What are the cases of deletion in a binary search tree?

The cases of deletion in a binary search tree are node with no child, node with one child, and node with two children.

In a binary search tree, deletion of nodes can be a bit complex compared to insertion and search operations. The complexity arises from the need to maintain the binary search tree property after every deletion. There are three main cases that you need to consider when deleting a node from a binary search tree.

The first case is when the node to be deleted has no children. This is the simplest case. You just need to replace the node with null in its parent node. If the node to be deleted is the root and has no children, then the root is set to null.

The second case is when the node to be deleted has only one child. In this case, you need to adjust the parent pointer of the deleted node to point to the child of the deleted node. If the node to be deleted is the root node and has one child, then the root is set to the child of the deleted node.

The third case is when the node to be deleted has two children. This is the most complex case. You need to find the in-order successor or the in-order predecessor of the node. The in-order successor of a node is the node with the smallest key greater than the key of the node. The in-order predecessor of a node is the node with the largest key smaller than the key of the node. You can replace the node with its in-order successor or predecessor. After replacing, you need to delete the in-order successor or predecessor which will fall into the first two cases.

In all these cases, it's important to ensure that the binary search tree property is maintained. This property states that for any node, the keys in its left subtree are smaller than its key, and the keys in its right subtree are larger than its key. This property allows for efficient search, insertion, and deletion operations.