1 Binary Search Trees II Chapter 6
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1
Binary Search Trees II
Chapter 6
2
Objectives
You will be able to use a binary search tree template with your own classes.
3
Getting Started
Download project from last class: http://www.cse.usf.edu/~turnerr/Data_Structures/Down
loads/2011_03_07_Binary_Search_Tree/ File BST_Demo.zip
Build and run.
4
Program Running
5
Add Display()
Let's add a function to display the tree showing its structure. Not in the book.
For ease of coding Root at left side of the screen. Successive levels indented to the right.
Right child will be above a node. Left child will be below.
This permits a simple recursive implementation.
6
genBST1.h
#include <iostream>
#include <iomanip>
...
public:
...
// Display the tree on the screen in graphical format
void display(std::ostream & out) const {display(out, 0, root);};
protected:
// Display any subtree in graphical format
void display(std::ostream & out,
int indent,
const BSTNode<T>* subtreeRoot) const;
7
genBST1.h
// Display any subtree in graphical format
template<class T>
void BST<T>::display(ostream & out,
int indent,
const BSTNode<T>* subtreeRoot) const
{
if (subtreeRoot != 0)
{
display(out, indent + 8, subtreeRoot->right);
out << setw(indent) << " " << subtreeRoot->key << endl << endl;
display(out, indent + 8, subtreeRoot->left);
}
}
8
main.cpp
#include <iostream>
...
cout << endl << endl;
my_BST.display(cout);
cin.get();
return 0;
}
9
Display Method Output
10
Inserting Nodes in Different Order
What if we had added the items in increasing numerical order?
my_BST.insert(2);
my_BST.insert(10);
my_BST.insert(12);
my_BST.insert(13);
my_BST.insert(20);
my_BST.insert(25);
my_BST.insert(29);
my_BST.insert(31);
11
A Lopsided Tree
12
A Lopsided Tree
What will be the search time in this tree?
Efficiency of BST depends on keeping the tree reasonably well balanced. A lopsided tree is no better than a linked list.
Replace original insert code.
End of Section
13
Tree Traversal
Visit each node of the tree exactly once.
Many possible orders. Only a few are of practical interest.
Broad categories: Depth first Breadth first
14
Depth First Traversal
Three Versions Inorder
LNR: Left Subtree, Node, Right Subtree
Preorder NLR: Node, Left Subtree, Right Subtree
Postorder LRN: Left Subtree, Right Subree, Node
Name ("In", "Pre", "Post") indicates where the Node is visited relative to its subtrees.
15
genBST1.h
public:
...
// Traversal methods
void preorder() { preorder(root); }
void inorder() { inorder(root); }
void postorder() { postorder(root);}
protected:
...
void preorder(BSTNode<T>*);
void inorder(BSTNode<T>*);
void postorder(BSTNode<T>*);
virtual void visit(BSTNode<T>* p)
{
cout << p->key << ' ';
}
Why virtual?
16
Preorder Traversal
At end of genBST1.h:template<class T>
void BST<T>::preorder(BSTNode<T> *p)
{
if (p != 0)
{
visit(p);
preorder(p->left);
preorder(p->right);
}
}
17
Using Preorder Traversal
At end of main.cpp:
cout << endl << endl << "Preorder traversal: " << endl;
my_BST.preorder();
cout << endl;
18
Output from Preorder Traversal
19
Inorder Traversal
At end of genBST1.h:
template<class T>
void BST<T>::inorder(BSTNode<T> *p)
{
if (p != 0)
{
inorder(p->left);
visit(p);
inorder(p->right);
}
}
20
Using Inorder Traversal
In main.cpp:
cout << endl << endl << "Inorder traversal: " << endl;
my_BST.inorder();
cout << endl;
21
Inorder Traversal Output
Note that elements are in numerical order.
22
Postorder Traversal
At end of genBST1.h:
template<class T>
void BST<T>::postorder(BSTNode<T>* p)
{
if (p != 0)
{
postorder(p->left);
postorder(p->right);
visit(p);
}
}
23
Using Postorder Traversal
In main.cpp:
cout << endl << endl << "Postorder traversal: " << endl;
my_BST.postorder();
cout << endl;
24
Postorder Traversal Output
End of Section
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