Fraction to Recurring Decimal

Last Updated : 07 Feb, 2025

Given two integers a and b(b != 0), the task is to return the fraction a/b in string format. If the fractional part is repeating, enclose the repeating part in parentheses.

Examples:

Input: a = 1, b = 2
Output: "0.5"
Explanation: 1/2 = 0.5 with no repeating part.

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

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 (a % b) in a hash 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.

C++

// C++ Program to convert fraction to string

#include <iostream>
#include <unordered_map>
using namespace std;

string calculateFraction(int a, int b) {
  
    // If the numerator is zero, answer is 0
    if (a == 0)
        return "0";

    // If exactly one of the numerator or denominator
    // is negative, then result will be negative
    string res = (a < 0) ^ (b < 0) ? "-" : "";

    a = abs(a);
    b = abs(b);

    // Calculate and Append the part before decimal point
    res += to_string(a / b);

    int rem = a % b;
  
    // If completely divisible, return res
    if (rem == 0)
        return res;

    res.append(".");
    unordered_map<int, int> mp;
  
    while (rem > 0) {

        // If this remainder is already seen,
        // then there exists a repeating fraction.
        if (mp.find(rem) != mp.end()) {

            res.insert(mp[rem], "(");
            res.append(")");
            break;
        }
        
        // If the remainder is seen for the first time,
        // store its index
        mp[rem] = res.size();

        rem = rem * 10;

        // Calculate quotient, append it to result and
        // calculate next remainder
        res += to_string(rem / b);
        rem = rem % b;
    }

    return res;
}

int main() {
    int a = 50, b = 22;
    cout << calculateFraction(a, b) << endl;
    return 0;
}

#include <stdio.h>
#include <stdlib.h>
#include <string.h>

char* calculateFraction(int a, int b) {
    // If the numerator is zero, answer is 0
    if (a == 0) {
        char* result = (char*)malloc(2);
        strcpy(result, "0");
        return result;
    }

    // If exactly one of the numerator or denominator
    // is negative, then result will be negative
    char* res = (char*)malloc(100);
    int isNegative = (a < 0) ^ (b < 0);
    if (isNegative) {
        strcpy(res, "-");
    } else {
        strcpy(res, "");
    }

    a = abs(a);
    b = abs(b);

    // Calculate and Append the part before decimal point
    char temp[20];
    sprintf(temp, "%d", a / b);
    strcat(res, temp);

    int rem = a % b;

    // If completely divisible, return res
    if (rem == 0) {
        return res;
    }

    strcat(res, ".");
    int index = strlen(res);
    int seen[10000] = {0}; // To store the index of seen remainders

    while (rem > 0) {
        // If this remainder is already seen,
        // then there exists a repeating fraction.
        if (seen[rem] != 0) {
            // Insert '(' at the index of first occurrence
            memmove(res + seen[rem] + 1, res + seen[rem], index - seen[rem] + 1);
            res[seen[rem]] = '(';
            strcat(res, ")");
            break;
        }

        // If the remainder is seen for the first time,
        // store its index
        seen[rem] = index;

        rem = rem * 10;

        // Calculate quotient, append it to result and
        // calculate next remainder
        sprintf(temp, "%d", rem / b);
        strcat(res, temp);
        rem = rem % b;
        index = strlen(res);
    }

    return res;
}

int main() {
    int a = 50, b = 22;
    char* result = calculateFraction(a, b);
    printf("%s\n", result);
    free(result);
    return 0;
}

Java

// Java Program to convert fraction to string

import java.util.HashMap;

class GfG {
    static String calculateFraction(int a, int b) {
        
        // If the numerator is zero, answer is "0"
        if (a == 0)
            return "0";

        // If exactly one of the numerator or denominator
        // is negative, then result will be negative
        String res = (a < 0) ^ (b < 0) ? "-" : "";

        a = Math.abs(a);
        b = Math.abs(b);

        // Calculate and Append the part before decimal point
        res += Integer.toString(a / b);

        int rem = a % b;

        // If completely divisible, return res
        if (rem == 0)
            return res;

        res += ".";
        HashMap<Integer, Integer> mp = new HashMap<>();

        while (rem > 0) {
            
            // If this remainder is already seen,
            // then there exists a repeating fraction.
            if (mp.containsKey(rem)) {
                res = res.substring(0, mp.get(rem)) + "(" + res.substring(mp.get(rem)) + ")";
                break;
            }

            // If the remainder is seen for the first time,
            // store its index
            mp.put(rem, res.length());

            rem = rem * 10;

            // Calculate quotient, append it to result and
            // calculate next remainder
            res += Integer.toString(rem / b);
            rem = rem % b;
        }

        return res;
    }

    public static void main(String[] args) {
        int a = 50, b = 22;
        System.out.println(calculateFraction(a, b));
    }
}

Python

# Python Program to convert fraction to string

def calculateFraction(a, b):
  
    # If the numerator is zero, answer is "0"
    if a == 0:
        return "0"

    # If exactly one of the numerator or denominator
    # is negative, then result will be negative
    res = "-" if (a < 0) ^ (b < 0) else ""

    a = abs(a)
    b = abs(b)

    # Calculate and Append the part before decimal point
    res += str(a // b)

    rem = a % b

    # If completely divisible, return res
    if rem == 0:
        return res

    res += "."
    mp = {}

    while rem > 0:
      
        # If this remainder is already seen,
        # then there exists a repeating fraction.
        if rem in mp:
            res = res[:mp[rem]] + "(" + res[mp[rem]:] + ")"
            break
        
        # If the remainder is seen for the first time,
        # store its index
        mp[rem] = len(res)

        rem = rem * 10

        # Calculate quotient, append it to result and
        # calculate next remainder
        res += str(rem // b)
        rem = rem % b

    return res

if __name__ == "__main__":
    a = 50
    b = 22
    print(calculateFraction(a, b))

// C# Program to convert fraction to string

using System;
using System.Collections.Generic;

class GfG {
    static string calculateFraction(int a, int b) {
      
        // If the numerator is zero, answer is "0"
        if (a == 0)
            return "0";

        // If exactly one of the numerator or denominator
        // is negative, then result will be negative
        string res = (a < 0) ^ (b < 0) ? "-" : "";

        a = Math.Abs(a);
        b = Math.Abs(b);

        // Calculate and Append the part before decimal point
        res += a / b;

        int rem = a % b;

        // If completely divisible, return res
        if (rem == 0)
            return res;

        res += ".";
        Dictionary<int, int> mp = new Dictionary<int, int>();

        while (rem > 0) {
          
            // If this remainder is already seen,
            // then there exists a repeating fraction.
            if (mp.ContainsKey(rem)) {
                res = res.Insert(mp[rem], "(");
                res += ")";
                break;
            }

            // If the remainder is seen for the first time,
            // store its index
            mp[rem] = res.Length;

            rem = rem * 10;

            // Calculate quotient, append it to result and
            // calculate next remainder
            res += rem / b;
            rem = rem % b;
        }

        return res;
    }

    static void Main() {
        int a = 50, b = 22;
        Console.WriteLine(calculateFraction(a, b));
    }
}

JavaScript

// JavaScript Program to convert fraction to string

function calculateFraction(a, b) {
    
    // If the numerator is zero, answer is "0"
    if (a === 0) {
        return "0";
    }

    // If exactly one of the numerator or denominator
    // is negative, then result will be negative
    let res = (a < 0) ^ (b < 0) ? "-" : "";

    a = Math.abs(a);
    b = Math.abs(b);

    // Calculate and Append the part before decimal point
    res += Math.floor(a / b);

    let rem = a % b;

    // If completely divisible, return res
    if (rem === 0) {
        return res;
    }

    res += ".";
    let mp = new Map();

    while (rem > 0) {
        // If this remainder is already seen,
        // then there exists a repeating fraction.
        if (mp.has(rem)) {
            let repeatIndex = mp.get(rem);
            res = res.substring(0, repeatIndex) + "(" 
            			+ res.substring(repeatIndex) + ")";
            break;
        }

        // If the remainder is seen for the first time,
        // store its index
        mp.set(rem, res.length);

        rem = rem * 10;

        // Calculate quotient, append it to result and
        // calculate next remainder
        res += Math.floor(rem / b);
        rem = rem % b;
    }

    return res;
}

// Driver Code
let a = 50, b = 22;
console.log(calculateFraction(a, b));