Roman to Integer easy

Problem Statement

Roman numerals are represented by seven different symbols: I, V, X, L, C, D and M.

| Symbol | Value | |---|---| | I | 1 | | V | 5 | | X | 10 | | L | 50 | | C | 100 | | D | 500 | | M | 1000 |

For example, 2 is written as II in Roman numeral, just two one's added together. 12 is written as XII, which is simply X + II. The number 27 is written as XXVII, which is XX + V + II.

Roman numerals are usually written largest to smallest from left to right. However, the numeral for four is not IIII. Instead, the number four is written as IV. Because the one is before the five we subtract it making four. The same principle applies to the number nine, which is written as IX. There are six instances where subtraction is used:

• I can be placed before V (5) and X (10) to make 4 and 9.
• X can be placed before L (50) and C (100) to make 40 and 90.
• C can be placed before D (500) and M (1000) to make 400 and 900.

Given a roman numeral, convert it to an integer.

Example 1:

Input: s = "III" Output: 3 Explanation: III = 3.

Example 2:

Input: s = "LVIII" Output: 58 Explanation: L = 50, V= 5, III = 3.

Steps

1. Create a mapping: Establish a dictionary that maps Roman numerals to their integer values.
2. Iterate through the Roman numeral string: Process the string from left to right.
3. Handle subtractive cases: Check if the current numeral's value is less than the next numeral's value. If it is, subtract the current value from the total; otherwise, add the current value to the total.
4. Return the total: After processing the entire string, the accumulated total represents the integer equivalent of the Roman numeral.

Explanation

The core idea is to efficiently handle the subtractive cases in Roman numerals. By iterating through the string and comparing adjacent numerals, we can correctly determine whether to add or subtract their values. The dictionary provides a straightforward way to access the integer value of each Roman numeral symbol.

Code

def romanToInt(s: str) -> int:
    """
    Converts a Roman numeral string to an integer.

    Args:
        s: The Roman numeral string.

    Returns:
        The integer equivalent of the Roman numeral.
    """

    roman_map = {'I': 1, 'V': 5, 'X': 10, 'L': 50, 'C': 100, 'D': 500, 'M': 1000}
    result = 0
    prev_value = 0

    for i in range(len(s) - 1, -1, -1):  # Iterate from right to left
        current_value = roman_map[s[i]]
        if current_value < prev_value:
            result -= current_value
        else:
            result += current_value
        prev_value = current_value

    return result

Complexity

• Time Complexity: O(n), where n is the length of the Roman numeral string. We iterate through the string once.
• Space Complexity: O(1). We use a constant amount of extra space for the roman_map dictionary. The space used does not depend on the input size.