What is a recursive data structure?

A recursive data structure is a data structure that is partially composed of smaller instances of the same type of data structure.

In more detail, recursive data structures are a fundamental concept in computer science, particularly in the field of data structures and algorithms. They are essentially self-referential structures, where each instance of the structure contains a reference to other instances of the same structure. This self-referential nature is what gives recursive data structures their unique properties and capabilities.

There are several types of recursive data structures, including linked lists, trees, and graphs. In a linked list, each node contains a reference to the next node in the list, forming a chain-like structure. In a tree, each node can have multiple children nodes, but only one parent node, forming a hierarchical structure. In a graph, each node can be connected to any number of other nodes, forming a network-like structure.

Recursive data structures are particularly useful for representing hierarchical or nested data. For example, a file system can be represented as a tree, where each node is a file or a directory, and each directory can contain other files or directories. Similarly, a webpage can be represented as a graph, where each node is a web page, and each edge is a hyperlink to another web page.

The recursive nature of these data structures also lends itself well to recursive algorithms, which are algorithms that solve a problem by solving smaller instances of the same problem. For example, many tree and graph traversal algorithms are recursive, as they involve visiting a node and then recursively visiting all its children or connected nodes.

Understanding recursive data structures and how to work with them is a key skill in computer science. They provide a powerful way to organise and manipulate data, and are used in many areas of computing, from databases and file systems to artificial intelligence and machine learning.