## Binary search trees, Data Structure & Algorithms

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A Binary Search Tree is binary tree which is either empty or a node having a key value, left child & right child.

By analyzing the above definition, we notice that BST comes into two variants namely empty BST & non-empty BST.

The empty BST contain no added structure, whereas the non-empty BST contain three components.

The non-empty BST satisfies the given conditions:

a) The key within the left child of node (if exists) is less than the key in its parent node.

b) The key within the right child of a node (if exists) is greater than the key in its parent node.

c) The left & right sub trees of the root are binary search trees again.

The given are some operations which can be performed on Binary search trees:

• formation of an empty tree
• Traversing the BST
• Counting internal nodes (non-leaf nodes)
• Counting external nodes (leaf nodes)
• Counting total number of nodes
• Determining the height of tree
• Insertion of a new node
• Searching for an element
• Determination smallest element
• determination largest element
• Deletion of a node.

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