How Can LINQ Compute the Cartesian Product of Multiple Object Sets?

Use LINQ to calculate the Cartesian product of multiple object collections

In object-oriented programming, you may encounter data structures that form hierarchies or relationships, such as a person who owns multiple dogs, and each dog has multiple puppies. To perform certain operations on this kind of data, you might need to calculate the Cartesian product of multiple collections of objects. This article explores how to achieve this using LINQ (Language Integrated Query) in C#.

Explanation of the problem

Consider the following data structure:

• People
  • Dogs (Dog 1, Dog 2, etc.)
  • Puppies (Puppy A, Puppy B, etc.)

Every person owns one or more dogs, and every dog ​​owns one or more puppies. Suppose you want to generate a list of all possible combinations, taking one puppy from every dog ​​belonging to every person. For example:

• Dog 1 Puppy A, Dog 2 Puppy A
• Dog 1 Puppy A, Dog 2 Puppy B
• Dog 1 puppy B, Dog 2 puppy A
• Dog 1 puppy B, Dog 2 puppy B

This represents the Cartesian product of the set of puppies belonging to each dog.

LINQ based solution

If you are using SQL, you can write a query to "multiply" the tables containing dogs and puppies, thus calculating their Cartesian product. In LINQ, you can achieve something similar using the following steps:

1. Define the Cartesian product method

Assume you don't know the number of dog sets at compile time. To handle this, you can define a generic method called CartesianProduct<t></t> that accepts a collection of sets as input and returns a collection of tuples representing all possible combinations. For details on how to implement this approach, please refer to the resources provided in the original question.

2. Generate Cartesian product

Once the CartesianProduct<t></t> method is defined, it can be called to compute the Cartesian product of the set of puppies belonging to each dog. This can be done using the following code:

var combinations = CartesianProduct(from dog in person.Dogs select dog.Puppies);

The resulting set combinations contains tuples of puppies, representing all possible combinations.

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