Skip to content
Related Articles

Related Articles

Improve Article
Save Article
Like Article

Sort an array of Roman Numerals in ascending order

  • Last Updated : 16 Nov, 2021

Given an array arr[] of N Roman Numerals, the task is to sort these Roman Numerals in ascending order.

Examples: 

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.  To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.

In case you wish to attend live classes with experts, please refer DSA Live Classes for Working Professionals and Competitive Programming Live for Students.

Input: arr[] = { “MCMIV”, “MIV”, “MCM”, “MMIV” } 
Output: MIV MCM MCMIV MMIV 
Explanation: 
The roman numerals in their corresponding decimal system are: 
MIV: 1004 
MCM: 1900 
MCMIV: 1904 
MMIV: 2004



Input: arr = { “MV”, “MIV”, “MCM”, “MM” } 
Output: MIV MV MCM MM 
Explanation: 
The roman numerals in their corresponding decimal system are: 
MIV 1004 
MV 1005 
MCM 1900 
MM 2000 

Approach: The idea to solve this problem is to store each element with its Roman to Integer value in a vector pair and then sort all the elements of the vector according to Roman to Integer value stored. 

  • Iterate the given roman number.
  • Convert the roman number to the decimal and store them as a pair in a vector.
  • Sort the vector based on the decimal numbers stored in them.
  • Finally, print the roman numbers in sorted order.

Below is the implementation of the above approach:

C++




// C++ program to sort an array of
// Roman Numerals in ascending order
 
#include <bits/stdc++.h>
using namespace std;
 
// Function to return the value
// of a Roman symbol
int value(char r)
{
    // I in roman is equal to
    // 1 in decimal
    if (r == 'I')
        return 1;
 
    // V in roman is equal to
    // 5 in decimal
    if (r == 'V')
        return 5;
 
    // X in roman is equal to
    // 10 in decimal
    if (r == 'X')
        return 10;
 
    // L in roman is equal to
    // 50 in decimal
    if (r == 'L')
        return 50;
 
    // C in roman is equal to
    // 100 in decimal
    if (r == 'C')
        return 100;
 
    // D in roman is equal to
    // 500 in decimal
    if (r == 'D')
        return 500;
 
    // M in roman is equal to
    // 1000 in decimal
    if (r == 'M')
        return 1000;
 
    return -1;
}
 
// Function to return the decimal value
// of a roman numaral
int romanToDecimal(string& str)
{
    // Initialize result
    int res = 0;
 
    // Traverse given input
    for (int i = 0; i < str.length(); i++) {
 
        // Getting value of symbol s[i]
        int s1 = value(str[i]);
 
        if (i + 1 < str.length()) {
 
            // Getting value of symbol s[i+1]
            int s2 = value(str[i + 1]);
 
            // Comparing both values
            if (s1 >= s2) {
 
                // Value of current symbol
                // is >= the next symbol
                res = res + s1;
            }
            else {
 
                // Value of current symbol
                // is < the next symbol
                res = res + s2 - s1;
                i++;
            }
        }
        else {
            res = res + s1;
        }
    }
    return res;
}
 
// Function to sort the array according to
// the increasing order
void sortArr(string arr[], int n)
{
    // Vector to store the roman to integer
    // with respective elements
    vector<pair<int, string> > vp;
 
    // Inserting roman to integer
    // with respective elements in vector pair
    for (int i = 0; i < n; i++) {
        vp.push_back(make_pair(
            romanToDecimal(
                arr[i]),
            arr[i]));
    }
 
    // Sort the vector, this will sort the pair
    // according to the increasing order.
    sort(vp.begin(), vp.end());
 
    // Print the sorted vector content
    for (int i = 0; i < vp.size(); i++)
        cout << vp[i].second << " "
             << vp[i].first << "\n";
}
 
// Driver code
int main()
{
    string arr[] = { "MCMIV", "MIV",
                     "MCM", "MMIV" };
    int n = sizeof(arr) / sizeof(arr[0]);
 
    sortArr(arr, n);
 
    return 0;
}

Java




// Java program to sort an array of
// Roman Numerals in ascending order
import java.io.*;
import java.util.*;
 
// User defined Pair class
class Pair
{
    int x;
    String y;
     
    public Pair(int a, String b)
    {
        this.x = a;
        this.y = b;
    }
}
 
// Class to define user defined conparator
class Compare
{
    static void compare(ArrayList<Pair> vp)
    {
         
        // Comparator to sort the pair according
        // to first element
        Collections.sort(vp, new Comparator<Pair>()
        {
            @Override public int compare(Pair p1, Pair p2)
            {
                return p1.x - p2.x;
            }
        });
    }
}
 
class GFG{
 
// Function to return the value
// of a Roman symbol
static int value(char r)
{
     
    // I in roman is equal to
    // 1 in decimal
    if (r == 'I')
        return 1;
 
    // V in roman is equal to
    // 5 in decimal
    if (r == 'V')
        return 5;
 
    // X in roman is equal to
    // 10 in decimal
    if (r == 'X')
        return 10;
 
    // L in roman is equal to
    // 50 in decimal
    if (r == 'L')
        return 50;
 
    // C in roman is equal to
    // 100 in decimal
    if (r == 'C')
        return 100;
 
    // D in roman is equal to
    // 500 in decimal
    if (r == 'D')
        return 500;
 
    // M in roman is equal to
    // 1000 in decimal
    if (r == 'M')
        return 1000;
 
    return -1;
}
 
// Function to return the decimal value
// of a roman numaral
static int romanToDecimal(String str)
{
     
    // Initialize result
    int res = 0;
 
    // Traverse given input
    for(int i = 0; i < str.length(); i++)
    {
         
        // Getting value of symbol s[i]
        int s1 = value(str.charAt(i));
 
        if (i + 1 < str.length())
        {
             
            // Getting value of symbol s[i+1]
            int s2 = value(str.charAt(i + 1));
 
            // Comparing both values
            if (s1 >= s2)
            {
                 
                // Value of current symbol
                // is >= the next symbol
                res = res + s1;
            }
            else
            {
                 
                // Value of current symbol
                // is < the next symbol
                res = res + s2 - s1;
                i++;
            }
        }
        else
        {
            res = res + s1;
        }
    }
    return res;
}
 
// Function to sort the array according to
// the increasing order
static void sortArr(String[] arr, int n)
{
     
    // Vector to store the roman to integer
    // with respective elements
    ArrayList<Pair> vp = new ArrayList<Pair>();
 
    // Inserting roman to integer
    // with respective elements in vector pair
    for(int i = 0; i < n; i++)
    {
        vp.add(new Pair(romanToDecimal(arr[i]),
                                       arr[i]));
    }
 
    // Sort the vector, this will sort the pair
    // according to the increasing order.
    Compare obj = new Compare();
    obj.compare(vp);
 
    // Print the sorted vector content
    for(int i = 0; i < vp.size(); i++)
        System.out.println(vp.get(i).y + " " +
                           vp.get(i).x + "\n");
}
 
// Driver Code
public static void main(String[] args)
{
    String arr[] = { "MCMIV", "MIV", "MCM", "MMIV" };
    int n = arr.length;
 
    sortArr(arr, n);
}
}
 
// This code is contributed by akhilsaini

Python3




# Python3 program to sort an array of
# Roman Numerals in ascending order
 
# Function to return the value
# of a Roman symbol
def value(r):
 
    # I in roman is equal to
    # 1 in decimal
    if (r == 'I'):
        return 1
 
    # V in roman is equal to
    # 5 in decimal
    if (r == 'V'):
        return 5
 
    # X in roman is equal to
    # 10 in decimal
    if (r == 'X'):
        return 10
         
    # L in roman is equal to
    # 50 in decimal
    if (r == 'L'):
        return 50
 
    # C in roman is equal to
    # 100 in decimal
    if (r == 'C'):
        return 100
 
    # D in roman is equal to
    # 500 in decimal
    if (r == 'D'):
        return 500
 
    # M in roman is equal to
    # 1000 in decimal
    if (r == 'M'):
        return 1000
 
    return -1
 
# Function to return the decimal value
# of a roman numaral
def romanToDecimal(st):
 
    # Initialize result
    res = 0
 
    # Traverse given input
    i = 0
    while i < len(st):
 
        # Getting value of symbol s[i]
        s1 = value(st[i])
 
        if (i + 1 < len(st)):
 
            # Getting value of symbol s[i+1]
            s2 = value(st[i + 1])
 
            # Comparing both values
            if (s1 >= s2):
 
                # Value of current symbol
                # is >= the next symbol
                res = res + s1
             
            else :
 
                # Value of current symbol
                # is < the next symbol
                res = res + s2 - s1
                i += 1
         
        else :
            res = res + s1
             
        i += 1
     
    return res
 
# Function to sort the array according to
# the increasing order
def sortArr(arr, n):
 
    # Vector to store the roman to integer
    # with respective elements
    vp = {}
 
    # Inserting roman to integer
    # with respective elements in vector pair
    for i in range(n):
        p = romanToDecimal(arr[i])
        vp[p] = arr[i]
 
    # Sort the vector, this will sort the pair
    # according to the increasing order.
    for i in sorted(vp):
        print(vp[i], i)
 
# Driver code
if __name__ == "__main__":
     
    arr = [ "MCMIV", "MIV",
            "MCM", "MMIV" ]
    n = len(arr)
 
    sortArr(arr, n)
 
# This code is contributed by chitranayal

C#




// C# program to sort an array of
// Roman Numerals in ascending order
using System;
using System.Collections;
using System.Collections.Generic;
 
class ABC : IComparer<Pair>
{
    public int Compare(Pair p1, Pair p2)
    {
        if (p1.x == 0 || p2.x == 0)
        {
            return 0;
        }
           
        // CompareTo() method
        return p1.x.CompareTo(p2.x);
    }
}
 
// User defined Pair class
public class Pair
{
    public int x;
    public string y;
     
    public Pair(int a, string b)
    {
        this.x = a;
        this.y = b;
    }
}
 
class GFG{
     
// Function to return the value
// of a Roman symbol
static int value(char r)
{
     
    // I in roman is equal to
    // 1 in decimal
    if (r == 'I')
        return 1;
 
    // V in roman is equal to
    // 5 in decimal
    if (r == 'V')
        return 5;
 
    // X in roman is equal to
    // 10 in decimal
    if (r == 'X')
        return 10;
 
    // L in roman is equal to
    // 50 in decimal
    if (r == 'L')
        return 50;
 
    // C in roman is equal to
    // 100 in decimal
    if (r == 'C')
        return 100;
 
    // D in roman is equal to
    // 500 in decimal
    if (r == 'D')
        return 500;
 
    // M in roman is equal to
    // 1000 in decimal
    if (r == 'M')
        return 1000;
 
    return -1;
}
 
// Function to return the decimal value
// of a roman numaral
static int romanToDecimal(string str)
{
     
    // Initialize result
    int res = 0;
 
    // Traverse given input
    for(int i = 0; i < str.Length; i++)
    {
         
        // Getting value of symbol s[i]
        int s1 = value(str[i]);
 
        if (i + 1 < str.Length)
        {
             
            // Getting value of symbol s[i+1]
            int s2 = value(str[i + 1]);
 
            // Comparing both values
            if (s1 >= s2)
            {
                 
                // Value of current symbol
                // is >= the next symbol
                res = res + s1;
            }
            else
            {
 
                // Value of current symbol
                // is < the next symbol
                res = res + s2 - s1;
                i++;
            }
        }
        else
        {
            res = res + s1;
        }
    }
    return res;
}
 
// Function to sort the array according to
// the increasing order
static void sortArr(String[] arr, int n)
{
     
    // Vector to store the roman to integer
    // with respective elements
    List<Pair> vp = new List<Pair>();
 
    // Inserting roman to integer
    // with respective elements in vector pair
    for(int i = 0; i < n; i++)
    {
        vp.Add(new Pair(romanToDecimal(arr[i]),
                                       arr[i]));
    }
 
    // Sort the vector, this will sort the pair
    // according to the increasing order.
    ABC gg = new ABC();
    vp.Sort(gg);
 
    // Print the sorted vector content
    for(int i = 0; i < vp.Count; i++)
        Console.WriteLine(vp[i].y + " " +
                          vp[i].x + "\n");
}
 
// Driver Code
static public void Main ()
{
     string[] arr = { "MCMIV", "MIV", "MCM", "MMIV" };
    int n = arr.Length;
 
    sortArr(arr, n);
}
}
 
// This code is contributed by akhilsaini

Javascript




<script>
 
// JavaScript implementation of
// the above approach
 
// Function to return the value
// of a Roman symbol
function value(r)
{
    // I in roman is equal to
    // 1 in decimal
    if (r == 'I')
        return 1;
 
    // V in roman is equal to
    // 5 in decimal
    if (r == 'V')
        return 5;
 
    // X in roman is equal to
    // 10 in decimal
    if (r == 'X')
        return 10;
 
    // L in roman is equal to
    // 50 in decimal
    if (r == 'L')
        return 50;
 
    // C in roman is equal to
    // 100 in decimal
    if (r == 'C')
        return 100;
 
    // D in roman is equal to
    // 500 in decimal
    if (r == 'D')
        return 500;
 
    // M in roman is equal to
    // 1000 in decimal
    if (r == 'M')
        return 1000;
 
    return -1;
}
 
// Function to return the decimal value
// of a roman numaral
function romanToDecimal(str)
{
    // Initialize result
    var res = 0;
 
    // Traverse given input
    for (var i = 0; i < str.length; i++) {
 
        // Getting value of symbol s[i]
        var s1 = value(str[i]);
 
        if (i + 1 < str.length) {
 
            // Getting value of symbol s[i+1]
            var s2 = value(str[i + 1]);
 
            // Comparing both values
            if (s1 >= s2) {
 
                // Value of current symbol
                // is >= the next symbol
                res = res + s1;
            }
            else {
 
                // Value of current symbol
                // is < the next symbol
                res = res + s2 - s1;
                i++;
            }
        }
        else {
            res = res + s1;
        }
    }
    return res;
}
 
// Function to sort the array according to
// the increasing order
function sortArr(arr, n)
{
    // Vector to store the roman to integer
    // with respective elements
    var vp = new Array(n);
    // Inserting roman to integer
    // with respective elements in vector pair
    for (var i = 0; i < n; i++) {
        vp[i] = [romanToDecimal(arr[i]),arr[i]];
    }
 
    // Sort the vector, this will sort the pair
    // according to the increasing order.
    vp.sort();
 
    // Print the sorted vector content
    for (var i = 0; i < n; i++)
        document.write(vp[i][1]+" "+vp[i][0]+"<br>");
}
 
// Driver Code
var arr = ["MCMIV", "MIV",
           "MCM", "MMIV"];
var n = arr.length;
sortArr(arr, n);
 
</script>
Output: 
MIV 1004
MCM 1900
MCMIV 1904
MMIV 2004

 

Time Complexity: O(N * log(N)), where N is the number of elements in the array.

Auxiliary Space: O(N)
 




My Personal Notes arrow_drop_up
Recommended Articles
Page :