Binary Search Tree

A binary search tree (BST) is a data structure that stores elements in a way that allows for efficient search, insertion, and deletion operations. A BST is a type of binary tree, where each node has a

Introduction Binary Search Tree (BST)

A binary search tree (BST) is a data structure that stores elements in a way that allows for efficient search, insertion, and deletion operations. A BST is a type of binary tree, where each node has at most two children: a left child and a right child.

The BST satisfies the following property: for any node in the tree, the value of the node's left child is less than the node's value, and the value of the node's right child is greater than the node's value. This means that values in the tree are organized in a way that allows for efficient searching: if we want to search for a value x in the tree, we can start at the root and follow the appropriate branches based on whether x is greater or less than the values we encounter, until we find the value we're looking for or determine that it's not in the tree.

Insertion and deletion operations in a BST also maintain this property. When inserting a new value, we start at the root and follow the appropriate branches until we find an empty spot to insert the new value. When deleting a value, we first search for the node containing the value, and then replace it with its successor (the next highest value in the tree) or its predecessor (the next lowest value in the tree), maintaining the BST property.

The efficiency of BST operations depends on the balance of the tree. A balanced BST has a height of O(log n), where n is the number of nodes in the tree, allowing for efficient operations. However, an unbalanced BST can have a height of O(n), reducing the efficiency of operations.

Inorder Tree Traversal

Inorder traversal is a way of visiting all the nodes in a binary search tree (BST) in a specific order. Inorder traversal follows a left-root-right order when visiting nodes. Here's the algorithm for inorder traversal:

1. Check if the current node is null. If it is, return.

2. Traverse the left subtree by recursively calling the inorder function on the left child of the current node.

3. Visit the current node.

4. Traverse the right subtree by recursively calling the inorder function on the right child of the current node.

In other words, inorder traversal involves visiting the left subtree, then visiting the current node, and then visiting the right subtree.

In a BST, inorder traversal will visit nodes in ascending order, because the left subtree of any node contains values less than the node's value, and the right subtree contains values greater than the node's value. Therefore, by visiting the left subtree first, we are guaranteed to visit all smaller values before visiting the current node, and by visiting the right subtree last, we are guaranteed to visit all larger values after visiting the current node.