Applications of Height-Balanced Binary Tree

Conditions for Height-Balanced Binary Tree:

Following are the conditions for a height-balanced binary tree:...

What is the Height Balance of a node?

To check if the binary tree is height-balanced or not, you have to check the height balance of each node. For this, you need to calculate the heights of the two subtrees for each node making this impractical. Instead, we store the height balance information of every subtree in the root node of that subtree. Thus, each node not only maintains its data and children’s information but also a height balance value.The height balance of a node is calculated as follows:...

Height of a Height-Balanced Binary Tree:

The height of a node in a tree is the length of the longest path from that node downward to a leaf, counting both the start and end vertices of the path. The height of a leaf is 1. The height of a nonempty tree is the height of its root. It can be proved that the height of a height-balanced binary tree with N nodes is O(logN)....

Why do we need a Height-Balanced Binary Tree?

Let’s understand the need for a balanced binary tree through an example....

Applications of Height-Balanced Binary Tree:

Balanced trees are mostly used for in-memory sorts of sets and dictionaries. Balanced trees are also used extensively in database applications in which insertions and deletions are fewer but there are frequent lookups for data required. It is used in applications that require improved searching apart from database applications. It has applications in storyline games as well. It is used mainly in corporate sectors where they have to keep the information about the employees working there and their change in shifts....

Advantages of Height-Balanced Binary Tree:

It will improve the worst-case lookup time at the expense of making a typical case roughly one lookup less. As a general rule, a height-balanced tree would work better when the request frequencies across the data set are more evenly spread,   It gives better search time complexity....

Disadvantages of Height-Balanced Binary Tree:

Longer running times for the insert and remove operations. Must keep balancing info in each node. To find nodes to balance, must go back up in the tree....

How to check if a given tree is height-balanced:

You can check if a tree is height-balanced using recursion based on the idea that every subtree of the tree will also be height-balanced. To check if a tree is height-balanced perform the following operations:...