What is a binary search tree and how does it work?

A binary search tree (BST) is a type of binary tree where each node has a key/value pair, and the keys in the left subtree are smaller than the key in the node, while the keys in the right subtree are greater. This property allows for efficient searching, insertion, and deletion operations.

The working principle of a binary search tree is based on the concept of binary search. When searching for a specific key in the tree, the process starts at the root node. If the key is equal to the key in the current node, the search is successful. If the key is less than the key in the current node, the search continues in the left subtree. If the key is greater, the search continues in the right subtree. This process is repeated recursively until the key is found or a leaf node (null) is reached, indicating that the key is not present in the tree.

For insertion, the process is similar to searching. Starting at the root, the key to be inserted is compared with the key in the current node. If the key is less, the insertion continues in the left subtree. If the key is greater, the insertion continues in the right subtree. This process is repeated until a suitable empty position is found, and the new node is inserted.

Deletion in a binary search tree involves three cases:
1. If the node to be deleted is a leaf node, it is simply removed from the tree.
2. If the node to be deleted has only one child, the child node replaces the deleted node in the tree.
3. If the node to be deleted has two children, it is replaced by the smallest node in its right subtree (or the largest node in its left subtree), and then that node is deleted from its original position.

The efficiency of a binary search tree depends on its balancedness. A balanced BST ensures that the height of the tree remains logarithmic, resulting in efficient operations. However, if the tree becomes highly imbalanced, it can degrade into a linked list, leading to poor performance.

In summary, a binary search tree is a data structure that allows for efficient searching, insertion, and deletion operations by maintaining a specific order of keys in its nodes. It works by recursively comparing keys and navigating through the tree based on their values.