To find the optimal binary search tree, we will **determine the frequency of searching a key**. Let’s assume that frequencies associated with the keys 10, 20, 30 are 3, 2, 5. The above trees have different frequencies. The tree with the lowest frequency would be considered the optimal binary search tree.

## Consequently, how many children does a binary tree have?

**all the keys in the right sub-tree are greater**.

## In this manner, is binary search most efficient?

**Binary search is faster than linear search except for small arrays**. However, the array must be sorted first to be able to apply binary search. There are specialized data structures designed for fast searching, such as hash tables, that can be searched more efficiently than binary search.

## What are advantages and disadvantages of Optimal binary search tree?

Compared to linear search (checking each element in the array starting from the first), binary search is **much faster**. Linear search takes, on average N/2 comparisons (where N is the number of elements in the array), and worst case N comparisons. Binary search takes an average and worst-case log2(N)log2(N) comparisons.

## What is AVL tree?

An AVL tree is **another balanced binary search tree**. Named after their inventors, Adelson-Velskii and Landis, they were the first dynamically balanced trees to be proposed. Like red-black trees, they are not perfectly balanced, but pairs of sub-trees differ in height by at most 1, maintaining an O(logn) search time.

## What is BST in DAA?

A **Binary Search Tree** (BST) is a tree in which all the nodes follow the below-mentioned properties − The value of the key of the left sub-tree is less than the value of its parent (root) node’s key. The value of the key of the right sub-tree is greater than or equal to the value of its parent (root) node’s key.

## What is meant by Optimal binary search tree?

In computer science, an optimal binary search tree (Optimal BST), sometimes called a weight-balanced binary tree, is a binary search tree which **provides the smallest possible search time (or expected search time) for a given sequence of accesses (or access probabilities)**.

## What is Obst problem?

The OBST problem is **to construct an optimal binary search tree**, given the keys and their access probabilities.

## What is optimal search?

A search algorithm is optimal if no other search algorithm uses less time or space or expands fewer nodes, both with a guarantee of solution quality. The optimal search algorithm would be **one that picks the correct node at each choice**.

## What is running cost of BST?

Let us first define the cost of a BST. The cost of a BST node is **the level of that node multiplied by its frequency**. The level of the root is 1.

## What is the advantage of an optimal binary search tree?

10. What are the conditions for an optimal binary search tree and what is its advantage? Explanation: For an optimal binary search The tree should not be modified and we need to find how often keys are accessed. Optimal binary search **improves the lookup cost**.

## What is the Speciality about the inorder?

4. What is the speciality about the inorder traversal of a binary search tree? Explanation: An inorder traversal **can return the elements in increasing order since a binary search tree** has elements that are less than the node to the left and those that are greater than the node to the right.

## Which searching algorithm is best?

## Why is binary search optimal?

Yes, binary search is optimal. This is **easily seen by appealing to information theory**. It takes log N bits merely to identify a unique element out of N elements. But each comparison only gives you one bit of information.