Final answer:
The recursive version of the TREE-INSERT procedure works by checking if the current tree is empty, or recursing to either the left or right subtree depending on the key's value, then inserting the key in the correct position.
Step-by-step explanation:
To provide a recursive version of the TREE-INSERT procedure, we assume that we are dealing with a binary search tree and that the function takes two arguments: the root of the tree and the key to insert.
Recursive TREE-INSERT Procedure
Here is a basic recursive form of the TREE-INSERT procedure:
If the tree is empty, return a new tree with the key as its root.
If the key is less than the current node's key, recurse on the left subtree. If the left child does not exist, insert the new key here.
If the key is greater than the current node's key, recurse on the right subtree. If the right child does not exist, insert the new key here.
By calling the procedure with the initial root of the tree and the key to be inserted, the key will be added to the correct position maintaining the binary search tree property.