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Fraction to Recurring Decimal

Certification: Intermediate Level Accuracy: 0% Submissions: 0 Points: 10

Write a C program to convert a fraction (numerator/denominator) to its decimal representation. If the decimal part is recurring, enclose the recurring part in parentheses. The program should handle both positive and negative fractions and return the result as a string.

Example 1
    
      
  • Input: numerator = 1, denominator = 2
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  • Output: "0.5"
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  • Explanation: 1/2 = 0.5. There is no recurring decimal part. Therefore, the result is "0.5".
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Example 2
    
      
  • Input: numerator = 2, denominator = 3
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  • Output: "0.(6)"
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  • Explanation: 2/3 = 0.666... The digit 6 repeats indefinitely. Therefore, the result is "0.(6)".
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Constraints
    
      
  • -2^31 ≤ numerator, denominator ≤ 2^31 - 1
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  • denominator != 0
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  • The result string length should not exceed 10^4 characters
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  • Time Complexity: O(denominator)
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  • Space Complexity: O(denominator)
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Hint
Solution

Solution Hints

    
      
  • Handle the sign of the result first (negative if numerator and denominator have different signs)
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  • Convert both numerator and denominator to positive values to simplify calculation
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  • Calculate the integer part by dividing numerator by denominator
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  • Use a hash map to track remainders and their positions to detect recurring patterns
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  • For each remainder, multiply by 10 and divide by denominator to get the next decimal digit
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  • If a remainder repeats, you've found the start of the recurring cycle
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Steps to solve by this approach:

 Step 1: Handle the special case where numerator is 0, return "0"
 Step 2: Determine the sign of the result based on numerator and denominator signs
 Step 3: Convert both numerator and denominator to positive values for easier calculation
 Step 4: Calculate and append the integer part of the division to the result string
 Step 5: If there's no remainder after integer division, return the result
 Step 6: Add decimal point and use a hash map to track remainders and their positions
 Step 7: For each remainder, multiply by 10, divide by denominator, and check for recurring pattern

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