Roman to Integer

Problem

https://leetcode.com/problems/roman-to-integer/

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 ones 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.

Example 3:

Input: s = "MCMXCIV"
Output: 1994
Explanation: M = 1000, CM = 900, XC = 90 and IV = 4.

Constraints:

• 1 <= s.length <= 15

• s contains only the characters ('I', 'V', 'X', 'L', 'C', 'D', 'M').

• It is guaranteed that s is a valid roman numeral in the range [1, 3999].

Pattern

Hash Table, Math, String

Solution

Observe that the value of a Roman numeral is the sum of the value of the letters, but the letters may be negative or positive depending on their position. Since there are only 6 instances of subtractive notation, we can store these in a set. If these are present, we subtract the value of the numeral. Otherwise add up the numeral values.

Code

def roman_to_int(s: str):
    """Convert Roman numeral ``s`` to integer.
    """
    additions = {
        'I': 1,
        'V': 5,
        'X': 10,
        'L': 50,
        'C': 100,
        'D': 500,
        'M': 1000
    }
    subtractions = {
        'IV',
        'IX',
        'XL',
        'XC',
        'CD',
        'CM'
    }

    value = 0
    for i, numeral in enumerate(s):
        if s[i:i + 2] in subtractions:
            value -= additions[numeral]
        else:
            value += additions[numeral]

    return value

Test

>>> from roman_to_integer__approach_1 import roman_to_int
>>> roman_to_int('III')
3
>>> roman_to_int('LVIII')
58
>>> roman_to_int('MCMXCIV')
1994

Complexity

\(n\) is the length of the string

Time: \(O(n)\) — single pass through the string

Auxiliary Space: \(O(1)\) — fixed-size maps for roman numeral symbols

roman_to_integer__approach_1.roman_to_int(s: str)

Convert Roman numeral s to integer.