How Can LINQ Perform a Cartesian Product with a Variable Number of Sets?

Implementing Cartesian product with variable number of sets using LINQ

Suppose a class structure contains a person, multiple dogs, and multiple puppies for each dog. The goal is to generate a list of all possible puppy combinations, selecting one puppy from each dog.

In SQL, this can be achieved using the Cartesian product operation, for example:

<code class="language-sql">select * from puppies a, puppies b where a.parent='dog1' and b.parent='dog2'</code>

Is it possible to perform similar operations using LINQ?

If the set size of dogs (i.e. the number of dogs) is known at compile time, a straightforward approach can be used:

<code class="language-csharp">from p1 in dog1.Puppies
from p2 in dog2.Puppies
from p3 in dog3.Puppies
select new {p1, p2, p3};</code>

However, if the collection number of dogs is unknown, a more general approach is needed. Eric Lippert details a solution in his article and on StackOverflow that involves creating a custom method to calculate the Cartesian product:

<code class="language-csharp">public static IEnumerable<IEnumerable<T>> CartesianProduct<T>(IEnumerable<IEnumerable<T>> sets) {
    // ... implementation omitted for brevity
}</code>

Using this method, the desired query can be expressed as:

<code class="language-csharp">CartesianProduct(from dog in person.Dogs select dog.Puppies)</code>

This will return a sequence of puppy sequences, where each sequence represents a combination of one puppy from each dog. For example, if dogs 'dog1' and 'dog2' have puppies 'p11', 'p12' and 'p21' respectively, the output will be:

<code>{p11, p21}
{p11, p22}
{p12, p21}
{p12, p22}</code>

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