Comparing two collections for equality irrespective of the order of items in them

A simple and fairly efficient solution is to sort both collections and then compare them for equality:

bool equal = collection1.OrderBy(i => i).SequenceEqual(
                 collection2.OrderBy(i => i));

This algorithm is O(N*logN), while your solution above is O(N^2).

If the collections have certain properties, you may be able to implement a faster solution. For example, if both of your collections are hash sets, they cannot contain duplicates. Also, checking whether a hash set contains some element is very fast. In that case an algorithm similar to yours would likely be fastest.

Create a Dictionary "dict" and then for each member in the first collection, do dict[member]++;

Then, loop over the second collection in the same way, but for each member do dict[member]--.

At the end, loop over all of the members in the dictionary:

    private bool SetEqual (List<int> left, List<int> right) {

        if (left.Count != right.Count)
            return false;

        Dictionary<int, int> dict = new Dictionary<int, int>();

        foreach (int member in left) {
            if (dict.ContainsKey(member) == false)
                dict[member] = 1;
            else
                dict[member]++;
        }

        foreach (int member in right) {
            if (dict.ContainsKey(member) == false)
                return false;
            else
                dict[member]--;
        }

        foreach (KeyValuePair<int, int> kvp in dict) {
            if (kvp.Value != 0)
                return false;
        }

        return true;

    }

Edit: As far as I can tell this is on the same order as the most efficient algorithm. This algorithm is O(N), assuming that the Dictionary uses O(1) lookups.

This is my (heavily influenced by D.Jennings) generic implementation of the comparison method (in C#):

/// <summary>
/// Represents a service used to compare two collections for equality.
/// </summary>
/// <typeparam name="T">The type of the items in the collections.</typeparam>
public class CollectionComparer<T>
{
    /// <summary>
    /// Compares the content of two collections for equality.
    /// </summary>
    /// <param name="foo">The first collection.</param>
    /// <param name="bar">The second collection.</param>
    /// <returns>True if both collections have the same content, false otherwise.</returns>
    public bool Execute(ICollection<T> foo, ICollection<T> bar)
    {
        // Declare a dictionary to count the occurence of the items in the collection
        Dictionary<T, int> itemCounts = new Dictionary<T,int>();

        // Increase the count for each occurence of the item in the first collection
        foreach (T item in foo)
        {
            if (itemCounts.ContainsKey(item))
            {
                itemCounts[item]++;
            }
            else
            {
                itemCounts[item] = 1;
            }
        }

        // Wrap the keys in a searchable list
        List<T> keys = new List<T>(itemCounts.Keys);

        // Decrease the count for each occurence of the item in the second collection
        foreach (T item in bar)
        {
            // Try to find a key for the item
            // The keys of a dictionary are compared by reference, so we have to
            // find the original key that is equivalent to the "item"
            // You may want to override ".Equals" to define what it means for
            // two "T" objects to be equal
            T key = keys.Find(
                delegate(T listKey)
                {
                    return listKey.Equals(item);
                });

            // Check if a key was found
            if(key != null)
            {
                itemCounts[key]--;
            }
            else
            {
                // There was no occurence of this item in the first collection, thus the collections are not equal
                return false;
            }
        }

        // The count of each item should be 0 if the contents of the collections are equal
        foreach (int value in itemCounts.Values)
        {
            if (value != 0)
            {
                return false;
            }
        }

        // The collections are equal
        return true;
    }
}

You could use a Hashset. Look at the SetEquals method.

EDIT: I realized as soon as I posed that this really only works for sets -- it will not properly deal with collections that have duplicate items. For example { 1, 1, 2 } and { 2, 2, 1 } will be considered equal from this algorithm's perspective. If your collections are sets (or their equality can be measured that way), however, I hope you find the below useful.

The solution I use is:

return c1.Count == c2.Count && c1.Intersect(c2).Count() == c1.Count;

Linq does the dictionary thing under the covers, so this is also O(N). (Note, it's O(1) if the collections aren't the same size).

I did a sanity check using the "SetEqual" method suggested by Daniel, the OrderBy/SequenceEquals method suggested by Igor, and my suggestion. The results are below, showing O(N*LogN) for Igor and O(N) for mine and Daniel's.

I think the simplicity of the Linq intersect code makes it the preferable solution.

__Test Latency(ms)__
N, SetEquals, OrderBy, Intersect    
1024, 0, 0, 0    
2048, 0, 0, 0    
4096, 31.2468, 0, 0    
8192, 62.4936, 0, 0    
16384, 156.234, 15.6234, 0    
32768, 312.468, 15.6234, 46.8702    
65536, 640.5594, 46.8702, 31.2468    
131072, 1312.3656, 93.7404, 203.1042    
262144, 3765.2394, 187.4808, 187.4808    
524288, 5718.1644, 374.9616, 406.2084    
1048576, 11420.7054, 734.2998, 718.6764    
2097152, 35090.1564, 1515.4698, 1484.223

If you use Shouldly, you can use ShouldAllBe with Contains.

collection1 = {1, 2, 3, 4};
collection2 = {2, 4, 1, 3};

collection1.ShouldAllBe(item=>collection2.Contains(item)); // true

And finally, you can write an extension.

public static class ShouldlyIEnumerableExtensions
{
    public static void ShouldEquivalentTo<T>(this IEnumerable<T> list, IEnumerable<T> equivalent)
    {
        list.ShouldAllBe(l => equivalent.Contains(l));
    }
}

UPDATE

A optional parameter exists on ShouldBe method.

collection1.ShouldBe(collection2, ignoreOrder: true); // true

Here's my extension method variant of ohadsc's answer, in case it's useful to someone

static public class EnumerableExtensions 
{
    static public bool IsEquivalentTo<T>(this IEnumerable<T> first, IEnumerable<T> second)
    {
        if ((first == null) != (second == null))
            return false;

        if (!object.ReferenceEquals(first, second) && (first != null))
        {
            if (first.Count() != second.Count())
                return false;

            if ((first.Count() != 0) && HaveMismatchedElement<T>(first, second))
                return false;
        }

        return true;
    }

    private static bool HaveMismatchedElement<T>(IEnumerable<T> first, IEnumerable<T> second)
    {
        int firstCount;
        int secondCount;

        var firstElementCounts = GetElementCounts<T>(first, out firstCount);
        var secondElementCounts = GetElementCounts<T>(second, out secondCount);

        if (firstCount != secondCount)
            return true;

        foreach (var kvp in firstElementCounts)
        {
            firstCount = kvp.Value;
            secondElementCounts.TryGetValue(kvp.Key, out secondCount);

            if (firstCount != secondCount)
                return true;
        }

        return false;
    }

    private static Dictionary<T, int> GetElementCounts<T>(IEnumerable<T> enumerable, out int nullCount)
    {
        var dictionary = new Dictionary<T, int>();
        nullCount = 0;

        foreach (T element in enumerable)
        {
            if (element == null)
            {
                nullCount++;
            }
            else
            {
                int num;
                dictionary.TryGetValue(element, out num);
                num++;
                dictionary[element] = num;
            }
        }

        return dictionary;
    }

    static private int GetHashCode<T>(IEnumerable<T> enumerable)
    {
        int hash = 17;

        foreach (T val in enumerable.OrderBy(x => x))
            hash = hash * 23 + val.GetHashCode();

        return hash;
    }
}

Based on this answer of a duplicate question, and the comments below the answer, and @brian-genisio answer I came up with these:

        public static bool AreEquivalentIgnoringDuplicates<T>(this IEnumerable<T> items, IEnumerable<T> otherItems)
        {
            var itemList = items.ToList();
            var otherItemList = otherItems.ToList();
            var except = itemList.Except(otherItemList);
            return itemList.Count == otherItemList.Count && except.IsEmpty();
        }

        public static bool AreEquivalent<T>(this IEnumerable<T> items, IEnumerable<T> otherItems)
        {
            var itemList = items.ToList();
            var otherItemList = otherItems.ToList();
            var except = itemList.Except(otherItemList);
            return itemList.Distinct().Count() == otherItemList.Count && except.IsEmpty();
        }

Tests for these two:

        [Test]
        public void collection_with_duplicates_are_equivalent()
        {
            var a = new[] {1, 5, 5};
            var b = new[] {1, 1, 5};

            a.AreEquivalentIgnoringDuplicates(b).ShouldBe(true); 
        }

        [Test]
        public void collection_with_duplicates_are_not_equivalent()
        {
            var a = new[] {1, 5, 5};
            var b = new[] {1, 1, 5};

            a.AreEquivalent(b).ShouldBe(false); 
        }

erickson is almost right: since you want to match on counts of duplicates, you want a Bag. In Java, this looks something like:

(new HashBag(collection1)).equals(new HashBag(collection2))

I'm sure C# has a built-in Set implementation. I would use that first; if performance is a problem, you could always use a different Set implementation, but use the same Set interface.

There are many solutions to this problem. If you don't care about duplicates, you don't have to sort both. First make sure that they have the same number of items. After that sort one of the collections. Then binsearch each item from the second collection in the sorted collection. If you don't find a given item stop and return false. The complexity of this: - sorting the first collection: NLog(N) - searching each item from second into the first: NLOG(N) so you end up with 2*N*LOG(N) assuming that they match and you look up everything. This is similar to the complexity of sorting both. Also this gives you the benefit to stop earlier if there's a difference. However, keep in mind that if both are sorted before you step into this comparison and you try sorting by use something like a qsort, the sorting will be more expensive. There are optimizations for this. Another alternative, which is great for small collections where you know the range of the elements is to use a bitmask index. This will give you a O(n) performance. Another alternative is to use a hash and look it up. For small collections it is usually a lot better to do the sorting or the bitmask index. Hashtable have the disadvantage of worse locality so keep that in mind. Again, that's only if you don't care about duplicates. If you want to account for duplicates go with sorting both.

Allowing for duplicates in the IEnumerable<T> (if sets are not desirable\possible) and "ignoring order" you should be able to use a .GroupBy().

I'm not an expert on the complexity measurements, but my rudimentary understanding is that this should be O(n). I understand O(n^2) as coming from performing an O(n) operation inside another O(n) operation like ListA.Where(a => ListB.Contains(a)).ToList(). Every item in ListB is evaluated for equality against each item in ListA.

Like I said, my understanding on complexity is limited, so correct me on this if I'm wrong.

public static bool IsSameAs<T, TKey>(this IEnumerable<T> source, IEnumerable<T> target, Expression<Func<T, TKey>> keySelectorExpression)
    {
        // check the object
        if (source == null && target == null) return true;
        if (source == null || target == null) return false;

        var sourceList = source.ToList();
        var targetList = target.ToList();

        // check the list count :: { 1,1,1 } != { 1,1,1,1 }
        if (sourceList.Count != targetList.Count) return false;

        var keySelector = keySelectorExpression.Compile();
        var groupedSourceList = sourceList.GroupBy(keySelector).ToList();
        var groupedTargetList = targetList.GroupBy(keySelector).ToList();

        // check that the number of grouptings match :: { 1,1,2,3,4 } != { 1,1,2,3,4,5 }
        var groupCountIsSame = groupedSourceList.Count == groupedTargetList.Count;
        if (!groupCountIsSame) return false;

        // check that the count of each group in source has the same count in target :: for values { 1,1,2,3,4 } & { 1,1,1,2,3,4 }
        // key:count
        // { 1:2, 2:1, 3:1, 4:1 } != { 1:3, 2:1, 3:1, 4:1 }
        var countsMissmatch = groupedSourceList.Any(sourceGroup =>
                                                        {
                                                            var targetGroup = groupedTargetList.Single(y => y.Key.Equals(sourceGroup.Key));
                                                            return sourceGroup.Count() != targetGroup.Count();
                                                        });
        return !countsMissmatch;
    }

This simple solution forces the IEnumerable's generic type to implement IComparable. Because of OrderBy's definition.

If you don't want to make such an assumption but still want use this solution, you can use the following piece of code :

bool equal = collection1.OrderBy(i => i?.GetHashCode())
   .SequenceEqual(collection2.OrderBy(i => i?.GetHashCode()));

If comparing for the purpose of Unit Testing Assertions, it may make sense to throw some efficiency out the window and simply convert each list to a string representation (csv) before doing the comparison. That way, the default test Assertion message will display the differences within the error message.

Usage:

using Microsoft.VisualStudio.TestTools.UnitTesting;

// define collection1, collection2, ...

Assert.Equal(collection1.OrderBy(c=>c).ToCsv(), collection2.OrderBy(c=>c).ToCsv());

Helper Extension Method:

public static string ToCsv<T>(
    this IEnumerable<T> values,
    Func<T, string> selector,
    string joinSeparator = ",")
{
    if (selector == null)
    {
        if (typeof(T) == typeof(Int16) ||
            typeof(T) == typeof(Int32) ||
            typeof(T) == typeof(Int64))
        {
            selector = (v) => Convert.ToInt64(v).ToStringInvariant();
        }
        else if (typeof(T) == typeof(decimal))
        {
            selector = (v) => Convert.ToDecimal(v).ToStringInvariant();
        }
        else if (typeof(T) == typeof(float) ||
                typeof(T) == typeof(double))
        {
            selector = (v) => Convert.ToDouble(v).ToString(CultureInfo.InvariantCulture);
        }
        else
        {
            selector = (v) => v.ToString();
        }
    }

    return String.Join(joinSeparator, values.Select(v => selector(v)));
}

Here's my stab at the problem. It's based on this strategy but also borrows some ideas from the accepted answer.

public static class EnumerableExtensions
{
    public static bool SequenceEqualUnordered<TSource>(this IEnumerable<TSource> source, IEnumerable<TSource> second)
    {
        return SequenceEqualUnordered(source, second, EqualityComparer<TSource>.Default);
    }
   
    public static bool SequenceEqualUnordered<TSource>(this IEnumerable<TSource> source, IEnumerable<TSource> second, IEqualityComparer<TSource> comparer)
    {
        if (source == null)
            throw new ArgumentNullException(nameof(source));

        if (second == null)
            throw new ArgumentNullException(nameof(second));

        if (source.TryGetCount(out int firstCount) && second.TryGetCount(out int secondCount))
        {
            if (firstCount != secondCount)
                return false;

            if (firstCount == 0)
                return true;
        }

        IEqualityComparer<ValueTuple<TSource>> wrapperComparer = comparer != null ? new WrappedItemComparer<TSource>(comparer) : null;

        Dictionary<ValueTuple<TSource>, int> counters;
        ValueTuple<TSource> key;
        int counter;

        using (IEnumerator<TSource> enumerator = source.GetEnumerator())
        {
            if (!enumerator.MoveNext())
                return !second.Any();

            counters = new Dictionary<ValueTuple<TSource>, int>(wrapperComparer);

            do
            {
                key = new ValueTuple<TSource>(enumerator.Current);

                if (counters.TryGetValue(key, out counter))
                    counters[key] = counter + 1;
                else
                    counters.Add(key, 1);
            }
            while (enumerator.MoveNext());
        }

        foreach (TSource item in second)
        {
            key = new ValueTuple<TSource>(item);

            if (counters.TryGetValue(key, out counter))
            {
                if (counter <= 0)
                    return false;

                counters[key] = counter - 1;
            }
            else
                return false;
        }

        return counters.Values.All(cnt => cnt == 0);
    }

    private static bool TryGetCount<TSource>(this IEnumerable<TSource> source, out int count)
    {
        switch (source)
        {
            case ICollection<TSource> collection:
                count = collection.Count;
                return true;
            case IReadOnlyCollection<TSource> readOnlyCollection:
                count = readOnlyCollection.Count;
                return true;
            case ICollection nonGenericCollection:
                count = nonGenericCollection.Count;
                return true;
            default:
                count = default;
                return false;
        }
    }

    private sealed class WrappedItemComparer<TSource> : IEqualityComparer<ValueTuple<TSource>>
    {
        private readonly IEqualityComparer<TSource> _comparer;

        public WrappedItemComparer(IEqualityComparer<TSource> comparer)
        {
            _comparer = comparer;
        }

        public bool Equals(ValueTuple<TSource> x, ValueTuple<TSource> y) => _comparer.Equals(x.Item1, y.Item1);

        public int GetHashCode(ValueTuple<TSource> obj) => _comparer.GetHashCode(obj.Item1);
    }
}

Improvements on the MS solution:

• Doesn't take the ReferenceEquals(first, second) shortcut because it's kind of debatable. For example, consider a custom IEnumerable<T> which has an implementation like this: public IEnumerator<T> GetEnumerator() => Enumerable.Repeat(default(T), new Random().Next(10)).GetEnumerator().
• Takes possible shortcuts when both enumerable is a collection but checks not only for ICollection<T> but also for other collection interfaces.
• Handles null values properly. Counting null values separately from the other (non-null) values also doesn't look 100% fail-safe. Consider a custom equality comparer which handles null values in a non-standard way.

This solution is also available in my utility NuGet package.