LeetCode: 13. Roman to Integer

The Problem

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

Symbol       ValueI             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.

Examples

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].

The Solution

We opted for a simple approach using a for loop, this was the result:

unordered_map<char, int> values = {
	{'I', 1}, {'V', 5}, {'X', 10}, {'L', 50}, {'C', 100},  {'D', 500}, {'M', 1000}
};

int romanToInt(string s) {

	int currentValue, lastValue = values[s.back()];
	int ans = lastValue;

	for(int i = s.size() - 2; i >= 0; --i) {
		currentValue = values[s[i]];

		if (currentValue >= lastValue) ans += currentValue;
		else  ans -= currentValue;

		lastValue = currentValue;
	}

	return ans;
}

Let's break down the code step by step:

unordered_map<char, int> values = {...}:

• This line declares an unordered map named values which maps characters (Roman numerals) to their corresponding integer values.
• Each key-value pair represents a Roman numeral character and its corresponding integer value.
• For example, 'I' maps to 1, 'V' maps to 5, 'X' maps to 10, and so on.

int romanToInt(string s):

• This line defines a function named romanToInt that takes a string s as input and returns an integer.

int currentValue, lastValue = values[s.back()];:

• This line declares two integer variables currentValue and lastValue.
• lastValue is initialized with the integer value corresponding to the last character of the input string s.
• For instance, if s is "IX", then lastValue will be initialized with the integer value corresponding to 'X'.

int ans = lastValue;:

• This line initializes the variable ans with the value of lastValue.
• ans will hold the final result of converting the Roman numeral string to an integer.

for(int i = s.size() - 2; i >= 0; --i) { ... }:

• This is a for loop that iterates over the characters of the input string s in reverse order, starting from the second-to-last character.
• The loop continues until it reaches the first character of the string.

currentValue = values[s[i]];:

• Inside the loop, currentValue is assigned the integer value corresponding to the character at index i in the string s.
• For example, if s[i] is 'I', then currentValue will be assigned 1.

if (currentValue >= lastValue) ans += currentValue; else ans -= currentValue;:

• This if statement checks whether the current integer value (currentValue) is greater than or equal to the previous integer value (lastValue).
• If currentValue is greater than or equal to lastValue, it adds currentValue to ans.
• Otherwise, it subtracts currentValue from ans.
• This logic is based on the rule of Roman numerals where smaller numerals to the right of larger ones are added, and smaller numerals to the left of larger ones are subtracted.

lastValue = currentValue;:

• This line updates lastValue with the value of currentValue for the next iteration of the loop.

return ans;:

• Finally, the function returns the calculated integer value ans, which represents the conversion of the Roman numeral string s to an integer.