Represent the fraction of two numbers in the string format

Given two integers representing the Numerator and Denominator of a fraction, return the fraction in string format. If the fractional part is repeating, enclose the repeating part in parentheses.

Examples: 

Input: Numerator = 1, Denominator = 2
Output: "0.5"
1/2 = 0.5 with no repeating part.

Input: Numerator = 50, Denominator = 22
Output: "2.(27)"
50/22 = 2.27272727... Since fractional part (27) 
is repeating, it is enclosed in parentheses.

Prerequisites :Recurring Sequence in a Fraction

Approach: The idea is to first calculate the integral quotient (absolute part before decimal point) and then calculate the fractional part. To check if the fractional part is repeating, insert the remainder (numerator % denominator) in a map with key as remainder and value as the index position at which this remainder occurs. If at any point of time, the remainder becomes zero, then there doesn’t exist a repeating fraction otherwise if the remainder is already found in the map, then there exists a repeating fraction.

Below is the implementation of above approach.  

C++

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// C++ program to calculate
// fraction of two numbers
#include <bits/stdc++.h>
using namespace std;
 
// Function to return the required fraction
// in string format
string calculateFraction(int num, int den)
{
    // If the numerator is zero, answer is 0
    if (num == 0)
        return "0";
 
    // If any one (out of numerator and denominator)
    // is -ve, sign of resultant answer -ve.
    int sign = (num < 0) ^ (den < 0) ? -1 : 1;
 
    num = abs(num);
    den = abs(den);
 
    // Calculate the absolute part (before decimal point).
    int initial = num / den;
 
    // Output string to store the answer
    string res;
 
    // Append sign
    if (sign == -1)
        res += "-";
 
    // Append the initial part
    res += to_string(initial);
 
    // If completely divisible, return answer.
    if (num % den == 0)
        return res;
 
    res += ".";
 
    // Initialize Remainder
    int rem = num % den;
    map<int, int> mp;
 
    // Position at which fraction starts repeating
    // if it exists
    int index;
    bool repeating = false;
    while (rem > 0 && !repeating) {
 
        // If this remainder is already seen,
        // then there exists a repeating fraction.
        if (mp.find(rem) != mp.end()) {
 
            // Index to insert parentheses
            index = mp[rem];
            repeating = true;
            break;
        }
        else
            mp[rem] = res.size();
 
        rem = rem * 10;
 
        // Calculate quotient, append it to result and
        // calculate next remainder
        int temp = rem / den;
        res += to_string(temp);
        rem = rem % den;
    }
 
    // If repeating fraction exists, insert parentheses.
    if (repeating) {
        res += ")";
        res.insert(index, "(");
    }
 
    // Return result.
    return res;
}
 
// Drivers Code
int main()
{
    int num = 50, den = 22;
    cout << calculateFraction(num, den) << endl;
 
    num = -1, den = 2;
    cout << calculateFraction(num, den) << endl;
    return 0;
}

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Java

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// Java program to calculate fraction
// of two numbers
import java.io.*;
import java.util.*;
 
class GFG{
     
   
// Function to return the required fraction
// in string format
public static String calculateFraction(int num,
                                       int den)
{
     
    // If the numerator is zero, answer is 0
    if (num == 0)
        return "0";
         
    // Divide by zero exception,
    // hence invalid
    if (den == 0)
        return "Invalid";
         
    // Check the numerator or
    // denominator is negative
    boolean neg = false;
    if (num < 0 || den <0)
        neg = true;
         
    // If the denominator divides
    // the numerator with remainder
    // as zero
    if (num % den == 0)
    {
        int res1 = (num / den);
        return Integer.toString(res1);
    }
     
    // Arraylist to store the numbers
    // after the decimal point
    ArrayList<Integer> Fraction = new ArrayList<>();
     
    // String Builder for returning the
    // result in string format with
    // specific format
    StringBuilder str = new StringBuilder();
     
    // If the numerator or denominator
    // is negative the result will be
    // negative, hence append the string
    // with "-" at beginning
    if (neg == true)
    {
        str.append("-");
    }
     
    // Taking only the absolute values
    // from the numerator and denominator
    num = Math.abs(num);
    den = Math.abs(den);
     
    // Appending the number before
    // the decimal point
    str.append(num / den);
     
    // Decimal point
    str.append(".");
    while(true)
    {
         
        // Calculating remainder
        int rem = num % den;
         
          // The remainder becomes zero,
          // then the result will have no
          // recurring digits after decimal point
        if (rem == 0)
        {
            for(int i = 0;i < Fraction.size(); i++)
            {
                str.append(Fraction.get(i));
            }
            break;
        }
         
        // The numerator for next iteration
        // will be the product of remainder
        // and 10
        num = rem * 10;
         
        // Calculating quotient
        int quo = num / den;
         
        // Adding the digit to the Fraction
        // list only if it does not exists in it
        if (!(Fraction.contains(quo)))
        {
            Fraction.add(quo);
        }
         
        // If the quotient exists in the Fraction list
        else if(Fraction.contains(quo))
        {
             
            // Retrieving the index of the
            // number upto which the quotient
            // is not recurring
            int ind = Fraction.indexOf(quo);
            for(int i = 0; i <= ind - 1; i++)
            {
                str.append(Fraction.get(i));
            }
             
            // Printing the recurring pattern
            // within brackets
            str.append("(");
            for(int i = ind; i < Fraction.size(); i++)
            {
                str.append(Fraction.get(i));
            }
            str.append(")");
            break;
        }
    }
     
    // Convert str to String and
    // return the result
    return str.toString();
}
 
// Driver code
public static void main (String[] args)
{
    int num = 50;
    int den = 22;
     
    String resString1 = calculateFraction(num, den);
     
    num = -1;
    den = 2;
     
    String resString2 = calculateFraction(num, den);
     
    System.out.println(resString1);
    System.out.println(resString2);
}
}
 
// This code is contributed by Hithesh Kumar C M
// hitheshkumarcm33309

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Python3

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# Python3 program to calculate fraction
# of two numbers
 
# Function to return the required
# fraction in string format
def calculateFraction(num, den) :
 
    # If the numerator is zero, answer is 0
    if (num == 0):
        return "0"
 
    # If any one (out of numerator and denominator)
    # is -ve, sign of resultant answer -ve.
    sign = -1 if (num < 0) ^ (den < 0) else 1
 
    num = abs(num)
    den = abs(den)
 
    # Calculate the absolute part
    # (before decimal point).
    initial = num // den
 
    # Output string to store the answer
    res = ""
 
    # Append sign
    if (sign == -1):
        res += "-"
 
    # Append the initial part
    res += str(initial)
 
    # If completely divisible, return answer.
    if (num % den == 0):
        return res
 
    res += "."
 
    # Initialize Remainder
    rem = num % den
    mp = {}
 
    # Position at which fraction starts
    # repeating if it exists
    index = 0
    repeating = False
    while (rem > 0 and not repeating) :
 
        # If this remainder is already seen,
        # then there exists a repeating fraction.
        if ( rem in mp):
 
            # Index to insert parentheses
            index = mp[rem]
            repeating = True
            break
         
        else:
            mp[rem] = len(res)
 
        rem = rem * 10
 
        # Calculate quotient, append it to result
        # and calculate next remainder
        temp = rem // den
        res += str(temp )
        rem = rem % den
     
    # If repeating fraction exists,
    # insert parentheses.
    if (repeating) :
        res += ")"
        x = res[:index]
        x += "("
        x += res[index:]
        res = x
     
    # Return result.
    return res
 
# Driver code
if __name__ =="__main__":
    num = 50
    den = 22
    print(calculateFraction(num, den))
    num = -1
    den = 2
    print(calculateFraction(num, den))
 
# This code is contributed
# Shubham Singh(SHUBHAMSINGH10)

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Output: 

2.(27)
-0.5









 

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