Data Structures Questions
The concept of disjoint sets refers to a data structure that represents a collection of disjoint (non-overlapping) sets. Each set is represented by a representative element, which is typically chosen as the root of a tree-like structure.
The operations commonly associated with disjoint sets are:
1. MakeSet(x): Creates a new set with a single element x.
2. Union(x, y): Combines the sets containing elements x and y into a single set. This operation involves finding the representatives of both sets and merging them together.
3. Find(x): Returns the representative element of the set that contains element x. This operation is used to determine whether two elements belong to the same set or not.
These operations are typically implemented using efficient data structures such as disjoint-set forests or union-find data structures. The disjoint set data structure is commonly used in various algorithms and applications, including graph algorithms, network connectivity problems, and image processing.