Largest Roman Numeral possible by rearranging characters of a given string

Last Updated : 23 Jul, 2025

Given a string S of length N, the task is to print the highest roman number possible by rearranging the characters of the given string, if the given string is a valid roman number. If found to be not possible, then print "Invalid".

Examples:

Input: S = "MCMIV"
Output: MMCVI
Explanation: The given string S is valid Roman numeral. Rearranging characters to obtain the string "MMCVI" generates the highest roman numeral possible using given set of characters.

Input: S = "XCYVM"
Output: Invalid

Approach: The idea is to use the sorting by the second element. Follow the steps below to solve the problem:

Iterate over the characters of the string.
Check if the string contains any character other than { 'I', 'V', 'X', 'L', 'C', 'D', 'M' } or not. If found to be true, then print "Invalid".
Otherwise, sort the string in descending order with respect to the decimal value of the characters of the string.
Now convert the roman value to equivalent decimal and store it in a variable, say X.
Now find the equivalent roman value of the decimal number X and store it in a variable, say Y.
Now print the string S if S is found to be equal to Y. Otherwise print "Invalid".

Below is the implementation of the above approach:

C++

// C++ implementation of the above approach
#include <bits/stdc++.h>
using namespace std;

// Function to find decimal
// value of a roman character
int charVal(char c)
{
    if (c == 'I')
        return 1;
    if (c == 'V')
        return 5;
    if (c == 'X')
        return 10;
    if (c == 'L')
        return 50;
    if (c == 'C')
        return 100;
    if (c == 'D')
        return 500;
    if (c == 'M')
        return 1000;

    return -1;
}

// Function to convert string representing
// roman number to equivalent decimal value
int romanToDec(string S)
{
    // Stores the decimal value
    // of the string S
    int res = 0;

    // Stores the size of the S
    int n = S.size();

    // Update res
    res = charVal(S[n - 1]);

    // Traverse the string
    for (int i = n - 2; i >= 0; i--) {

        if (charVal(S[i]) < charVal(S[i + 1]))
            res -= charVal(S[i]);
        else
            res += charVal(S[i]);
    }

    // Return res
    return res;
}

// Function to convert decimal
// to equivalent roman numeral
string DecToRoman(int number)
{
    // Stores the string
    string res = "";

    // Stores all the digit values of a roman digit
    int num[] = { 1, 4, 5, 9, 10, 40, 50,
                  90, 100, 400, 500, 900, 1000 };

    string sym[]
        = { "I", "IV", "V", "IX", "X", "XL", "L",
            "XC", "C", "CD", "D", "CM", "M" };

    int i = 12;

    // Iterate while number
    // is greater than 0
    while (number > 0) {

        int div = number / num[i];
        number = number % num[i];
        while (div--) {
            res += sym[i];
        }
        i--;
    }

    // Return res
    return res;
}

// Function to sort the string
// in descending order of values
// assigned to characters
bool compare(char x, char y)
{
    // Return character with
    // highest decimal value
    int val_x = charVal(x);
    int val_y = charVal(y);

    return (val_x > val_y);
}

// Function to find largest roman
// value possible by rearranging
// the characters of the string
string findLargest(string S)
{
    // Stores all roman characters
    set<char> st = { 'I', 'V', 'X', 'L', 'C', 'D', 'M' };

    // Traverse the string
    for (auto x : S) {

        // If X is not found
        if (st.find(x) == st.end())
            return "Invalid";
    }
    sort(S.begin(), S.end(), compare);

    // Stores the decimal value
    // of the roman number
    int N = romanToDec(S);

    // Find the roman value equivalent
    // to the decimal value of N
    string R = DecToRoman(N);

    if (S != R)
        return "Invalid";

    // Return result
    return S;
}

// Driver Code
int main()
{
    string S = "MCMIV";
    cout << findLargest(S);
}

Java

// Java program for the above approach
import java.io.*;
import java.lang.*;
import java.util.*;

class GFG{

// Function to find decimal
// value of a roman character
static int charVal(char c)
{
    if (c == 'I')
        return 1;
    if (c == 'V')
        return 5;
    if (c == 'X')
        return 10;
    if (c == 'L')
        return 50;
    if (c == 'C')
        return 100;
    if (c == 'D')
        return 500;
    if (c == 'M')
        return 1000;

    return -1;
}

// Function to convert string representing
// roman number to equivalent decimal value
static int romanToDec(String S)
{
    
    // Stores the decimal value
    // of the string S
    int res = 0;

    // Stores the size of the S
    int n = S.length();

    // Update res
    res = charVal(S.charAt(n - 1));

    // Traverse the string
    for(int i = n - 2; i >= 0; i--) 
    {
        if (charVal(S.charAt(i)) < 
            charVal(S.charAt(i + 1)))
            res -= charVal(S.charAt(i));
        else
            res += charVal(S.charAt(i));
    }

    // Return res
    return res;
}

// Function to convert decimal
// to equivalent roman numeral
static String DecToRoman(int number)
{
    
    // Stores the string
    String res = "";

    // Stores all the digit values of a roman digit
    int num[] = { 1,  4,   5,   9,   10,  40,  50,
                  90, 100, 400, 500, 900, 1000 };

    String sym[] = { "I",  "IV", "V",  "IX", 
                     "X",  "XL", "L", "XC", 
                     "C",  "CD", "D",  "CM", "M" };

    int i = 12;

    // Iterate while number
    // is greater than 0
    while (number > 0)
    {
        int div = number / num[i];
        number = number % num[i];
        
        while (div-- > 0)
        {
            res += sym[i];
        }
        i--;
    }

    // Return res
    return res;
}

// Function to find largest roman
// value possible by rearranging
// the characters of the string
static String findLargest(String S)
{
    char arr[] = { 'I', 'V', 'X', 'L', 'C', 'D', 'M' };

    // Stores all roman characters
    Set<Character> st = new HashSet<>();
    for(char x : arr)
        st.add(x);

    Character s[] = new Character[S.length()];
    for(int i = 0; i < S.length(); i++)
        s[i] = S.charAt(i);

    // Traverse the string
    for(char x : s) 
    {
        
        // If X is not found
        if (!st.contains(x))
            return "Invalid";
    }

    Arrays.sort(s, new Comparator<Character>() 
    {
        @Override
        public int compare(Character x, Character y)
        {
            return charVal(y) - charVal(x);
        }
    });

    String ss = "";
    for(char ch : s)
        ss += ch;

    // Stores the decimal value
    // of the roman number
    int N = romanToDec(ss);

    // Find the roman value equivalent
    // to the decimal value of N
    String R = DecToRoman(N);

    if (!ss.equals(R))
        return "Invalid";

    // Return result
    return ss;
}

// Driver Code
public static void main(String[] args)
{
    
    // Input
    String S = "MCMIV";
    int N = S.length();

    System.out.println(findLargest(S));
}
}

// This code is contributed by Kingash

Python3

# Python program for the above approach

# Function to find decimal
# value of a roman character
from functools import cmp_to_key

def mycmp(a, b):
    return -charVal(a) + charVal(b)

def charVal(c):
  if (c == 'I'):
    return 1
  if (c == 'V'):
    return 5
  if (c == 'X'):
    return 10
  if (c == 'L'):
    return 50
  if (c == 'C'):
    return 100
  if (c == 'D'):
    return 500
  if (c == 'M'):
    return 1000

  return -1

# Function to convert string representing
# roman number to equivalent decimal value
def romanToDec(S):

  # Stores the decimal value
  # of the string S
  res = 0

  # Stores the size of the S
  n = len(S)

  # Update res
  res = charVal(S[n - 1])

  # Traverse the string
  for i in range(n-2,-1,-1):
    if (charVal(S[i]) < charVal(S[i + 1])):
      res -= charVal(S[i])
    else:
      res += charVal(S[i])
  

  # Return res
  return res

# Function to convert decimal
# to equivalent roman numeral
def DecToRoman(number):

  # Stores the string
  res = ""

  # Stores all the digit values of a roman digit
  num = [1, 4, 5, 9, 10, 40, 50,
    90, 100, 400, 500, 900, 1000]

  sym = ["I", "IV", "V", "IX",
    "X", "XL", "L", "XC",
    "C", "CD", "D", "CM", "M"]

  i = 12

  # Iterate while number
  # is greater than 0
  while (number > 0):
    div = number // num[i]
    number = number % num[i]

    while (div > 0):
      res += sym[i]
      div -= 1
    
    i -= 1

  # Return res
  return res

# Function to find largest roman
# value possible by rearranging
# the characters of the string
def findLargest(S):
  arr = ['I', 'V', 'X', 'L', 'C', 'D', 'M']

  # Stores all roman characters
  st = set()
  for x in arr:
    st.add(x)

  s = [0 for i in range(len(S))]
  for i in range(len(S)):
    s[i] = S[i]

  # Traverse the string
  for x in s:

    # If X is not found
    if (x not in st):
      return "Invalid"

  s.sort(key = cmp_to_key(mycmp))
  ss = ""
  for ch in s:
    ss += ch

  # Stores the decimal value
  # of the roman number
  N = romanToDec(ss)

  # Find the roman value equivalent
  # to the decimal value of N
  R = DecToRoman(N)

  if (ss != R):
    return "Invalid"

  # Return result
  return ss

# Driver Code

# Input
S = "MCMIV"
N = len(S)

print(findLargest(S))

# This code is contributed by Shinjanapatra

using System;
using System.Collections.Generic;

class Program {
  // Function to find decimal
  // value of a roman character
  static int CharVal(char c)
  {
    if (c == 'I')
      return 1;
    if (c == 'V')
      return 5;
    if (c == 'X')
      return 10;
    if (c == 'L')
      return 50;
    if (c == 'C')
      return 100;
    if (c == 'D')
      return 500;
    if (c == 'M')
      return 1000;

    return -1;
  }

  // Function to convert string representing
  // roman number to equivalent decimal value
  static int RomanToDec(string S)
  {
    // Stores the decimal value
    // of the string S

    int res = 0;

    // Stores the size of the S
    int n = S.Length;

    /// Update res
    res = CharVal(S[n - 1]);

    // Traverse the string
    for (int i = n - 2; i >= 0; i--) {
      if (CharVal(S[i]) < CharVal(S[i + 1]))
        res -= CharVal(S[i]);
      else
        res += CharVal(S[i]);
    }
    return res;
  }

  // Function to convert decimal
  // to equivalent roman numeral
  static string DecToRoman(int number)
  {
    // Stores the string
    string res = "";

    // Stores all the digit values of a roman digit
    int[] num = { 1,  4,   5,   9,   10,  40,  50,
                 90, 100, 400, 500, 900, 1000 };
    string[] sym
      = { "I",  "IV", "V",  "IX", "X",  "XL", "L",
         "XC", "C",  "CD", "D",  "CM", "M" };

    // Iterate while number
    // is greater than 0

    int i = 12;
    while (number > 0) {
      int div = number / num[i];
      number = number % num[i];
      while (div-- > 0) {
        res += sym[i];
      }
      i--;
    }
    return res;
  }

  // Function to find largest roman
  // value possible by rearranging
  // the characters of the string

  static string FindLargest(string S)
  {
    // Stores all roman characters

    char[] arr = { 'I', 'V', 'X', 'L', 'C', 'D', 'M' };

    // Traverse the string
    HashSet<char> st = new HashSet<char>();
    foreach(char x in arr) st.Add(x);
    char[] s = new char[S.Length];
    for (int i = 0; i < S.Length; i++)
      s[i] = S[i];
    foreach(char x in s)
    {
      if (!st.Contains(x))
        return "Invalid";
    }
    Array.Sort(s, delegate(char x, char y) {
      return CharVal(y) - CharVal(x);
    });
    string ss = "";
    foreach(char ch in s) ss += ch;

    // Stores the decimal value
    // of the roman number

    int N = RomanToDec(ss);

    // Find the roman value equivalent
    // to the decimal value of N

    string R = DecToRoman(N);
    if (!ss.Equals(R))
      return "Invalid";
    return ss;
  }

  // Driver code
  static void Main(string[] args)
  {
    string S = "MCMIV";
    Console.WriteLine(FindLargest(S));
  }
}

// This code is contributed by phasing17.

JavaScript

<script>
// Javascript program for the above approach

// Function to find decimal
// value of a roman character
function charVal(c) {
  if (c == 'I')
    return 1;
  if (c == 'V')
    return 5;
  if (c == 'X')
    return 10;
  if (c == 'L')
    return 50;
  if (c == 'C')
    return 100;
  if (c == 'D')
    return 500;
  if (c == 'M')
    return 1000;

  return -1;
}

// Function to convert string representing
// roman number to equivalent decimal value
function romanToDec(S) {

  // Stores the decimal value
  // of the string S
  let res = 0;

  // Stores the size of the S
  let n = S.length;

  // Update res
  res = charVal(S[n - 1]);

  // Traverse the string
  for (let i = n - 2; i >= 0; i--) {
    if (charVal(S[i]) <
      charVal(S[i + 1]))
      res -= charVal(S[i]);
    else
      res += charVal(S[i]);
  }

  // Return res
  return res;
}

// Function to convert decimal
// to equivalent roman numeral
function DecToRoman(number) {

  // Stores the string
  let res = "";

  // Stores all the digit values of a roman digit
  let num = [1, 4, 5, 9, 10, 40, 50,
    90, 100, 400, 500, 900, 1000];

  let sym = ["I", "IV", "V", "IX",
    "X", "XL", "L", "XC",
    "C", "CD", "D", "CM", "M"];

  let i = 12;

  // Iterate while number
  // is greater than 0
  while (number > 0) {
    let div = Math.floor(number / num[i]);
    number = number % num[i];

    while (div-- > 0) {
      res += sym[i];
    }
    i--;
  }

  // Return res
  return res;
}

// Function to find largest roman
// value possible by rearranging
// the characters of the string
function findLargest(S) {
  let arr = ['I', 'V', 'X', 'L', 'C', 'D', 'M'];

  // Stores all roman characters
  let st = new Set();
  for (let x of arr)
    st.add(x);

  let s = new Array(S.length);
  for (let i = 0; i < S.length; i++)
    s[i] = S[i];

  // Traverse the string
  for (let x of s) {

    // If X is not found
    if (!st.has(x))
      return "Invalid";
  }

  s.sort((a, b) => -charVal(a) + charVal(b))
  let ss = "";
  for (let ch of s)
    ss += ch;

  // Stores the decimal value
  // of the roman number
  let N = romanToDec(ss);

  // Find the roman value equivalent
  // to the decimal value of N
  let R = DecToRoman(N);

  if (ss != R)
    return "Invalid";

  // Return result
  return ss;
}

// Driver Code

// Input
let S = "MCMIV";
let N = S.length;

document.write(findLargest(S));

// This code is contributed by Saurabh Jaiswal
</script>

Output:

MMCVI

Time Complexity: O(N*log(N))
Auxiliary Space: O(1)

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