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Deleting Nodes w/ 2 Children from a BST

  1. Mar 4, 2014 #1
    I guess the problem is mostly due to the fact that I still don't understand recursion very well. What my prof is trying to do is to teach it to us by directly applying it to data structures that may use them, such as the Binary Search Tree. I've already been able to delete a node with no children and one children but a node with 2 children is very confusing. I am supposed to write the _delete_node operation. The idea is to replace the deleted node with the node containing the maximum value in its left subtree. By the way, all changes are performed on the nodes, rather than on the values in the nodes. An alternate approach would be to move values between nodes in order to preserve the BST structure (which I think would be easier).

    So, once I get into the _delete_node operation with a node with two children, I can find the maximum value in the left subtree easily. With that idea, I came up with this:

    Code (Text):

            else: #Last condition: two children
               
                old = node
                max_node = node._left
               
                while (max_node._right is not None):
                    max_node = max_node._right
                   
                node = _BSTNode (max_node._value)
                node._left = old._left
                node._right = old._right

                max_node = self.remove(max_node._value)
     
    This can successfully delete the node at the top of the tree, but with any other node in the tree with two children, it won't work (it keeps the max_node in the original position, but replaces the deleted node correctly). Another thing is that in my profs call trace, it doesn't seem as if he is calling the remove function again to remove max_node. Any help regarding this approach would be fantastic.

    Relevant Code:

    Code (Text):

        def remove(self, key):
            """
            -------------------------------------------------------
            Removes a node with a value matching key from the bst.
            Returns the value matched.
            Use: value = bst.remove( key )
            -------------------------------------------------------
            Preconditions:
              key - data to search for (?)
            Postconditions:
              returns:
              value - value matching key if found,
              otherwise returns None. Update structure of bst as required.
            -------------------------------------------------------
            """
            self._root, value = self._remove_aux(self._root, key)
            return value

        def _remove_aux(self, node, key):
            """
            -------------------------------------------------------
            Attempts to find a value matching key in a BST node. Deletes the node
            if found and returns the sub-tree root.
            Private recursive operation called only by remove.
            Use: node, value = self._remove_aux(node, key)
            -------------------------------------------------------
            Preconditions:
              node - a bst node (_BSTNode)
              key - data to search for (?)
            Postconditions:
              returns:
              node - the node to search for key (_BSTNode)
              value - value of node containing key if it exists, None otherwise.
            -------------------------------------------------------
            """
            if node is None:
                # Base Case: the key is not in the tree.
                value = None
            elif key < node._value:
                # Search the left subtree.
                node._left, value = self._remove_aux(node._left, key)
            elif key > node._value:
                # Search the right subtree.
                node._right, value = self._remove_aux(node._right, key)
            else:
                # Value has been found.
                value = node._value
                # Replace this node with another node.
                node = self._delete_node(node)
                self._count -= 1

            if node is not None and value is not None:
                # If the value was found, update the ancestor heights.
                node._update_height()
            return node, value
     
    Code (Text):

        def _delete_node(self, node):
            """
            -------------------------------------------------------
            Removes a node from the bst.
            Use: node = self._delete_node(node)
            -------------------------------------------------------
            Preconditions:
              node - the bst node to be deleted (_BSTNode)
            Postconditions:
              returns:
              node - the node that replaces the deleted node. This node is the node
              with the maximum value in the current node's left subtree (_BSTNode)
            -------------------------------------------------------
            """
           
            # Your code here.
           
            return node
     
     
  2. jcsd
  3. Mar 5, 2014 #2
    It looks generally like the right approach, but I think the problem is that you don't update node's parent to point to the maximum node you find. You reassign node (at least, that's what I think
    Code (Text):
    node = _BSTNode (max_node._value)
    means -- unfamiliar with this language, is it Python?), but this doesn't fully remove node from the tree. Try instead starting by telling node's parent to point to the maximum node, and then modifying this new node's children.
     
  4. Mar 5, 2014 #3
    Yes it's Python! I tried drawing out on paper what the procedure was and I came up with some new code which seems to work. I found two different cases regarding the parent node of the maximum node. Does this look correct?

    Code (Text):

            else: #Last condition: two children
               
                parent = node
                max_node = node._left
               
                while (max_node._right is not None):
                    parent = max_node
                    max_node = max_node._right

               
                if (parent is node):                    
                    max_node._left = None
                else:
                    parent._right = max_node._left
                    max_node._left = parent
                   
                parent._update_height()
                max_node._right = node._right
                node = max_node
     
     
  5. Mar 5, 2014 #4
    Yes, it looks better now. I'm having a bit of trouble with this line though:
    Code (Text):
    max_node._left = parent
    I get the line before, but not really this one -- could you briefly explain what it'll do?

    I think there might even be a simpler way though. Is it possible to get access to the parent of the node you want to delete? Here would be my process:

    1. Identify max_node
    2. Set max_node's parent's right child to be max_node's left child
    3. Set max_node's left and right children to node's left and right children
    4. Tell node's parent to point to max_node

    That should avoid the conditional you have in the middle and make it simpler overall -- maybe try making code for these steps and see if it works the same as your code.
     
  6. Mar 5, 2014 #5
    I tried that, but it goes into infinite recursion:

    Code (Text):

                parent = node
                max_node = node._left
               
                while (max_node._right is not None):
                    parent = max_node
                    max_node = max_node._right
                   
                parent._right = max_node._left
               
                max_node._left = node._left
                max_node._right = node._right
               
                node = max_node

               
            return node    
     
    Testing with values = [36, 50, 84, 6, 65, 17, 85, 49, 42, 4, 12], if I remove 36 it works fine, however, if I remove 84, then it keeps printing 65 after it prints the BST.
     
  7. Mar 5, 2014 #6
    Hmm. I guess what I mean is can you do something like
    Code (Text):
    node.parent
    to get a node's parent? Or is that covered when you assign nodes to other nodes?
     
  8. Mar 5, 2014 #7
    No, the _BSTNode doesn't have that property.
     
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