## Recursive Data Structures

Read this page. In the previous unit of our course we studied recursive algorithms. Recursion is a concept that also applies to data. Here we look at recursive data structures - lists, trees, and sets. A list is a structure that consists of elements linked together. If an element is linked to more than one element, the structure is a tree. If each element is linked to two (sub) elements, it is called a binary tree. Trees can be implemented using lists, as shown in the resource for this unit. Several examples of the wide applicability of lists are presented. A link points to all the remaining links, i.e. the rest of the list or the rest of the tree; thus, a link points to a list or to a tree - this is data recursion.

The efficiency of the programming process includes both running time and size of data. This page discusses the latter for recursive lists and trees.

Lastly, why read the last section on sets? Sets are another recursive data structure and the last section 2.7.6, indicates their connection with trees, namely, a set data type can be implemented in several different ways using a list or a tree data type. Thus, the programming process includes implementation decisions, in addition, to design or algorithm decisions. Each of these types of decisions is constrained by the features of the programming language used. The decision choices, such as which data structure to use, will impact efficiency and effectiveness of the program's satisfaction of the program's requirements.

Note: You will notice an unusual use of C++ here. What the author is doing is showing how to pass a fixed-value data-structure as a calling argument.

### 1. Why Recursive Data Structures?

In this essay, we are going to look at recursive algorithms, and how sometimes, we can organize an algorithm so that it resembles the data structure it manipulates, and organize a data structure so that it resembles the algorithms that manipulate it.

When algorithms and the data structures they manipulate are isomorphic, the code we write is easier to understand for exactly the same reason that code like template strings and regular expressions are easy to understand: The code resembles the data it consumes or produces.

We'll finish up by observing that we also can employ optimizations that are only possible when algorithms and the data structures they manipulate are isomorphic.

Here we go.

Source: Reg Braithwaite, https://raganwald.com/2016/12/27/recursive-data-structures.html