Roman to Integer

Clarify the problem:

• The problem requires converting a Roman numeral string to an integer.
• We need to implement a function that takes a Roman numeral string as input and returns its corresponding integer value.

Analyze the problem:

• Input: A string representing a Roman numeral.
• Output: The integer value of the Roman numeral.
• Constraints:
  • The input string represents a valid Roman numeral.
  • The Roman numerals consist of the following symbols: 'I', 'V', 'X', 'L', 'C', 'D', 'M'.
  • The symbols have the following integer values: 'I' = 1, 'V' = 5, 'X' = 10, 'L' = 50, 'C' = 100, 'D' = 500, 'M' = 1000.
  • The input string is guaranteed to be a valid Roman numeral with a value between 1 and 3999.

Design an algorithm:

• We can solve this problem by iterating through the Roman numeral string from left to right.
• Initialize a variable result to store the final integer value.
• Iterate over the string and process each character:
  • Check the current character and the next character to determine if it represents a subtractive pair (e.g., 'IV', 'IX', 'XL', 'XC', 'CD', 'CM').
  • If it is a subtractive pair, subtract the value of the current character from the result and move the index two steps forward.
  • If it is not a subtractive pair, add the value of the current character to the result and move the index one step forward.
• Return the final value stored in the result variable.

Explain your approach:

• We will implement a function called romanToInt that takes a Roman numeral string, s, as input.
• We will initialize a dictionary to map each Roman numeral symbol to its corresponding integer value.
• We will initialize a variable result to store the final integer value.
• We will iterate over the string, checking each character and its next character to determine if it represents a subtractive pair.
• If it is a subtractive pair, we will subtract the value of the current character from the result and move the index two steps forward.
• If it is not a subtractive pair, we will add the value of the current character to the result and move the index one step forward.
• Finally, we will return the value stored in the result variable.

Write clean and readable code:

python

def romanToInt(s):
    roman_values = {
        'I': 1,
        'V': 5,
        'X': 10,
        'L': 50,
        'C': 100,
        'D': 500,
        'M': 1000
    }

    result = 0
    i = 0
    n = len(s)

    while i < n:
        if i < n - 1 and roman_values[s[i]] < roman_values[s[i + 1]]:
            result += roman_values[s[i + 1]] - roman_values[s[i]]
            i += 2
        else:
            result += roman_values[s[i]]
            i += 1

    return result

Test your code:

python

# Test case 1
# Roman numeral: 'III'
# Corresponding integer value: 3
assert romanToInt('III') == 3

# Test case 2
# Roman numeral: 'IV'
# Corresponding integer value: 4
assert romanToInt('IV') == 4

# Test case 3
# Roman numeral: 'IX'
# Corresponding integer value: 9
assert romanToInt('IX') == 9

# Test case 4
# Roman numeral: 'LVIII'
# Corresponding integer value: 58
assert romanToInt('LVIII') == 58

# Test case 5
# Roman numeral: 'MCMXCIV'
# Corresponding integer value: 1994
assert romanToInt('MCMXCIV') == 1994

Optimize if necessary:

• The current solution has a time complexity of O(n), where n is the length of the input string.
• We iterate through the string once, processing each character.
• This solution is already optimal in terms of time complexity.

Handle error cases:

• The code assumes that the input string represents a valid Roman numeral.
• It does not handle invalid input, such as strings containing invalid Roman numeral symbols or incorrect Roman numeral representations.
• In such cases, the behavior of the code is undefined.

Discuss complexity analysis:

• The time complexity of the solution is O(n), where n is the length of the input string.
• The space complexity is O(1) since we are not using any additional data structures.
• The best-case scenario occurs when the length of the input string is 1, and the function returns the corresponding integer value in constant time.
• The worst-case scenario occurs when the length of the input string is large, and we need to iterate through the entire string. In this case, the function takes O(n) time.
• The average-case time complexity is also O(n), assuming random inputs.