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Represent the fraction of two numbers in the string format
• Difficulty Level : Hard
• Last Updated : 29 Jan, 2021

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++

 `// C++ program to calculate``// fraction of two numbers``#include ``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;``}`

## Java

 `// Java program to calculate fraction``// of two numbers``import` `java.util.*;` `class` `GFG {` `    ``// Function to return the required fraction``    ``// in string format` `    ``public` `static` `String calculateFraction(``int` `num, ``int` `den)``    ``{``        ``if` `(num == ``0``)``            ``return` `"0"``; ``// if numerator is zero``        ``if` `(den == ``0``)``            ``return` `""``; ``// if denominator is zero` `        ``// result StringBuilder` `        ``StringBuilder result = ``new` `StringBuilder();``        ``if` `((num < ``0``) ^ (den < ``0``))``            ``result.append(``"-"``); ``// check -ve sign` `        ``// absoulte values of num and den` `        ``num = Math.abs(num);``        ``den = Math.abs(den);` `        ``long` `quo = num / den; ``// Quotient``        ``long` `rem = num % den * ``10``; ``// calculating remainder` `        ``result.append(``            ``String.valueOf(quo)); ``// appending quotient``        ``if` `(rem == ``0``)``            ``return` `result``                ``.toString(); ``// return if remainder is 0` `        ``// if remainder is not zero, continue` `        ``result.append(``"."``);``        ``Map m``            ``= ``new` `HashMap<>(); ``// map for storing remainder``                               ``// and the indexes of the``                               ``// appropriate decimal in``                               ``// stringbuilder` `        ``while` `(rem != ``0``) {` `            ``if` `(m.containsKey(rem)) {` `                ``// if the rem is already present, find the``                ``// index and append ( )` `                ``int` `index = m.get(rem);``                ``String part1 = result.substring(``0``, index);``                ``String part2 = ``"("``                               ``+ result.substring(``                                   ``index, result.length())``                               ``+ ``")"``;``                ``return` `part1 + part2;``            ``}` `            ``// continue updating the map and appending quo``            ``// which was generated by dividing rem with den` `            ``m.put(rem, result.length());``            ``quo = rem / den;``            ``result.append(String.valueOf(quo));` `            ``// update rem``            ``rem = (rem % den) * ``10``;``        ``}``        ``return` `result.toString();``    ``}` `    ``// Driver code``    ``public` `static` `void` `main(String[] args)``    ``{``        ``int` `num = ``113``;``        ``int` `den = ``56``;` `        ``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 Saiteja Marisetti`

## Python3

 `# 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)`
Output:
```2.(27)
-0.5```

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