How do you delete a node from a binary tree?

To delete a node from a binary tree, you need to consider three scenarios: no child, one child, and two children.

Deleting a node from a binary tree is a bit more complex than adding one. The process depends on the number of children the node to be deleted has.

If the node to be deleted has no children, the process is straightforward. You simply remove the node from the tree. The parent of the deleted node will now point to null instead of the deleted node.

If the node to be deleted has one child, you need to adjust the parent node's pointer so that it points to the child of the deleted node. This effectively bypasses the deleted node and keeps the rest of the tree intact.

The most complex scenario is when the node to be deleted has two children. In this case, you need to find a replacement for the deleted node. This replacement is either the largest node in the left subtree or the smallest node in the right subtree. This replacement node will take the place of the deleted node and maintain the binary search tree property.

Once you've found the replacement node, you remove it from its original location and put it in the place of the node to be deleted. If the replacement node had a child, you need to adjust the pointers to maintain the binary search tree property.

Remember, the key to deleting a node from a binary tree is to maintain the binary search tree property: for any given node, all nodes in the left subtree are smaller, and all nodes in the right subtree are larger. This property must hold true for every node in the tree.

In terms of complexity, the time complexity for deleting a node from a binary tree is O(h), where h is the height of the tree. This is because in the worst-case scenario, you may have to traverse from the root to the deepest leaf node.