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Binary Search Trees III Delete. Chapter 6. Objectives. You will be able to write code to delete a node from a Binary Search Tree. Issues in Deletion from a BST. Deleting a node from a BST is more complex than adding a node. - PowerPoint PPT Presentation
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Binary Search Trees IIIDelete
Chapter 6
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Objectives
You will be able to write code to delete a node from a Binary Search Tree.
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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 >=.
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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.
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Deleting a Leaf
Case 1. The node, x, is a leaf.
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Deleting a Node with One Child
Case 2. The node, x, has one child.
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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
Replace contents of x with the contents of its inorder successor
K
Note that inorder successor will have no left child. Why?
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Delete the former inorder successor node as described for cases 1 and 2
Delete the former inorder successor node as described for cases 1 and 2
Deleting a Node with Two Children
K
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.
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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
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Downloaded Program Running
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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) ;
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Implementation
Copy: http://www.cse.usf.edu/~turnerr/Data_Structures/
Downloads/2011_03_21_Delete_Node/ File BST_Delete_Node.cpp.txt
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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;
}
}
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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
}
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Delete Node Method (continued)
// Delete leaf;
delete_leaf(p, prev);
}
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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);
}
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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;
}
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Deleting Leaf Node
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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;
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Deleting Nonexistent Node
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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
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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);
}
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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;
}
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Deleting Node with One Child
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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
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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;
}
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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);
}
}
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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;
}
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Deleting Node with Two Children
