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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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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