Roman To Integer

To solve this coding challenge, we need to convert a Roman numeral string to its corresponding integer value. The procedure for this involves understanding the rules of Roman numerals and implementing them in pseudocode form.

Explanation

Roman numerals are built using a set of symbols with corresponding integer values. The primary symbols and their values are: Symbol Value
  • ---- -----
  • I 1 V 5 X 10 L 50 C 100 D 500 M 1000
Basic Idea:
  1. Normally, Roman numerals are written from largest to smallest left to right. However, in a few cases, a smaller numeral is placed before a larger numeral to indicate subtraction.
  2. For example:
    • "IV" means 4 because it’s 5 (V) - 1 (I).
    • "IX" means 9 because it’s 10 (X) - 1 (I).
  3. To convert a Roman numeral to an integer, we traverse the string from left to right. If a numeral is smaller than the numeral following it, we subtract it from the total. Otherwise, we add it to the total.
  4. Detailed Steps in Pseudocode:
  5. First, create a dictionary to map Roman numeral symbols to their integer values.
  6. Initialize a result variable with the value of the last symbol in the string. This is because the last numeral is always added to the result.
  7. Loop through the string from the second last character to the first character:
    • a. If the current symbol is smaller than the next symbol, subtract its value from the result. b. Otherwise, add its value to the result.
    By following this methodology, we can accurately convert any valid Roman numeral string into its integer representation.

    Pseudocode

                                                
    # Create a mapping from Roman numerals to integers.
    roman_to_integer_map = {
    'I': 1,
    'V': 5,
    'X': 10,
    'L': 50,
    'C': 100,
    'D': 500,
    'M': 1000
    }
    
    # Function to convert Roman numeral to Integer.
    function romanToInt(roman_string):
    
    # Initialize result to the value of the last numeral.
    result = roman_to_integer_map[roman_string[length of roman_string - 1]]
    
    # Loop through the string from the second last character to the first.
    for index from length of roman_string - 2 down to 0:
    
    # If the current numeral is less than the next numeral.
    if roman_to_integer_map[roman_string[index]] < roman_to_integer_map[roman_string[index + 1]]:
    # Subtract the value of the current numeral from result.
    result = result - roman_to_integer_map[roman_string[index]]
    else:
    # Add the value of the current numeral to result.
    result = result + roman_to_integer_map[roman_string[index]]
    
    return result
    
                                            
    Let's walk through an example to clarify:
    Example: Convert "MCMXCIV"
  8. Initialize
    result
    with the value of the last numeral "V", so
    result = 5
    .
  9. Traverse from the second last to the first:
    • Check "I" (1):
      • Since 1 (I) < 5 (V), subtract 1 from
        result
        , now
        result = 4
        .
    • Check "C" (100):
      • Since 100 (C) < 4 (M), subtract 100, now
        result = 104
        .
    • Check "X" (10):
      • Since 10 (X) < 100 (C), subtract 10, now
        result = 194
        .
    • Continue until the first element.
By following the above pseudocode and detailed steps, you should be able to convert any valid Roman numeral to its integer counterpart effectively.