Binary Search Trees III
Delete
Chapter 6
1
Objectives

You will be able to write code to delete a
node from a Binary Search Tree.
2
Issues in Deletion from a BST



Deleting a node from a BST is more
complex than adding a node.
We have to ensure that the BST is still a
binary tree after we delete a node.
And that the BST constraints are still met.


Everything to the left of any node is <=.
Everything to the right of any node is >=.
3
Deletion from a BST
Three possible cases for deleting a node,
x, from a BST:
1. The node, x, is a leaf.
2. The node, x, has one child.
3. The node, x, has two children.
4
Deleting a Leaf
Case 1. The node, x, is a leaf.
5
Deleting a Node with One Child
Case 2. The node, x, has one child.
6
Deleting a Node with Two Children

Case 3: The node, x, has two children.

Deletion by copying. (Hibbard & Knuth)
Replace contents of x with the
contents of its inorder successor
K
Note that inorder successor will have no left child. Why?
7
Deleting a Node with Two Children
The node that was the inorder successor will either be
a leaf or have one child (a right child.)
In this example it has a right child.
Delete the former inorder
successor node as
described for cases 1 and 2
K
8
Implementing Deletion






Download most recent version of BST.
http://www.cse.usf.edu/~turnerr/Data_Structures/Downloads/
2011_03_21_Delete_Node/
BST_Vertical_Display
Expand.
Build and run.
Rename folder BST_with_Delete
9
Downloaded Program Running
10
Add Delete Node Method

In public section of BST class definition:
void delete_node(const T&);

In protected section of BST class definition:
void delete_leaf(BSTNode<T> *p,
BSTNode<T> *prev);
void delete_node_with_one_child(BSTNode<T> *p,
BSTNode<T> *prev) ;
void delete_node_with_two_children(BSTNode<T> *p) ;
11
Implementation


Copy:
http://www.cse.usf.edu/~turnerr/Data_Structures/Downloads/
2011_03_21_Delete_Node/ File BST_Delete_Node.cpp.txt
12
Below Class Defintion
template<class T>
void BST<T>::delete_node(const T& el)
{
BSTNode<T> *p = root;
BSTNode<T> *prev = 0;
// Find node to be deleted.
while (p != 0 && !(p->key == el))
{
prev = p;
if (p->key < el)
{
p = p->right;
}
else
{
p = p->left;
}
}
13
Delete Node Method (continued)
if (p == 0)
{
// Declare success!
cout << el << " is not in the tree\n";
return;
}
// p points to the node to be deleted.
if ((p->left != 0) && (p->right != 0))
{
// Delete node with two children
abort();
// Not yet implemented
}
if ((p->left != 0) || (p->right != 0))
{
// Delete node with one child.
abort();
// Not yet implemented
}
14
Delete Node Method (continued)
// Delete leaf;
delete_leaf(p, prev);
}
15
delete_leaf()
template<class T>
void BST<T>::delete_leaf(BSTNode<T> *p,
BSTNode<T> *prev)
{
cout << "Deleting leaf " << p->key << endl;
if (prev->left == p)
{
prev->left = 0;
}
else
{
prev->right = 0;
}
delete(p);
}
16
In main.cpp

Delete traversals.

Add at end:
cout << endl << "Deleting 20\n";
my_BST.delete_node(20);
cout << endl << "Updated tree:\n";
my_BST.display_v(cout);
cin.get();
return 0;
}
17
Deleting Leaf Node
18
Delete Nonexistent Node

Add at end of main:
cout << "\n\nDeleting nonexistent node, 15\n";
my_BST.delete_node(15);
my_BST.display_v(cout);
cout << endl << endl;
19
Deleting Nonexistent Node
20
Delete Node with One Child

In function delete_node:
if ((p->left != 0) || (p->right != 0))
{
// Delete node with one child.
delete_node_with_one_child(p, prev);
return;
}



Implementation:
http://www.cse.usf.edu/~turnerr/Data_Structures/Downloads/
2011_03_21_Delete_Node/
File delete_node_with_one_child.cpp.txt
21
Delete Node with One Child
template<class T>
void BST<T>::delete_node_with_one_child(BSTNode<T> *p,
BSTNode<T> *prev)
{
cout << "Deleting node with one child, " << p->key << endl;
BSTNode<T>* child;
if (p->left != 0)
{
child = p->left;
}
else
{
child = p->right;
}
if (prev->right == p)
{
prev->right = child;
}
else
{
prev->left = child;
}
delete(p);
22
main.cpp
cout << "\nDeleting node with one child, 31\n";
my_BST.delete_node(31);
cout << "\nUpdated tree:\n";
my_BST.display_v(cout);
cout << endl << endl;
cin.get();
return 0;
}
23
Deleting Node with One Child
24
Delete Node with Two Children
In Function delete_node():
if ((p->left != 0) && (p->right != 0))
{
// Delete node with two children
delete_node_with_two_children(p);
return;
}
Copy implementation from:
http://www.cse.usf.edu/~turnerr/Data_Structures/Downloads/
2011_03_21_Delete_Node/
File delete_node_with_two_children.cpp.txt
25
Delete Node with Two Children
template<class T>
void BST<T>::delete_node_with_two_children(BSTNode<T> *p)
{
cout << "Deleting node with two children, " << p->key << endl;
// Find inorder successor to node to be deleted.
BSTNode<T>* suc = p->right;
BSTNode<T>* prev = p;
while (suc->left != 0)
{
prev = suc;
suc = suc->left;
}
26
Delete Node with Two Children
// Copy data from inorder successor as data for the
// node to be deleted.
p->key = suc->key;
// Delete the node that was the inorder successor.
if (suc->right != 0)
{
// Delete node with one child.
delete_node_with_one_child(suc, prev);
}
else
{
delete_leaf(suc, prev);
}
}
27
In main.cpp
cout << "\nDeleting node with two children, 13\n";
my_BST.delete_node(13);
cout << "\nUpdated tree:\n";
my_BST.display_v(cout);
cout << endl << endl;
cin.get();
return 0;
}
28
Deleting Node with Two Children
29