Maximum rational number (or fraction) from an array

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 below approach.

Say number’s 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 number. so the LCM of this is 60, then divide with all denominator’s and multiple with all numerator’s, so the value of numerator’s are (30, 40, 45, 48)
Then find the max between these rational number’s. so here the last numerator is max then print last rational number. which is 4/5.

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// 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 LCM
int 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";
}

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Output:

4 5


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