A set is a collection of unique elements, it is typically implemented as a hash table, a balanced tree, or a combination of both. In this article, we will explore the properties and uses of set data structures in detail.

Properties of Set Data Structures

• Uniqueness: One of the key properties of a set is that it contains unique elements only. This means that there are no duplicates in a set.
• Order: The elements in a set are typically unordered. This means that the elements are not stored in a specific order, unlike a list or an array.
• Immutable: Sets are typically immutable, meaning that the elements of a set cannot be modified once they are added.
• Fast Membership Testing: Sets are designed to efficiently test whether a given element is a member of the set or not. This is typically done in O(1) time complexity, making it a very fast operation.

Use Cases of Set Data Structures

• Filtering Duplicates: One of the most common use cases of sets is to filter out duplicates from a collection of elements. For example, if you have a list of emails and you want to remove duplicates, you can use a set to store the unique emails.
• Checking Membership: Sets can be used to check if a given element is a member of the set or not. This is a very fast operation, making sets useful for many algorithms and data structures that need to check membership frequently.
• Set Operations: Sets can be used to perform set operations, such as union, intersection, and difference. These operations are typically very fast when implemented with a set data structure.
• Data Validation: Sets can be used to validate data before it is stored or processed. For example, you can use a set to store a list of valid inputs and then check if the input is a member of the set before processing it.

Implementing a Set

There are several ways to implement a set data structure, depending on the specific requirements and constraints of your application. Some of the most common implementations include:

• Hash Table: A hash table is a data structure that stores elements in an array, with each element being assigned a unique key. The key is used to quickly access the element in the array. Hash tables are typically used to implement sets because they can efficiently test for membership and insert new elements.
• Balanced Tree: A balanced tree is a data structure that stores elements in a tree, with each element having a unique key. The tree is typically balanced to ensure that the elements can be efficiently accessed. Balanced trees are typically used to implement sets when the elements need to be stored in a specific order.
• Combination of Both: Some set implementations use a combination of both hash tables and balanced trees to achieve the best of both worlds. For example, they may use a hash table to quickly test for membership and a balanced tree to store the elements in a specific order.

Python Simple way to Implement

s = set()

Python from scratch implementation

class MySet:
    def __init__(self):
        self.set = {}
    
    def add(self, value):
        self.set[value] = True
    
    def remove(self, value):
        del self.set[value]
    
    def search(self, value):
        return value in self.set
    
    def union(self, other_set):
        union_set = MySet()
        for value in self.set:
            union_set.add(value)
        for value in other_set.set:
            union_set.add(value)
        return union_set
    
    def intersect(self, other_set):
        intersect_set = MySet()
        for value in self.set:
            if value in other_set.set:
                intersect_set.add(value)
        return intersect_set

Conclusion

In conclusion, set data structures are a powerful tool in computer science, providing an efficient way to store and manipulate unique elements. They have many use cases, including filtering duplicates, checking membership, performing set operations and data validation. With the right implementation, sets can be a valuable addition to any program or data structure.