Integer to Roman Number - Visualization

Strings

Contents

ProblemExamplesSolutionAlgorithmCodeTimeSpace

Problem Statement❯

Given a positive integer num, your task is to convert it into a Roman numeral as per the classical Roman numeral system.

  • Roman numerals use combinations of letters from the Latin alphabet: I, V, X, L, C, D, and M.
  • There are specific rules for combining symbols to represent numbers, including using subtraction (e.g., IV for 4, IX for 9).

Note: The input number will be a positive integer between 1 and 3999 (inclusive). If the input is outside this range or invalid (like 0 or negative), return an appropriate message or handle it gracefully.

Examples❯

Input Output Description
1 I Smallest valid Roman numeral
4 IV Special case using subtraction rule
9 IX Another subtraction case
58 LVIII L = 50, V = 5, III = 3 → 50 + 5 + 3
1994 MCMXCIV M = 1000, CM = 900, XC = 90, IV = 4
3999 MMMCMXCIX Largest number representable in standard Roman numerals
0 Invalid input Roman numerals start from 1, so 0 is not valid
-5 Invalid input Negative numbers can't be converted

Solution❯

Understanding the Problem

Roman numerals are a numeral system originating from ancient Rome. They use combinations of letters from the Latin alphabet to represent values. The basic symbols are:

  • I = 1
  • V = 5
  • X = 10
  • L = 50
  • C = 100
  • D = 500
  • M = 1000

The goal is to convert an integer (between 1 and 3999) into its Roman numeral representation by applying a set of well-defined rules.

Step-by-Step Solution with Example

Step 1: Create the mapping

We start by preparing a list of Roman symbols along with their corresponding integer values. This list must be ordered from largest to smallest, and should also include the special subtractive forms like IV (4), IX (9), XL (40), etc.

Step 2: Pick an example

Let's say the number is 58. We will walk through converting this number step-by-step using our list of Roman numerals.

Step 3: Match the highest symbol

We find the largest Roman numeral value less than or equal to 58. This is L = 50. So we subtract 50 from 58, leaving us with 8. We also add 'L' to our result.

Step 4: Continue subtracting

Now we match the largest value ≤ 8. It is V = 5. Subtract 5 → we now have 3. Add 'V' to the result.

Step 5: Final subtractions

The remaining value is 3, which is represented by three I's. Add 'III' to the result.

Step 6: Final result for example

Combining all symbols we collected: L + V + III = LVIII. This is the Roman numeral representation of 58.

Step 7: General algorithm

  1. Create a list of value-symbol pairs sorted in descending order.
  2. Initialize an empty result string.
  3. Iterate over the value-symbol list:
  4. While the current value can be subtracted from the number:
  5. Subtract it and append the corresponding symbol to the result.
  6. Continue until the number becomes 0.

Example for 1994: Break it down as M (1000) + CM (900) + XC (90) + IV (4) → Result is MCMXCIV.

Edge Cases

  • Zero or Negative Numbers: Roman numerals do not support 0 or negative values. Return an error or message like "Invalid input".
  • Numbers above 3999: The standard Roman numeral system does not represent numbers above 3999. Again, return a clear message.
  • Empty input or non-numeric input: Return "Invalid input" if input is null, empty, or not a number.

Finally

This problem teaches how to translate a number system based on values and subtractive combinations into code. By breaking the number from the highest Roman value down, we ensure a valid and readable representation. With proper checks for invalid cases and a clear mapping, this algorithm remains simple, efficient, and beginner-friendly.

Algorithm Steps❯

  1. Create two arrays: one for the integer values and one for corresponding Roman symbols, both sorted in descending order.
  2. Initialize an empty string to hold the result.
  3. Loop over the integer values array:
  4. → While the input number is greater than or equal to the current integer value:
  5. → Subtract that value and append the corresponding Roman symbol to the result.
  6. Repeat until the number becomes 0.
  7. Return the result string.

Code

C
C++
Python
Java
JS
Go
Rust
Kotlin
Swift
TS
#include <stdio.h>
#include <string.h>

void intToRoman(int num, char *result) {
  int val[] = {1000, 900, 500, 400, 100, 90, 50, 40, 10, 9, 5, 4, 1};
  char *syms[] = {"M", "CM", "D", "CD", "C", "XC", "L", "XL", "X", "IX", "V", "IV", "I"};
  result[0] = '\0';
  for (int i = 0; i < 13; i++) {
    while (num >= val[i]) {
      strcat(result, syms[i]);
      num -= val[i];
    }
  }
}

int main() {
  char roman[100];
  intToRoman(1994, roman);
  printf("%s\n", roman);
  return 0;
}

Time Complexity❯

CaseTime ComplexityExplanation
Best CaseO(1)The number of iterations is limited to a small fixed set of Roman numeral values (13 in total).
Average CaseO(1)Regardless of the input size, the logic loops through at most 13 Roman symbols.
Worst CaseO(1)Even for the maximum input (3999), the loop runs a constant number of times.

Space Complexity❯

O(1)

Explanation: Only a few variables and fixed arrays are used. No additional memory scales with input.


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