What is the time complexity of Integer to Roman?

The optimal solution has a time complexity of O(1).

What data structures are used to solve Integer to Roman?

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

What are the key insights for solving Integer to Roman?

Insight 1: Recognizing the significance of subtractive notation (IV, IX, XL, XC, CD, CM) is crucial. These combinations avoid repeating a symbol four times. Insight 2: Using a pre-defined mapping of integer values to Roman numeral symbols allows for an efficient iterative approach.

Which companies ask LeetCode 12. Integer to Roman in interviews?

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

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Integer to Roman - LeetCode 12 Solution

Integer to Roman - Complete Solution Guide

Integer to Roman is LeetCode problem 12, a Medium level challenge. This complete guide provides step-by-step explanations, multiple solution approaches, and optimized code in python3, java, cpp, c.

Problem Statement

Seven different symbols represent Roman numerals with the following values: Symbol Value I 1 V 5 X 10 L 50 C 100 D 500 M 1000 Roman numerals are formed by appending the conversions of decimal place values from highest to lowest. Converting a decimal place value into a Roman numeral has the following rules: If the value does not start with 4 or 9, select the symbol of the maximal value that can be subtracted from the input, append that symbol to the result, subtract its value, and convert the rem

Detailed Explanation

The problem requires converting a given integer (between 1 and 3999) into its Roman numeral representation. Roman numerals use specific symbols (I, V, X, L, C, D, M) to represent numbers. The conversion follows a set of rules involving direct symbol mappings and subtractive notation (e.g., IV for 4, IX for 9). The goal is to produce a string containing the Roman numeral equivalent of the input integer.

Solution Approach

The solution uses a greedy approach with a pre-defined mapping of integer values and their corresponding Roman numeral symbols, including those using subtractive notation. It iterates through this mapping, and for each value, it repeatedly subtracts that value from the input integer and appends the corresponding symbol to the result as long as the input integer is greater than or equal to the value. This ensures the largest possible values are used first.

Step-by-Step Algorithm

Step 1: Initialize a list (or array) `val_sym_map` containing pairs of integer values and their Roman numeral representations. This list is sorted in descending order by the integer values. The list includes pairs for subtractive notation (e.g., (900, "CM")).
Step 2: Initialize an empty string `roman_numeral` to store the result.
Step 3: Iterate through the `val_sym_map` list. For each pair (val, sym):
Step 4: While the input integer `num` is greater than or equal to `val`, append `sym` to the `roman_numeral` string and subtract `val` from `num`.
Step 5: After iterating through all pairs in `val_sym_map`, return the `roman_numeral` string.

Key Insights

Insight 1: Recognizing the significance of subtractive notation (IV, IX, XL, XC, CD, CM) is crucial. These combinations avoid repeating a symbol four times.
Insight 2: Using a pre-defined mapping of integer values to Roman numeral symbols allows for an efficient iterative approach.
Insight 3: Processing the input integer from largest to smallest value ensures the Roman numeral is constructed correctly from left to right.

Complexity Analysis

Time Complexity: O(1)

Space Complexity: O(1)

Topics

This problem involves: Hash Table, Math, String.

Companies

Asked at: Accenture, Adobe, Agoda, Amazon, Apple, Arista Networks, Atlassian, Bloomberg, Booking.com, Citadel, Docusign, Geico, Goldman Sachs, Google, IBM, Infosys, J.P. Morgan, LinkedIn, Meta, Microsoft, NinjaCart, Oracle, Palo Alto Networks, Salesforce, Swiggy, TikTok, Uber, UiPath, VMware, Visa, Wix, X, Yahoo, Zoho, eBay.

Integer to Roman | LeetCode 12

Medium

Hash Table Math String

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

Solution Code

Available in:

class Solution {
    public String intToRoman(int num) {
        int[] val = {1000, 900, 500, 400, 100, 90, 50, 40, 10, 9, 5, 4, 1};
        String[] sym = {"M", "CM", "D", "CD", "C", "XC", "L", "XL", "X", "IX", "V", "IV", "I"};

        StringBuilder romanNumeral = new StringBuilder();

        for (int i = 0; i < val.length; i++) {
            while (num >= val[i]) {
                romanNumeral.append(sym[i]);
                num -= val[i];
            }
        }

        return romanNumeral.toString();
    }
}

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Problem Info

Description

Problem 12: Integer to Roman - Detailed explanation and solution approaches.

Topics

Hash Table Math String

Companies

AccentureAdobeAgodaAmazonAppleArista NetworksAtlassianBloomberg

Stats

Difficulty:Medium

Languages:4

Companies:35

Problem #:12

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

5 steps

1
Step 1: Initialize a list (or array) `val_sym_map` containing pairs of integer values and their Roman numeral representations. This list is sorted in descending order by the integer values. The list includes pairs for subtractive notation (e.g., (900, "CM")).
2
Step 2: Initialize an empty string `roman_numeral` to store the result.
3
Step 3: Iterate through the `val_sym_map` list. For each pair (val, sym):
4
Step 4: While the input integer `num` is greater than or equal to `val`, append `sym` to the `roman_numeral` string and subtract `val` from `num`.
5
Step 5: After iterating through all pairs in `val_sym_map`, return the `roman_numeral` string.

💡

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(1)

⚡ Constant time - Super fast! Same speed regardless of input size.

💾

Space Complexity

O(1)

💪 Constant space - Uses same memory regardless of input!

📝

Why?

The time complexity is O(1) because the number of iterations is bounded by the size of the `val_sym_map` list, which is constant (13 in this case). The input `num` is constrained to be between 1 and 3999, and the algorithm iterates a maximum of 13 times, independent of the specific input value within that range. The space complexity is O(1) because the space used by the `val_sym_map` and the `roman_numeral` string is constant. The `roman_numeral` string can have a maximum length, but this length is still bounded by a constant due to the input constraint of 3999 (MMMCMXCIX, length 7). The other variables use constant space.

📖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

Alternative Approaches

Recursive approach

A recursive approach could be used to break down the problem into smaller subproblems. Define a recursive function that checks if the current number is greater than or equal to a certain value and appends its symbol accordingly.

Time: O(1)Space: O(1) in the best case, O(log n) in the worst case due to recursive calls.

Trade-offs: While conceptually interesting, a recursive solution adds overhead and stack space usage that isn't necessary for this problem, making the iterative approach generally better.

✨

Key Insights

1Insight 1: Recognizing the significance of subtractive notation (IV, IX, XL, XC, CD, CM) is crucial. These combinations avoid repeating a symbol four times.
2Insight 2: Using a pre-defined mapping of integer values to Roman numeral symbols allows for an efficient iterative approach.
3Insight 3: Processing the input integer from largest to smallest value ensures the Roman numeral is constructed correctly from left to right.

📚

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: Input close to the upper limit (3999). The solution correctly handles cases like 3888 (MMMDCCLXXXVIII) by repeatedly appending 'M', 'D', 'C', 'L', 'X', 'V', and 'I'.
Edge case 2: Numbers involving subtractive notation (e.g., 4, 9, 40, 90, 400, 900). The pre-defined mapping `val_sym_map` explicitly includes these cases, so the solution naturally handles them without special logic.
Edge case 3: The minimum possible input (1). The algorithm correctly maps 1 to 'I'.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Failing to include subtractive notation. This leads to incorrect results, such as representing 4 as IIII instead of IV.

✗Common mistake 2: Incorrect ordering of values in the mapping. The values must be sorted in descending order to ensure the greedy approach works correctly.

✗Common mistake 3: Incorrect implementation of the loop condition. The condition should check if the number is *greater than or equal to* the current value; otherwise, values might be skipped.

✅

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: Historical representation of numbers in documents or inscriptions. Roman numerals are still used in limited contexts, such as clock faces, book chapters, and copyright dates.

🏦Real-world scenario 2: Generating unique identifiers or labels where a different numbering system is desired for aesthetic or historical reasons.

💡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

Medium problems are the bread and butter of technical interviews. Practice explaining your approach before coding.

⚠️ 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 13, 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

I was asked this exact problem at my Google interview. The interviewer wanted me to optimize space complexity.

@InterviewProJul 13

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

@CodeNinjaJul 6

❓

Frequently Asked Questions

What are the trade-offs of using a hash table?

Hash tables provide O(1) average-case lookup, insertion, and deletion, making them ideal for frequency counting and duplicate detection. However, they use O(n) extra space and may degrade to O(n) time in worst-case scenarios with hash collisions. Always consider if the space trade-off is acceptable.

What techniques are commonly tested in medium-difficulty problems?

Medium problems often require combining multiple techniques: two-pointer with hash maps, BFS/DFS with state tracking, dynamic programming with optimization, or divide-and-conquer approaches. They test your ability to recognize patterns and choose the right combination of techniques.

How should I practice algorithm problems effectively?

Focus on understanding patterns rather than memorizing solutions. After solving a problem, review optimal solutions and understand the intuition. Group similar problems to recognize patterns. Practice explaining your approach out loud. Review problems after a few days to test retention.

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

For this medium-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?