When it comes to implementing the disjoint sets data structure, there are several options available. Each data structure has its own advantages and disadvantages, so it’s important to choose the one that best fits your specific needs. In this article, we will explore some of the commonly used data structures that can be used to implement the disjoint sets data structure.

## Arrays

One of the simplest ways to implement the disjoint sets data structure is by using arrays. In this approach, each element in the array represents a set, and the value at each index represents the parent of that element. Initially, each element is its own parent, indicating that it is a representative of its own set.

To perform operations like union and find on this array-based implementation, we need to keep track of the parent pointers for each element. Union operation involves updating the parent pointer of one set to point to another set’s representative. Find operation traverses through parent pointers until it reaches a representative, which indicates which set an element belongs to.

## Linked Lists

Another way to implement disjoint sets is by using linked lists. In this approach, each node in the linked list represents an element, and each linked list represents a set. The head node of each linked list acts as a representative for that set.

To perform union operation on linked lists implementation, we simply append one list at the end of another list and update its representative accordingly. Find operation involves traversing through nodes until we find the representative node for a given element.

## Trees

Trees are also commonly used for implementing disjoint sets. In this approach, each tree node represents an element and its parent pointer points to its parent node. The root node of each tree acts as a representative for that set.

To perform union operation on tree-based implementation, one of the tree roots is made a child of the other tree root. The choice of which root becomes the parent can be based on various factors like the size or rank of the trees. Find operation involves traversing up through parent pointers until we reach the root node, which represents the set that an element belongs to.

## Hash Tables

Hash tables can also be used to implement disjoint sets. In this approach, each element is stored as a key in the hash table, and its value represents its parent or representative.

To perform union operation using hash tables, we update the parent value for one set’s representative to point to another set’s representative. Find operation involves looking up the hash table for a given element and following its parent pointers until we reach a representative.

## Conclusion

These are some of the commonly used data structures that can be used to implement the disjoint sets data structure. Each data structure has its own trade-offs in terms of time complexity and space complexity. The choice of which data structure to use depends on factors such as the size of elements, expected number of operations, and memory constraints.

Remember, understanding these different implementations will help you choose the most appropriate one for your specific use case. Experimenting with different data structures will give you a deeper understanding of their strengths and weaknesses.