Coding

Roman to Integer

Asked atHTHexaview Technologies

1Give yourself 5 minutes

2Answer out loud, not in your head

3Then compare with the answer below

The problem

Roman numerals are represented by seven different symbols:

I = 1
V = 5
X = 10
L = 50
C = 100
D = 500
M = 1000

Roman numerals are typically written from largest to smallest, left to right. However, in specific cases, a smaller numeral placed before a larger one indicates subtraction.

The following subtractive combinations are valid:

I before V (5) and X (10) → 4 and 9
X before L (50) and C (100) → 40 and 90
C before D (500) and M (1000) → 400 and 900

Given a Roman numeral, convert it to an integer.

**Input: **s = "III" **Output: **3 **Explanation: **III = 1 + 1 + 1 = 3

**Input: **s = "XLII" **Output: **42 **Explanation: **XL = 40, II = 2 → 40 + 2 = 42

**Input: **s = "DCCCXC"

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]

cpp

class Solution {
public:
    int romanToInt(string s) {
        // Your code goes here
    }
};

java

class Solution {
    public int romanToInt(String s) {
        // Your code goes here
    }
}

python

class Solution:
    def romanToInt(self, s: str) -> int:
        # Your code goes here

javascript

class Solution {
    romanToInt(s) {
        // Your code goes here
    }
}

csharp

public class Solution
{
    public int RomanToInt(string s)
    {
        // Your code goes here
    }
}

func romanToInt(s string) int {
    // Your code goes here
}

Stuck? Show a way to structure it+

01Map each Roman symbol to its value.
02Scan from right to left.
03Track the largest value seen to the right.
04Subtract a smaller symbol before a larger one.
05Otherwise add it and update the maximum.

Reference answer

Create a map for I, V, X, L, C, D, and M, then scan from right to left. Keep maxRight, the largest symbol value already seen. If the current value is less than maxRight, subtract it because it participates in a subtractive pair such as IV or IX; otherwise add it and update maxRight. For MCMXCIV, this naturally subtracts C before M and X before C. The method works because valid Roman notation permits a smaller value before a larger value only to denote subtraction. A left-to-right version can compare each symbol to the next, but the right-to-left invariant is often easier to articulate. Time is O(n), space is O(1) because the symbol table has fixed size. If validation of arbitrary invalid Roman strings is required, say so explicitly; standard interview variants assume valid input.

Then expect these follow-ups

How would you convert an integer to Roman numerals?
Tests: follow-up reasoning
How would you validate canonical Roman notation?
Tests: follow-up reasoning

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