all rational //number denominator int lcm = lcmOfDenominator(ra_num); // take maximum for get maximum index int maximum = 0; int maximumind = 0; // find the index which contain maximum value for (int i = 0; i < ra_num.size(); i++) { // divide lcm with denominator // and multiple with numerator temp[i] = (ra_num.get(i).nume) * (lcm / ra_num.get(i).deno); // get the maximum numerator if (maximum < temp[i]) { maximum = temp[i]; maximumind = i; } } // return index which contain // maximum rational number return maximumind; } static int __gcd(int a, int b) { if (b == 0) return a; return __gcd(b, a % b); }// Driver Codepublic static void main(String[] args) { // given rational number Vector<Rational> ra_num = new Vector<Rational>(); ra_num.add(new Rational( 1, 2 )); ra_num.add(new Rational( 2, 3 )); ra_num.add(new Rational( 3, 4 )); ra_num.add(new Rational( 4, 5 )); // get the index which contain maximum value int index_max = maxRational(ra_num); // print numerator and denominator System.out.println(ra_num.get(index_max).nume + " " + ra_num.get(index_max).deno); }}// This code is contributed by Princi Singh |
Python3
# Python3 program to find the maximum rational # number in an array. class Rational: def __init__(self, nume, deno): # Numerator and Denominator self.nume = nume self.deno = denodef computeGCD(x, y): while(y): x, y = y, x % y return x # Here we find the Denominator LCM def lcmOfDenominator(ra_num): # Get the first Denominator as lcm lcm = ra_num[0].deno # Find the lcm of all relational # number Denominator for i in range(1, len(ra_num)): lcm = ((lcm * (ra_num[i].deno)) // computeGCD(lcm, ra_num[i].deno)) # return the lcm return lcmdef maxRational(ra_num): # Take a temp array for find # maximum numerator after multiple temp = [0 for i in range(len(ra_num))] # Get here the lcm of all rational # number denominator lcm = lcmOfDenominator(ra_num) # Take maximum for get maximum index maximum = 0 maximumind = 0 # Find the index which contain # maximum value for i in range(len(ra_num)): # Divide lcm with denominator # and multiple with numerator temp[i] = ((ra_num[i].nume) * (lcm // ra_num[i].deno)) # Get the maximum numerator if (maximum < temp[i]): maximum = temp[i] maximumind = i # Return index which contain # maximum rational number return maximumind# Driver codeif __name__=="__main__": # Given rational number ra_num = [] ra_num.append(Rational(1, 2)) ra_num.append(Rational(2, 3)) ra_num.append(Rational(3, 4)) ra_num.append(Rational(4, 5)) # Get the index which contain maximum value index_max = maxRational(ra_num) # Print numerator and denominator print(str(ra_num[index_max].nume) + " " + str(ra_num[index_max].deno)) # This code is contributed by rutvik_56 |
C#
// C# program to find the maximum rational // number in an array.using System;using System.Collections.Generic; class GFG {public class Rational{ // numerator and Denominator public int nume, deno; public Rational(int nume, int deno) { this.nume = nume; this.deno = deno; } }; // here we find the Denominator LCM static int lcmOfDenominator(List<Rational> ra_num) { // get the first Denominator as lcm int lcm = ra_num[0].deno; int i; // find the lcm of all relational // number Denominator for (i = 1; i < ra_num.Count; i++) lcm = (lcm * (ra_num[i].deno)) / __gcd(lcm, ra_num[i].deno); // return the lcm return lcm; } static int maxRational(List<Rational> ra_num) { // take a temp array for find // maximum numerator after multiple int []temp = new int[ra_num.Count]; // get here the lcm of all rational //number denominator int lcm = lcmOfDenominator(ra_num); // take maximum for get maximum index int maximum = 0; int maximumind = 0; // find the index which contain maximum value for (int i = 0; i < ra_num.Count; i++) { // divide lcm with denominator // and multiple with numerator temp[i] = (ra_num[i].nume) * (lcm / ra_num[i].deno); // get the maximum numerator if (maximum < temp[i]) { maximum = temp[i]; maximumind = i; } } // return index which contain // maximum rational number return maximumind; } static int __gcd(int a, int b) { if (b == 0) return a; return __gcd(b, a % b); }// Driver Codepublic static void Main(String[] args) { // given rational number List<Rational> ra_num = new List<Rational>(); ra_num.Add(new Rational( 1, 2 )); ra_num.Add(new Rational( 2, 3 )); ra_num.Add(new Rational( 3, 4 )); ra_num.Add(new Rational( 4, 5 )); // get the index which contain maximum value int index_max = maxRational(ra_num); // print numerator and denominator Console.WriteLine(ra_num[index_max].nume + " " + ra_num[index_max].deno); }}// This code is contributed by PrinciRaj1992 |
Javascript
<script> // JavaScript program to find the maximum rational // number in an array. class Rational { constructor(nume, deno) { this.nume = nume; this.deno = deno; } } // here we find the Denominator LCM function lcmOfDenominator(ra_num) { // get the first Denominator as lcm var lcm = ra_num[0].deno; var i; // find the lcm of all relational // number Denominator for (i = 1; i < ra_num.length; i++) lcm = (lcm * ra_num[i].deno) / __gcd(lcm, ra_num[i].deno); // return the lcm return lcm; } function maxRational(ra_num) { // take a temp array for find // maximum numerator after multiple var temp = new Array(ra_num.Count); // get here the lcm of all rational //number denominator var lcm = lcmOfDenominator(ra_num); // take maximum for get maximum index var maximum = 0; var maximumind = 0; // find the index which contain maximum value for (var i = 0; i < ra_num.length; i++) { // divide lcm with denominator // and multiple with numerator temp[i] = ra_num[i].nume * (lcm / ra_num[i].deno); // get the maximum numerator if (maximum < temp[i]) { maximum = temp[i]; maximumind = i; } } // return index which contain // maximum rational number return maximumind; } function __gcd(a, b) { if (b === 0) return a; return __gcd(b, a % b); } // Driver Code // given rational number var ra_num = []; ra_num.push(new Rational(1, 2)); ra_num.push(new Rational(2, 3)); ra_num.push(new Rational(3, 4)); ra_num.push(new Rational(4, 5)); // get the index which contain maximum value var index_max = maxRational(ra_num); // print numerator and denominator document.write(ra_num[index_max].nume + " " + ra_num[index_max].deno); </script> |
Output:
4 5
Time Complexity: O(N*log(K)) where N is the size of the given array and K can be the largest denominator of the array.
Auxiliary Space: O(N)
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