Roman to Integer – Solution & Complexity

Q: What is the time and space complexity of Roman to Integer?

The optimal Roman to Integer solution runs in `O(n)` time and `O(1)` space. Add each numeral's value, subtracting when a smaller numeral precedes a larger one.

Q: What is the most efficient way to solve Roman to Integer?

Add each numeral's value, subtracting when a smaller numeral precedes a larger one. This gives `O(n)` time complexity, and is a classic strings, math, and hashmap problem.

Q: How do you solve Roman to Integer in Python, JavaScript, Java, Go, Rust, C++ & Ruby?

We provide a worked Roman to Integer solution in Python, JavaScript, Java, Go, Rust, C++ & Ruby with a step-by-step explanation above. You can also open the interactive editor to write and run your own Python solution against the test cases in the browser.

Q: Is Roman to Integer an easy or hard interview question?

Roman to Integer is generally rated **Easy**. It tests strings, math, and hashmap, which are common coding-interview patterns.

Watch: Roman to Integer in one pass

Add each symbol's value, except when a smaller symbol comes before a larger one, as in IV or CM; then subtract it. One left-to-right pass with a lookup table: O(n) time.

Solution Walkthrough

Step 1: Understanding the Problem
- You are given a Roman numeral, and you need to convert it to an integer.
- Roman numerals are made up of symbols (I, V, X, L, C, D, M) with respective values.
- The numeral can range from 1 to 3999, and subtraction cases (like IV for 4) must be handled.
Step 2: List Roman Numerals and Values
- Roman numerals are represented by seven different symbols with specific values:
```
Symbol    Value 
 I         1
 V         5
 X         10
 L         50
 C         100
 D         500
 M         1000
```
- Subtraction cases include:
  - I before V (5) and X (10) to make 4 and 9.
  - X before L (50) and C (100) to make 40 and 90.
  - C before D (500) and M (1000) to make 400 and 900.
Step 3: Create a Mapping for Roman Numerals
- Use a dictionary to map Roman numeral symbols to their corresponding integer values.
- This will allow for constant-time lookups during conversion.
def roman_to_integer(s: str) -> int: roman_map = {'I': 1, 'V': 5, 'X': 10, 'L': 50, 'C': 100, 'D': 500, 'M': 1000} return 0

Step 4: Iterate Through the String

To process the Roman numeral, iterate through the string from left to right.
For each character, look up its corresponding value using the dictionary.

def roman_to_integer(s: str) -> int:
    roman_map = {'I': 1, 'V': 5, 'X': 10, 'L': 50, 'C': 100, 'D': 500, 'M': 1000}
    total = 0
    for char in s:
        value = roman_map[char]
    return total

Step 5: Handle Subtraction Cases

Roman numerals use subtraction in specific cases (like IV = 4).
If a smaller value comes before a larger one, subtract the smaller value instead of adding it.

def roman_to_integer(s: str) -> int:
    roman_map = {'I': 1, 'V': 5, 'X': 10, 'L': 50, 'C': 100, 'D': 500, 'M': 1000}
    total = 0
    prev_value = 0
    for char in s:
        value = roman_map[char]
        if value > prev_value:
            total += value - 2 * prev_value  # Subtract twice the previous value
        else:
            total += value
        prev_value = value  # Update the previous value
    return total

Step 6: Return the Final Sum

After processing all characters in the Roman numeral string, return the accumulated total value, which represents the integer conversion.

def roman_to_integer(s: str) -> int:
    roman_map = {'I': 1, 'V': 5, 'X': 10, 'L': 50, 'C': 100, 'D': 500, 'M': 1000}
    total = 0
    prev_value = 0
    for char in s:
        value = roman_map[char]
        if value > prev_value:
            total += value - 2 * prev_value
        else:
            total += value
        prev_value = value
    return total

Step 7: Handle Edge Cases
- Make sure that input Roman numerals are valid and within the range (1-3999).
- Since the problem guarantees this, we don't need extra validation, but this could be added in a more general implementation.

Roman to Integer – Solution & Complexity

Watch: Roman to Integer in one pass

Solution Walkthrough

Step 1: Understanding the Problem

Step 2: List Roman Numerals and Values

Step 3: Create a Mapping for Roman Numerals

Step 4: Iterate Through the String

Step 5: Handle Subtraction Cases

Step 6: Return the Final Sum

Step 7: Handle Edge Cases

FAQ

What is the time and space complexity of Roman to Integer?

What is the most efficient way to solve Roman to Integer?

How do you solve Roman to Integer in Python, JavaScript, Java, Go, Rust, C++ & Ruby?

Is Roman to Integer an easy or hard interview question?

See also

Roman to Integer – Solution & Complexity

Watch: Roman to Integer in one pass

Solution Walkthrough

1Step 1: Understanding the Problem

2Step 2: List Roman Numerals and Values

3Step 3: Create a Mapping for Roman Numerals

4Step 4: Iterate Through the String

5Step 5: Handle Subtraction Cases

6Step 6: Return the Final Sum

7Step 7: Handle Edge Cases

FAQ

What is the time and space complexity of Roman to Integer?

What is the most efficient way to solve Roman to Integer?

How do you solve Roman to Integer in Python, JavaScript, Java, Go, Rust, C++ & Ruby?

Is Roman to Integer an easy or hard interview question?

See also

Step 1: Understanding the Problem

Step 2: List Roman Numerals and Values

Step 3: Create a Mapping for Roman Numerals

Step 4: Iterate Through the String

Step 5: Handle Subtraction Cases

Step 6: Return the Final Sum

Step 7: Handle Edge Cases