Integer to Roman
A medium Strings problem included in Love Babbar 450. Below: the roles whose interviews prioritise this topic, and how to practise it.
- Topic
- Strings
- Sheets
- 1
- Core for
- 13 roles
- Platform
- LeetCode
The problem
Convert a non-negative integer into its Roman numeral representation.
Example 1
- Input
- num=3
- Output
- "III"
Example 2
- Input
- num=58
- Output
- "LVIII"
Example 3
- Input
- num=1994
- Output
- "MCMXCIV"
Constraints
- 1 <= num <= 3999
How to think about it
Updated 2026-09-09Roman numerals are a greedy subtractive positional system with 13 discrete value tokens. By treating the 6 subtractive pairs (like IV for 4 and CM for 900) as independent building blocks on equal footing with single symbols, the translation reduces to repeatedly peeling off the largest denomination that fits.
Approaches, worst first
Digit position lookup tables
time O(1) · space O(1)
Extract thousands, hundreds, tens, and units places using division and modulus arithmetic. Map each decimal place to its corresponding Roman numeral segment using four static string tables, then concatenate the parts. It requires four hardcoded arrays covering thirty combinations.
Greedy value-symbol matchingWrite this one
time O(1) · space O(1)
Store all 13 standard value-symbol pairs sorted descending from 1000 ('M') down to 1 ('I'). Iterate through the pairs: while num is greater than or equal to the current pair's value, append its symbol to the result and subtract its value from num.
Where people lose marks · 3
- Treating 4, 9, 40, 90, 400, and 900 through custom branching logic instead of table entries.
- Repeated string concatenation without a buffer; Roman numerals for num <= 3999 are at most 15 characters, so a small array or string builder handles it cleanly.
- Off-by-one in the loop condition: use >= rather than > so exact multiples of denominations are consumed.
The theory behind it
Strings — the ground this problem stands on. All Strings problems
What Strings is
A string is an ordered necklace of text characters, like letters printed along a ribbon of paper. Each character sits at an exact numeric slot, holding a glyph such as a letter, punctuation mark, or digit. In many programming languages, ribbons cannot be edited after creation, meaning changing a single character requires pressing an entirely new ribbon from scratch.
When to reach for it
Reach for string techniques when inputs consist of words, DNA sequences, serialized data formats, or sentences. Clues include questions testing palindromes, anagram matches, substring patterns, parenthesis balancing, or character frequency counts. Whenever an algorithm asks to transform capitalization, parse structured tokens, or compute edits between two phrases, string representations are the core subject.
How the pattern works
Think of characters as small integer codes ranging across standard character sets. Frequency tables with fixed sizes often replace heavy hash maps when tallying occurrences. For search tasks, maintain rolling state using character indices or sliding borders. When building output text through repeated appends, accumulate pieces inside a mutable list or string builder rather than concatenating strings directly, avoiding quadratic copy overhead.
What each operation costs
| Operation | Time |
|---|---|
| read character by index | O(1) |
| concatenate two strings of total length n | O(n) |
| compare two strings of length n | O(n) |
What usually goes wrong with Strings
- Concatenating strings inside a loop using the plus operator, which silently creates full copies on each iteration and turns linear routines into quadratic slowdowns.
- Assuming all characters fall strictly within lowercase English letters without validating spaces, uppercase variants, punctuation marks, or multi-byte unicode symbols.
- Confusing substring length with end index when slicing, causing unexpected off-by-one truncations in languages that take length versus exclusive end position.
Which roles need this problem
Strings is a core topic for these 13 roles — if you're targeting one of them, this problem is early in your path, not optional.
Secondary for 7 more roles, including Data Engineer, Data Analyst, Embedded / Firmware Engineer.
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