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. 50 + 5 + 3 = 58

Steps:

1. Create a Map: Create a map (or object in JavaScript) to store the integer values of each Roman numeral symbol.
2. Iterate: Iterate through the Roman numeral string from left to right.
3. Check for Subtraction: For each symbol, check if the next symbol has a larger value. If it does, subtract the current symbol's value from the total; otherwise, add the current symbol's value to the total.
4. Return Total: After iterating through the entire string, return the accumulated total.

Explanation:

The key to solving this problem efficiently is handling the subtractive cases (IV, IX, XL, XC, CD, CM). By checking the next symbol, we can determine whether to add or subtract the current symbol's value. This avoids the need for complex nested loops or multiple passes through the string.

Code:

function romanToInt(s: string): number {
    const romanMap: { [key: string]: number } = {
        'I': 1,
        'V': 5,
        'X': 10,
        'L': 50,
        'C': 100,
        'D': 500,
        'M': 1000,
    };

    let result = 0;
    for (let i = 0; i < s.length; i++) {
        const currentVal = romanMap[s[i]];
        const nextVal = romanMap[s[i + 1]];

        if (nextVal && nextVal > currentVal) {
            result -= currentVal;
        } else {
            result += currentVal;
        }
    }

    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). The space used by the romanMap is constant regardless of the input string size.