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Documentation/src/enumerable-extensions/cartesian-product.md
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## CartesianProduct | ||
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In mathematics, specifically set theory, the Cartesian product of two sets A and B, denoted A×B, is the set of all ordered pairs (a, b) where a is in A and b is in B. | ||
In mathematics, specifically set theory, the Cartesian product of two sets A and B, denoted A×B, | ||
is the set of all ordered pairs (a, b) where a ∈ A and b ∈ B. | ||
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The CartesianProduct extension function returns all possible pairs of two given IEnumerables. | ||
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There are two overloads, one which lets you choose | ||
In other words: The Cartesian product produces all possible pairs of two given `IEnumerable`s. | ||
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![cartesian-product with marbles](cartesian-product.svg "Marble me!") | ||
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### Recipe | ||
The Cartesian product can be easily implemented ad-hoc using LINQ's built-in `SelectMany` extension function: | ||
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```cs | ||
using System; | ||
using System.Linq; | ||
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// Version A: Get each pair as a tuple | ||
var result = sequenceA.SelectMany(_ => sequenceB, ValueTuple.Create); | ||
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// Version B: Transform each pair using a selector | ||
var result = sequenceA.SelectMany(_ => sequenceB, (a, b) => ...); | ||
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// Version C: Using LINQs declarative query syntax | ||
var result = | ||
from a in sequenceA | ||
from b in sequenceB | ||
select ...; | ||
``` | ||
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### Examples | ||
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Two sequences as input: | ||
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``` | ||
``` | ||
smiles = [😀, 😐, 🙄] | ||
fruits = [🍉, 🍌, 🍇, 🍓] | ||
``` | ||
``` | ||
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The cartesian products of smiles and fruits: | ||
The Cartesian products of smiles and fruits: | ||
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``` | ||
smiles × fruits => [[😀, 🍉], [😀, 🍌], [😀, 🍇], [😀, 🍓], | ||
[😐, 🍉], [😐, 🍌], [😐, 🍇], [😐, 🍓], | ||
``` | ||
smiles × fruits => [[😀, 🍉], [😀, 🍌], [😀, 🍇], [😀, 🍓], | ||
[😐, 🍉], [😐, 🍌], [😐, 🍇], [😐, 🍓], | ||
[🙄, 🍉], [🙄, 🍌], [🙄, 🍇], [🙄, 🍓]] | ||
``` | ||
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In this C# example you see how all Playing cards are in fact a cartesian product of a suit and a value. | ||
In this C# example you see how all playing cards are in fact a Cartesian products of a suit and a value. | ||
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This example uses the overload with our own selector, because we just want a sequence of strings. | ||
This example uses the overload with a selector, because we just want a sequence of strings. | ||
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```cs | ||
var suits = ImmutableList.Create("♠", "♣", "♥", "♦"); | ||
var values = | ||
ImmutableList.Create("2", "3", "4", "5", "6", "7", "8", "9", "T", "J", "Q", "K", "A"); | ||
using System; | ||
using System.Linq; | ||
using Funcky; | ||
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var suits = Sequence.Return("♠", "♣", "♥", "♦"); | ||
var values = Sequence.Return("2", "3", "4", "5", "6", "7", "8", "9", "T", "J", "Q", "K", "A"); | ||
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var allCards = suits.CartesianProduct(values, (suit, value) => $"{value}{suit}"); | ||
``` | ||
var deck = suits.SelectMany(_ => values, (suit, value) => $"{value}{suit}"); | ||
``` |
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