Integer to Roman

Integer to Roman is a Medium Data Structures and Algorithms interview problem you can solve, run and submit on Thita.ai. It belongs to the String Manipulation Patterns pattern, in the Integer and Roman Conversion subpattern.

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 one's 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 an integer, convert it to a roman numeral.

Example 1: Input: num = 3 Output: "III"

Example 2: Input: num = 4 Output: "IV"

Example 3: Input: num = 9 Output: "IX"

Example 4: Input: num = 58 Output: "LVIII" Explanation: L = 50, V = 5, III = 3.

Example 5: Input: num = 1994 Output: "MCMXCIV" Explanation: M = 1000, CM = 900, XC = 90 and IV = 4.

Constraints: 1 <= num <= 3999

Topics and companies

Topics: Math, String.

Reported in interviews at Amazon, Bloomberg, Microsoft, Adobe, Google, Apple, Oracle.

How to practise Integer to Roman on Thita.ai

Starter code is provided in C, C#, C++, dart, elixir, erlang, Go, Java, JavaScript, Kotlin, PHP, Python, python3, racket, Ruby, Rust, Scala, Swift and TypeScript. Your solution runs against 5 test cases for this problem, with the AI coach available for a hint when you are stuck rather than a finished answer. The reference solution runs in O(n) time and O(1) space.

Open Integer to Roman in the code editor, or read the Integer to Roman editorial for a worked solution with its approach and complexity analysis.

Where Integer to Roman sits in the DSA pattern sheet

• String Manipulation Patterns pattern guide
• Integer and Roman Conversion subpattern
• The full DSA patterns sheet
• All coding practice problems

Problems related to Integer to Roman

Other problems that use the same Integer and Roman Conversion and String Manipulation Patterns techniques:

• Roman to Integer — Easy, same subpattern
• String to Integer (atoi) — Medium, same subpattern
• Add Strings — Easy, same pattern
• Find Beautiful Indices in the Given Array II — Hard, same pattern
• Find the Index of the First Occurrence in a String — Easy, same pattern
• Palindrome Number — Easy, same pattern