Finding a Cartesian product of multiple lists

Question

I came up with an extension method to find a Cartesian product of multiple IEnumerable sets. I was able to achieve lazy enumeration via yield return, but I didn't think of a way to do it non-recursively. The result ended up being a recursive lazy enumeration iterator method, the first of its kind! At least as far as I've ever written.

The idea of the problem came from a Stack Overflow question where a guy had many sets of characters, and wanted to generate a combination of all of them. Now I'm just interested because it's a fun problem!

I'd appreciate any kind of review, although here's two specific things I'm most interested in:

1. Can this algorithm can be de-recursed? If so - should it be, and how?
2. Is there some way it could be generalized even more, beyond what I've done?

---

public static class MultiCartesianExtension
{
 public static IEnumerable<TInput[]> MultiCartesian<TInput>(this IEnumerable<IEnumerable<TInput>> input)
 {
 return input.MultiCartesian(x => x);
 }
 public static IEnumerable<TOutput> MultiCartesian<TInput, TOutput>(this IEnumerable<IEnumerable<TInput>> input, Func<TInput[], TOutput> selector)
 {
 // Materializing here to avoid multiple enumerations.
 var inputList = input.ToList();
 var buffer = new TInput[inputList.Count];
 var results = MultiCartesianInner(inputList, buffer, 0);
 var transformed = results.Select(selector);
 return transformed;
 }
 private static IEnumerable<TInput[]> MultiCartesianInner<TInput>(IList<IEnumerable<TInput>> input, TInput[] buffer, int depth)
 {
 foreach (var current in input[depth])
 {
 buffer[depth] = current;
 if (depth == buffer.Length - 1)
 {
 // This is to ensure usage safety - the original buffer
 // needs to remain unmodified to ensure a correct sequence.
 var bufferCopy = (TInput[])buffer.Clone();
 yield return bufferCopy;
 }
 else
 {
 // Funky recursion here
 foreach (var a in MultiCartesianInner(input, buffer, depth + 1))
 {
 yield return a;
 }
 }
 }
 }
}

Usage:

var input = new string[]
{
 "AB",
 "123",
 "@#",
};
foreach (var result in input.MultiCartesian(x => new string(x)))
{
 Console.WriteLine(result);
}
// Results:
// A1@
// A1#
// A2@
// A2#
// A3@
// A3#
// B1@
// B1#
// B2@
// B2#
// B3@
// B3#

• Comintern: Possible bug - IEnumerable doesn't guarantee ordering, so you can't count on "a correct sequence". Consider var input = new HashSet<string> {"AB", "123", "@#"};
• Gediminas Masaitis: @Comintern Good catch! Although I'd argue that it should be up to the caller to ensure this doesn't happen. If the order doesn't matter - it's fine to use a HashSet. If it does matter - it's up to the caller to provide an ordered collection.
• jkdba: Wouldn't the a cartesian product of these sets also include results like 1A@
• Gediminas Masaitis: @JohnK No, a Cartesian product consists of only combinations. Take a look at this image. Finding the permutations would be very easy one you have the combinations though, with the MoreLinq's Permutations method.
• CiaPan: @GediminasMasaitis The link to Wikimedia Commons you provided is prone to rusting – the part /4/4e/ refers to some Commons' internal indices, which are rebuilt from time to time. It's safer to use a stable links to a resource instead, like https://commons.wikimedia.org/wiki/File:Cartesian_Product_qtl1.svg.

Answer 1

You can indeed create a cartesian product without recursion. What you need is to use the enumerator.

I used a non-generic enumerator to work with any types.

public static IEnumerable Cartesian(this IEnumerable<IEnumerable> items)
{
 var slots = items
 // initialize enumerators
 .Select(x => x.GetEnumerator())
 // get only those that could start in case there is an empty collection
 .Where(x => x.MoveNext())
 .ToArray();
 while (true)
 {
 // yield current values
 yield return slots.Select(x => x.Current);
 // increase enumerators
 foreach (var slot in slots)
 {
 // reset the slot if it couldn't move next
 if (!slot.MoveNext())
 {
 // stop when the last enumerator resets
 if (slot == slots.Last()) { yield break; }
 slot.Reset();
 slot.MoveNext();
 // move to the next enumerator if this reseted
 continue;
 }
 // we could increase the current enumerator without reset so stop here
 break;
 }
 }
}

Example:

var letters = new string[] { "A", "B" };
var numbers = new[] { 1, 2, 3 };
var symbols = new[] { "@", "#" };
var empty = new string[] { };
var collections = new IEnumerable[] { letters, numbers, symbols, empty };
collections.Cartesian()
 // this is just for show
 .Select(x => string.Join("", x.Cast<object>()))
 .OrderBy(x => x)
 .Dump(); // linqpad

result:

A1# 
A1@ 
A2# 
A2@ 
A3# 
A3@ 
B1# 
B1@ 
B2# 
B2@ 
B3# 
B3@

• Dmitry Nogin: It could be even shorter :)
• Pablo H: I think the code is missing the Dispose() of the enumerators (slots[i]). To be "fully correct" I would then need to be careful about exceptions...
• manoj jain: collections.Cartesian() // this is just for show .Select This will never execute as we can not apply extension methods on IEnumerable. It should be IEnumerable<T>. Need to Cast it in object[].. collections.GetCartesian().Cast<object[]>() // this is just for show .Select(x => string.Join("", x.Cast<object>())) .OrderBy(x => x);

Answer 2

Found this one from a number of years back. Seems short and to the point:

public static IEnumerable<IEnumerable<T>> CartesianProduct<T>(this IEnumerable<IEnumerable<T>> sequences)
{
 if (sequences == null)
 {
 return null;
 }
 IEnumerable<IEnumerable<T>> emptyProduct = new[] { Enumerable.Empty<T>() };
 return sequences.Aggregate(
 emptyProduct,
 (accumulator, sequence) => accumulator.SelectMany(
 accseq => sequence,
 (accseq, item) => accseq.Concat(new[] { item })));
}

• ShloEmi: example can be found here: stackoverflow.com/questions/4423838/…