Self-balancing trees
In this section, you will get to know two variants of a self-balancing tree, which keeps the tree balanced all the time while adding and removing nodes. However, why is it so important? As already mentioned, the lookup performance 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 an O(n) operation. With a correctly arranged tree, the performance can be significantly improved with 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 a 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 a significantly better breadth-depth ratio, which is shown on the right:
Figure 7.19 – Difference between an unbalanced...
