How Can LINQ Efficiently Generate Cartesian Products from Multi-Level Object Relationships?

Efficiently Generating Cartesian Products from Multi-Level Object Relationships with LINQ

Object-oriented programming often involves intricate multi-level relationships. Consider this example:

<code class="language-csharp">class Person {
    public List<Dog> Dogs { get; set; }
}

class Dog {
    public List<Puppy> Puppies { get; set; }
}

class Puppy {
    public string Name { get; set; }
}</code>

Here, a Person has multiple Dogs, and each Dog has multiple Puppys. The challenge is to generate the Cartesian product—all possible combinations of selecting one Puppy from each Dog.

Traditional SQL would use joins. LINQ offers a more elegant solution. For a fixed number of Dogs (known at compile time), a straightforward LINQ query suffices:

<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>

This yields combinations like:

<code>{p11, p21, p31},
{p11, p21, p32},
{p12, p21, p31},
{p12, p21, p32}</code>

However, when the number of Dogs is dynamic (unknown at compile time), a more generalized approach is needed. Eric Lippert's article (https://www.php.cn/link/f28c49d8be62973ac7716e0b87dae2f9) provides a robust solution for this scenario.

With a suitable CartesianProduct method (as described in Lippert's article), the query simplifies to:

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

This achieves the same result. LINQ's expressive power allows for concise and maintainable handling of complex multi-level object relationships, simplifying the creation of Cartesian products.

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