What is the time complexity of Roman to Integer?

The optimal solution has a time complexity of O(n).

What data structures are used to solve Roman to Integer?

This problem uses Hash Table, Math, String. Understanding these concepts is essential for solving this Easy problem efficiently.

What are the key insights for solving Roman to Integer?

Insight 1: Recognizing the subtractive notation is crucial. Simply summing the values of each symbol will be incorrect for cases like IV or IX. Insight 2: A hash map (or similar lookup structure) is efficient for quickly obtaining the integer value of each Roman numeral symbol.

Which companies ask LeetCode 13. Roman to Integer in interviews?

This problem is frequently asked at AMD, Accenture, Adobe, Amazon, Apple and 30 more companies.

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Roman to Integer - LeetCode 13 Solution

Roman to Integer - Complete Solution Guide

Roman to Integer is LeetCode problem 13, a Easy level challenge. This complete guide provides step-by-step explanations, multiple solution approaches, and optimized code in python3, java, cpp, c.

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 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

Detailed Explanation

The problem asks you to convert a Roman numeral string into its corresponding integer value. Roman numerals use a combination of seven symbols (I, V, X, L, C, D, M) representing 1, 5, 10, 50, 100, 500, and 1000 respectively. While typically written largest to smallest, subtractive notation is used for certain values (e.g., IV = 4, IX = 9). The input is a string representing a valid Roman numeral (between 1 and 3999), and the output is its integer equivalent.

Solution Approach

The provided Python and Java solutions use a hash map to store the integer values of each Roman numeral. They then iterate through the string, comparing the current symbol's value with the next one. If the current value is less than the next, it's a subtractive case, and the current value is subtracted; otherwise, it's added. The C++ solution uses a series of `if-else if` statements to achieve similar functionality. The C solution takes a more brute force approach by explicitly checking for all subtractive combinations.

Step-by-Step Algorithm

Step 1: Create a hash map (or equivalent) to store the integer value of each Roman numeral symbol.
Step 2: (Python/Java) Iterate through the input string from left to right (or right to left in Java).
Step 3: (Python/Java) Compare the value of the current symbol with the next symbol's value (if it exists). If the current value is smaller, subtract it from the result; otherwise, add it.
Step 4: (C++) Check each character and apply subtraction rule based on the next character if necessary.
Step 5: (C) Explicitly checks for all possible subtractive combinations.
Step 6: Return the final accumulated integer value.

Key Insights

Insight 1: Recognizing the subtractive notation is crucial. Simply summing the values of each symbol will be incorrect for cases like IV or IX.
Insight 2: A hash map (or similar lookup structure) is efficient for quickly obtaining the integer value of each Roman numeral symbol.
Insight 3: Iterating either from left-to-right or right-to-left can simplify the logic for handling subtractive notation. Right-to-left avoids the need to look ahead.

Complexity Analysis

Time Complexity: O(n)

Space Complexity: O(1)

Topics

This problem involves: Hash Table, Math, String.

Companies

Asked at: AMD, Accenture, Adobe, Amazon, Apple, Axon, BNY Mellon, Bloomberg, Booking.com, Capital One, DeltaX, Expedia, Geico, Goldman Sachs, IBM, Infosys, KLA, Meta, Microsoft, Oracle, Pwc, Salesforce, Snowflake, SoFi, Thomson Reuters, Uber, Visa, Warnermedia, Wipro, Wise, Wix, Yahoo, Zoho, eBay, tcs.

Roman to Integer | LeetCode 13

Easy

Hash Table Math String

Time: O(n)Space: O(1)

Solution Code

Available in:

class Solution {
    public int romanToInt(String s) {
        int result = 0;
        int prevValue = 0;

        for (int i = s.length() - 1; i >= 0; i--) {
            char c = s.charAt(i);
            int currentValue = 0;

            switch (c) {
                case 'I':
                    currentValue = 1;
                    break;
                case 'V':
                    currentValue = 5;
                    break;
                case 'X':
                    currentValue = 10;
                    break;
                case 'L':
                    currentValue = 50;
                    break;
                case 'C':
                    currentValue = 100;
                    break;
                case 'D':
                    currentValue = 500;
                    break;
                case 'M':
                    currentValue = 1000;
                    break;
            }

            if (currentValue < prevValue) {
                result -= currentValue;
            } else {
                result += currentValue;
            }

            prevValue = currentValue;
        }

        return result;
    }
}

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Problem Info

Description

Problem 13: Roman to Integer - Detailed explanation and solution approaches.

Topics

Hash Table Math String

Companies

AMDAccentureAdobeAmazonAppleAxonBNY MellonBloomberg

Stats

Difficulty:Easy

Languages:4

Companies:35

Problem #:13

Problem Explanation

💡

Think Before You Code

🤔 Ask Yourself

→What is the input? What output do I need?
→Can I solve a smaller version of this problem first?
→What patterns have I seen in similar problems?

✏️ Try This First

Before looking at the solution, try to solve it on paper with a simple example!

🚀 Try on LeetCode

Solution Approach

📋

Step-by-Step Solution

6 steps

1
Step 1: Create a hash map (or equivalent) to store the integer value of each Roman numeral symbol.
2
Step 2: (Python/Java) Iterate through the input string from left to right (or right to left in Java).
3
Step 3: (Python/Java) Compare the value of the current symbol with the next symbol's value (if it exists). If the current value is smaller, subtract it from the result; otherwise, add it.
4
Step 4: (C++) Check each character and apply subtraction rule based on the next character if necessary.
5
Step 5: (C) Explicitly checks for all possible subtractive combinations.
6
Step 6: Return the final accumulated integer value.

💡

Pro Tip for Students

Try tracing through each step with a small example on paper before coding. Understanding "why" each step happens is more important than memorizing the code!

⚡

Complexity Analysis

⏱️

Time Complexity

O(n)

👍 Linear - Good! Visits each element once.

💾

Space Complexity

O(1)

💪 Constant space - Uses same memory regardless of input!

📝

Why?

The dominant operation is the single pass through the string. The size of the hash map is fixed, regardless of input size. Therefore, the time complexity is linear, and the space complexity is constant.

📖New to Big O? Click to learn more

Big O Notation - Quick Guide

O(1)Best - Instant

O(log n)Excellent - Binary Search

O(n)Good - One loop

O(n log n)OK - Sorting

O(n²)Slow - Nested loops

O(2ⁿ)Very Slow - Recursion

Solution Approaches

Left to Right with Lookahead

Process left to right, checking next character for subtraction cases

Time: O(n)Space: O(1)

Right to Left

Process right to left, subtracting when current < previous

Time: O(n)Space: O(1)

Alternative Approaches

Iterative approach (right-to-left)

Iterate through the Roman numeral string from right to left. This simplifies the subtractive logic because you only need to check the previously processed symbol. The Java solution demonstrates this.

Time: O(n)Space: O(1)

Trade-offs: Right-to-left iteration can be slightly easier to implement and understand for handling subtractive notation, avoiding the need to look ahead.

✨

Key Insights

1Insight 1: Recognizing the subtractive notation is crucial. Simply summing the values of each symbol will be incorrect for cases like IV or IX.
2Insight 2: A hash map (or similar lookup structure) is efficient for quickly obtaining the integer value of each Roman numeral symbol.
3Insight 3: Iterating either from left-to-right or right-to-left can simplify the logic for handling subtractive notation. Right-to-left avoids the need to look ahead.

📚

Key Terms Explained

For Students

Hash Table

A data structure that maps keys to values for quick lookup. Like a dictionary!

String

A sequence of characters. Like a word or sentence in programming!

Edge Cases

Edge case 1: Empty string - The solutions handle this implicitly by the loop conditions. An empty string will result in 0.
Edge case 2: Single character string – The solutions correctly handle single Roman numeral characters like 'I', 'V', 'X', etc.
Edge case 3: Subtractive notation at the beginning (e.g., 'IX') - The solutions handle this by checking for the next character during iteration.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Forgetting to handle subtractive notation. Incorrectly summing the values of each symbol will lead to wrong results for Roman numerals like 'IV' or 'IX'.

✗Common mistake 2: Incorrect handling of edge cases like empty strings or strings with only one character.

✗Common mistake 3: Inefficient symbol-to-integer mapping (e.g., using multiple `if-else if` statements instead of a hash map in languages that support it).

✅

Learning Tip

Every mistake is a learning opportunity! When you make an error, understand why it happened before moving on.

🌍

Where is This Used in Real Life?

💼Real-world scenario 1: Converting dates or historical documents containing Roman numerals into a computer-readable format for analysis.

🏦Real-world scenario 2: Parsing and processing data from sources that use Roman numerals for version numbers or other identifiers.

💡Understanding real-world applications helps you see the "why" behind algorithms. It's not just about passing interviews—these concepts power the apps and websites you use every day!

Author's Notes

💡 Key Insight

Hash tables trade space for time. Before using one, consider if the problem constraints allow the extra memory. In interviews, always mention this trade-off.

🎯 Interview Tip

Use this problem to demonstrate clean code practices. Variable naming and code organization matter.

⚠️ Watch Out

Don't forget to handle key collisions and null/undefined keys. Consider what happens with duplicate values.

Written by Saswata Mondal

Software Engineer • Algorithms Enthusiast • Interview Coach

👨‍💻

About the Author

👨‍💻

Saswata MondalAuthor400+ LC Problems

B.Tech CSE, IEM Kolkata | LeetCode Rating: 1672 (Top 15%)

Certified: IBM Java Developer, NPTEL Programming in Java

Last updated: June 14, 2024LeetCode Profile GitHub

This solution has been crafted based on my experience solving 400+ LeetCode problems. Each explanation is designed to help you understand the underlying concepts, not just memorize the code.

Community Tips & Insights

Try solving this without using extra space first. It's a great exercise for understanding the underlying pattern.

@CodeNinjaJul 13

In a real interview, always clarify constraints first. Ask about input size and value ranges.

@TechLeadJul 6

Don't forget to handle the edge case when the input is empty. Many candidates miss this in interviews.

@DevExpert92Jun 29

❓

Frequently Asked Questions

How do I choose between a hash map and a hash set?

Use a hash set when you only need to track presence/absence of elements (like detecting duplicates). Use a hash map when you need to associate values with keys (like counting frequencies or storing indices). Hash sets use less memory since they only store keys.

What should I learn from easy problems?

Easy problems introduce core patterns that appear in harder problems. Master basic operations (iteration, conditionals, simple data structures), recognize common patterns (counting, searching, basic transformations), and practice explaining your thought process clearly.

What is the importance of time and space complexity analysis?

Complexity analysis is crucial because: 1) Interviewers always ask about it, 2) It helps you choose between approaches, 3) It demonstrates CS fundamentals. Always state both time and space complexity, and be prepared to explain how you derived them.

What is the optimal approach for "Roman to Integer"?

For this easy-level Hash Table problem, the key is to identify the core pattern. Analyze the input constraints to determine acceptable time complexity. Consider whether math techniques can optimize the solution. Always handle edge cases and validate your approach with examples before coding.

🤖 Need help with this problem?