If the node to be deleted has 2 children there are 2 obvious candidates to replace the key at that node:

• the next larger key
• the previous smaller key

Once this choice is made, we must decide how to change the tree to accomplish this replacement.

The following choices describe the deletion and is called Hibbard deletion.

• Choose the next larger key as the replacement
• Replace the key to be deleted with this next larger key.
• Delete the replacement key from the subtree where it was located.

Delete 40 from this tree. The next larger key is 50.

Replace key 40 with 50.

Now 50 is in two nodes. Delete 50 from the right subtree. Note that it in the right subtree 50 will not have a left child, so deleting it is handled by the simpler case 1 part of the code.

Set 50's left and right links to be 40's left child and the modified right child (50 was deleted from the right child).