LINQ: Generate a Cartesian Product

A Cartesian product by definition is a direct product of two sets. Take the following example. Assume you have these two lists:

{A, B, C} and {1, 2, 3}

A Cartesian product of the two lists would be the following:

{(A,1), (A,2), (A,3), (B,1), (B,2), (B,3), (C,1), (C,2), (C,3)}

Let us see how to achieve something similar in LINQ using the SelectMany method

LINQ Cartesian

Needless to say, this peice of code is the key to generating cartesian product in LINQ:

var cartesianLst = 
listA.SelectMany(a => listB.Select(b => a + b + ' '));

using which we are projecting each element of a sequence to an IEnumerable< T> ; projecting to a result sequence, which is the concatenation of the two.

OUTPUT

Also check out Combine Multiple Sequences in LINQ using the Zip Operator - .NET 4.0

About The Author

Suprotim Agarwal, Developer Technologies MVP (Microsoft Most Valuable Professional) is the founder and contributor for DevCurry, DotNetCurry and SQLServerCurry. He is the Chief Editor of a Developer Magazine called DNC Magazine. He has also authored two Books - 51 Recipes using jQuery with ASP.NET Controls. and The Absolutely Awesome jQuery CookBook.

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3 comments:

Anonymous said...: Finally, I found my Cross-Join operation :); June 28, 2011 at 5:40 AM
Fabricio Rateni said...: Good article. For those interested in getting the same result using query syntax:

var cartesian2 = from a in listA
from b in listB
select a + b + ' ';

Regards,
Fabricio.; October 6, 2012 at 10:36 AM
Dinesh Chrysler said...: it can also be done like this,
var l3 = new[] { "A","B", "C" };
var l4 = new[] { 1, 2, 3 };

var output3 = l3.Zip(l4,(Tfirst,Tsecond)=> Tfirst.ToString() + ' ' + Tsecond.ToString()).ToList();
//ouput3: A 1 B 2 C3 are in array list.
string output4 = output3.Aggregate((item1, item2) => item1 + ", " + item2);
//output4 = "A 1, B 2, C 3" are in single string.; May 14, 2013 at 12:29 AM