As someone who greatly enjoys fantasy football, the concept of a set it and forget it player is one that I am quite familiar with. It essentially refers to someone who is worth starting regardless of their matchup.

This week I was listening to a fantasy football and hearing set it and forget it made me think about sets in programming. When I had first heard the word set used in a programming context, I immediately thought of two things. The first was the card game, and the second was my high school math teacher.

It turns out, I wasn't actually too far off with either answer. To understand what a set is in programming, it would help to understand what a mathematical set is.

What is a Set in Mathematics?

For a start let's take a look at the Wikipedia definition.

A set is a well-defined collection of distinct objects. The objects that make up a set (also known as as the set's elements or members) can be anything: numbers, people, letters of the alphabet, other sets, and so on.

That seems pretty straightforward, the keywords there are distinct, and anything. Meaning that a set contains these unique objects and that it doesn't matter what they are.

Now that we have a rudimentary understand of Sets let's take a look at Sets in programming.

What is a Set in Programming?

Let's refer to Wikipedia for a definition once more.

A set is an abstract data type that can store unique values, without any particular order. It is a computer implementation of the mathematical concept of a finite set.

So we can see that a Set is a mathematical set simply implemented by a computer. If we take a look at the keywords again, they would be unique and without order. That means that we are again dealing with a collection of unique/distinct values. We are also working with a data type that does not have a specific order, similar to something like a dictionary, hash, or object.

What do they look like?

Let's take a look at sets in two particular languages, JavaScript, which has had sets since the release of EMCAScript 2015, and Python, which has supported sets since the release of 2.4.

Let's start with JavaScript, sets are created with the Set keyword. Just like with any other object that we are creating in JavaScript we use the new objectname syntax as we can see below.

const foo = new Set([1,2,3])
console.log(foo)
// Set { 1, 2, 3 }

In Python we use something similar, since set is a built in data type we have access to the set() method.

foo = set([1, 2, 3])
print(foo)
# {1, 2, 3}

Both Python and JavaScript are using a very similar syntax where we are creating a new set using a list/array respectively. Our set constructors only allow one argument so we have to use this intermediary data type to create a set with multiple values.

JavaScript

const foo = new Set(1,2,3)
// TypeError

Python

foo = set(1,2,3)
# TypeError

Trying to pass in multiple arguments would throw this type error since only 1 argument is accepted.

What purpose do they serve?

Now that we have an idea of what sets are and how they can be instantiated let's take a look at what we can do with them.

Remember when we were covering the definition of a set? One of the important features of a set is it's uniqueness. Therefore, one great purpose of sets is to check if a set contains a specific value.

const foo = new Set([1,2,3])
console.log(foo.has(1))
// true

foo = set([1, 2, 3])
print(1 in foo)
# True

As sets are not ordered we are able to do things like this, checking if a set contains a value, faster than we would be able to in a list/array. To expand on that further, let's see how we access values in a list/array.

const foo = [1, 2, 3]
for(let i = 0; i < foo.length; i++) {
    if (foo[i] == 2) {
        console.log(true)
    }
}
// true

const bar = [1, 2, 3]
bar.includes(2)
// true

foo = [1, 2, 3]
for num in foo:
    if num == 2:
        print(True)
# True

bar = [1, 2, 3]
print(2 in bar)
# True

So, I first used a simple for loop for our list and array. That is to indicate what our includes method or in statement are doing. Since a list/array is ordered, we can access an element via it's index with a runtime of O(1). However, when we need to check if a value is contained within said list/array, we need to iterate over the entire collection. This means that we are going to have a runtime of O(n) since we have to iterate over the collection to check for a value.

Sets can be very useful for things like removing duplicates and comparing for uniqueness due to them containing only unique values. Although sets are a mathematical concept, they don't need to feel or seem scary. As we just saw, they make looking up whether a set contains a value very easy and perhaps more importantly, very fast.

References

• https://en.wikipedia.org/wiki/Set_(mathematics)
• https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Set
• https://wiki.python.org/moin/TimeComplexity
• https://snakify.org/en/lessons/sets/
• https://en.wikipedia.org/wiki/Set_(abstract_data_type)