In this section, you will get to know one of the variants of self-balancing trees, which keeps the tree balanced all the time while adding and removing nodes. However, why is it so important? As already mentioned, the performance of the lookup time depends on the shape of the tree. In the case of improper organization of nodes, forming a list, the process of searching for a given value can be the O(n) operation. With a correctly arranged tree, the performance can be significantly improved to O(log n).

Do you know that a BST can very easily become an unbalanced tree? Let's make a simple test of adding the following nine numbers to the tree, from 1 to 9. Then, you will receive the tree with the shape shown in the following diagram on the left. However, the same values can be arranged in another way, as a balanced tree, with significantly better breadth-depth ratio, which is shown on the right:

You know what unbalanced and balanced trees are, as well as the aim of self-balancing trees...