LINQ Expression to Find All Modes of an Array

by Zoran Horvat
Jul 30, 2015

Mode of an array is the element which occurs more often than any other element of that array. We can write a LINQ expression which counts occurrences of every element of the array and then pick the element with largest count.

In the previous hint we have developed a LINQ expression which returns array mode ignoring the situation in which more than one element occurs the same number of times. For details, see LINQ Expression to Find Mode of an Array.

In this article, we will extend the same expression so that it returns a collection of numbers which occur equally many times, but more times than any other element of the array.

Below is the function which calculates all modes of a collection of integers.

IEnumerable<int> AllModes(IEnumerable<int> collection)
{

    var pairs =
        collection
            .GroupBy(value => value)
            .OrderByDescending(group => group.Count());

    int modeCount = pairs.First().Count();

    IEnumerable<int> modes =
        pairs
            .Where(pair => pair.Count() == modeCount)
            .Select(pair => pair.Key)
            .ToList();

    return modes;


}

This time, the function runs in two passes. The first pass is to take all distinct elements of the array and to count occurrences of each of them. In the same step, we are sorting distinct elements descending by their number of occurrences. The result is that all modes of the array will appear at the beginning of the resulting collection.

In the second pass, we are simply taking all the elements from the first collection which have the same count as the most frequent element. All those numbers are modes of the array.

If you are interested in more academic solutions to this same problem, please take a look at the exercise Finding Mode of an Array.

Demonstration

We can use this function in the context of integer arrays to find their mode. Here is the console application which demonstrates the AllModes function.

using System;
using System.Collections.Generic;
using System.Linq;

namespace ArrayMode
{

    class Program
    {

        static IEnumerable<int> AllModes(IEnumerable<int> collection)
        {

            var pairs =
                collection
                    .GroupBy(value => value)
                    .OrderByDescending(group => group.Count());

            int modeCount = pairs.First().Count();

            IEnumerable<int> modes =
                pairs
                    .Where(pair => pair.Count() == modeCount)
                    .Select(pair => pair.Key)
                    .ToList();

            return modes;

        }

        static void Print(int[] a)
        {

            for (int i = 0; i < a.Length; i++)
            {
                Console.Write("{0,3}", a[i]);
                if (i < a.Length - 1 && (i + 1) % 10 == 0)
                    Console.WriteLine();
            }
            Console.WriteLine();
            Console.WriteLine();

            var groups = a
                .GroupBy(value => value)
                .OrderBy(group => group.Key);

            foreach (var group in groups)
            {
                Console.WriteLine("{0,3} x {1}", group.Key, group.Count());
            }

        }

        static void Main(string[] args)
        {

            Random rnd = new Random();
            int n = 0;

            while (true)
            {

                Console.Write("Array length (0 to exit): ");
                n = int.Parse(Console.ReadLine());

                if (n <= 0)
                    break;

                int[] a = new int[n];
                for (int i = 0; i < a.Length; i++)
                    a[i] = rnd.Next(9) + 1;

                Print(a);

                IEnumerable<int> modes = AllModes(a);

                string separator = ": ";
                Console.Write("Modes");
                foreach (int mode in modes)
                {
                    Console.Write("{0}{1}", separator, mode);
                    separator = ", ";
                }
                Console.WriteLine();
                Console.WriteLine();

            }

        }

    }
}

When this application is run, it produces the following output:

Array length (0 to exit): 10
  8  2  4  4  1  7  9  3  2  9

  1 x 1
  2 x 2
  3 x 1
  4 x 2
  7 x 1
  8 x 1
  9 x 2
Modes: 2, 4, 9

Array length (0 to exit): 15
  8  1  9  3  5  8  8  6  2  4
  6  6  1  5  2

  1 x 2
  2 x 2
  3 x 1
  4 x 1
  5 x 2
  6 x 3
  8 x 3
  9 x 1
Modes: 6, 8

Array length (0 to exit): 42
  5  3  3  4  4  5  8  7  1  5
  1  2  1  1  3  1  3  1  6  6
  5  1  9  8  8  3  6  6  9  3
  3  1  8  3  6  5  7  8  7  5
  9  4

  1 x 8
  2 x 1
  3 x 8
  4 x 3
  5 x 6
  6 x 5
  7 x 3
  8 x 5
  9 x 3
Modes: 1, 3

Array length (0 to exit): 0