Discussing the article: "From Basic to Intermediate: Queues, Lists, and Trees (VIII)"

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In this article, we will examine how to implement a tree balancing algorithm. Here, I will present my own version of an implementation of this algorithm. There are many other algorithms that serve the same purpose. Nevertheless, each of them has its own advantages and disadvantages. You, my dear reader, will need to explore them and find the one that best suits your needs.

In the previous article “From Basic to Intermediate: queues, lists, and trees (VII)”, we explained one of the many possible ways to delete a node from a tree. You need to have a very good understanding of this operation in order to work with trees intended for different purposes. As we mentioned in our previous article, there are other ways to implement deletion. However, in my opinion, the version shown there is one of the simplest among those that do not use recursion. When deleting nodes, you should avoid recursion because, if you need to delete several data items stored in very deep nodes, you’ll have to push many calls onto the stack to reach each node and then pop them off the stack. This type of recursive traversal requires significant computational resources and increases the time needed to perform tree construction and maintenance operations.

So, it's important to understand everything that has been explained. Similarly, a search operation must be designed very carefully to prevent an unnecessary increase in its execution time. However, this presents an additional challenge: the tree's balancing must be maintained. Understanding this issue is just as important—and perhaps even more important—than understanding the insertion, deletion, and search algorithms that have already been implemented or are yet to be implemented.

So, in this article, we'll explore what it means to balance a tree and why it's so important. In addition, we will begin to understand why we sometimes cannot or should not rebalance the tree—an issue whose practical application will be discussed in another article—even though a height difference between certain subtrees remains in the structure. This structural imbalance may lengthen some traversals, but it is not, in and of itself, a measure of execution time. A search, insertion, or deletion operation will be faster or slower depending on the path it takes and the number of nodes it needs to visit. In any case, let's move on to the main topic of this article.

Author: CODE X