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Roman to Integer

Difficulty: Easy

Problem Description

Convert a given Roman numeral string into its corresponding integer value.

Key Insights

  • Roman numerals consist of specific symbols that represent different values.
  • Larger values precede smaller values, but there are specific cases where a smaller value precedes a larger one, indicating subtraction.
  • The six subtraction cases to remember are: IV (4), IX (9), XL (40), XC (90), CD (400), and CM (900).

Space and Time Complexity

Time Complexity: O(n) - where n is the length of the Roman numeral string, since we need to traverse each character once. Space Complexity: O(1) - since we are using a fixed amount of space for storing values regardless of the input size.

Solution

We can use a hash table (dictionary) to map each Roman numeral to its corresponding integer value. We then iterate through the string from left to right. For each numeral, we check if it is less than the numeral that follows it. If it is, we subtract its value from the total; otherwise, we add its value. This approach efficiently handles the special subtraction cases.

Code Solutions

def romanToInt(s: str) -> int:
    # Map of Roman numerals to their integer values
    roman_map = {
        'I': 1,
        'V': 5,
        'X': 10,
        'L': 50,
        'C': 100,
        'D': 500,
        'M': 1000
    }
    
    total = 0
    prev_value = 0
    
    # Traverse the Roman numeral from right to left
    for char in reversed(s):
        current_value = roman_map[char]
        # If the current value is less than the previous value, we subtract it
        if current_value < prev_value:
            total -= current_value
        else:
            total += current_value
        prev_value = current_value
    
    return total
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