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What is a Binary Search Tree?

Educative Answers Team

A Binary Search Tree is a binary tree where each node contains a key and an optional associated value. It allows particularly fast lookup, addition, and removal of items.

The nodes are arranged in a binary search tree according to the following properties:

  • The left subtree of a particular node will always contain nodes with keys less than that node’s key.

  • The right subtree of a particular node will always contain nodes with keys greater than that node’s key.

  • The left and the right subtree of a particular node will also, in turn, be binary search trees.

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Time Complexity

In average cases, the above mentioned properties enable the insert, search and deletion operations in O(logn)O(log n) time where n is the number of nodes in the tree. However, the time complexity for these operations is O(n)O(n) in the worst case when the tree becomes unbalanced.

Space Complexity

The space complexity of a binary search tree is O(n)O(n) in both the average and the worst cases.

Types of Traversals

The Binary Search Tree can be traversed in the following ways:

  1. Pre-order Traversal
  2. In-order Traversal
  3. Post-order Traversal

The pre-order traversal will visit nodes in Parent-LeftChild-RightChild order.

The in-order traversal will visit nodes in LeftChild-Parent-RightChild order. In this way, the tree is traversed in an ascending order of keys.

The post-order traversal will visit nodes in LeftChild-RightChild-Parent order.

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data structures
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