Explain the role of a key in a binary search tree.

A key in a binary search tree is used to organise and retrieve data efficiently based on its value.

In a binary search tree (BST), each node contains a key and two subtrees, the left and right child. The key plays a crucial role in maintaining the fundamental property of a BST: for every node, all elements in the left subtree are less than the node, and all elements in the right subtree are greater than the node. This property allows for efficient search, insertion, and deletion operations.

The key is essentially the value that we use to identify and access the data stored in the node. When we want to search for a specific piece of data in the tree, we compare the key of the node with the key we are looking for. If the key is less than the node's key, we move to the left child, and if it's greater, we move to the right child. This process continues until we either find the key or reach a null child, indicating that the key is not present in the tree.

When inserting a new node into the tree, we use the key to determine its correct position. Starting from the root, we compare the new key with the current node's key. If the new key is less, we move to the left child, and if it's greater, we move to the right child. We repeat this process until we find a null child, where we insert the new node.

Similarly, when deleting a node, we first need to find it using its key. Once we've found the node, we need to reorganise the tree to maintain the BST property. The exact process depends on whether the node has zero, one, or two children.

In summary, the key in a binary search tree is a fundamental component that determines the structure of the tree and enables efficient data operations. It's the basis for comparing, sorting, and accessing the data stored in the tree.