1CompSci 105 SS 2005

Principles of Computer Science

Lecture 22: Efficiency of BST Operations

Lecturer: Santokh Singh

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Inorder Traversalvoid printTree( TreeNode root)

if ( root != null )

printTree( root.getLeft () );

println(root.getRootItem());

printTree( root.getRight() );

}

Textbook, p. 434

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Deleting the root

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root root root root

No children

No rightchild

No leftchild

TwochildrenTextbook, p. 462

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Exercise

• Draw the BST that results from inserting the values D, C, G, B, E, F in order. Now draw the result of deleting the root.

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Treesort

Please refer to the prescribed Textbook, pages 478-479, now.

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ADT Table

City Country Population

Auckland New Zealand

1,300,000

London United Kingdom

9,400,000

Shanghai China 13,053,000

Textbook, p. 498-499

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ADT Table Operations

void create ()

int length()

void insert( item)

void delete( key )

item find(key)

City Country Population

Auckland New Zealand

1,300,000

London United Kingdom

9,400,000

Shanghai China 13,053,000

Textbook, p. 498-499

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ADT Table

UnsortedArray

SortedArray

UnsortedLinked List

SortedLinked List

BinarySearch Tree

ADT Table

Program that

uses a table

Textbook, p. 504-517

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BST Efficiency

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Textbook, p. 474-478

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BST Efficiency

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Textbook, p. 474-478

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Average Case?

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Textbook, p. 474-478

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Full and Complete Trees

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Textbook, p. 427

A full tree

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Full and Complete Trees

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Textbook, p. 427

A full tree A complete tree

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Minimising Tree Height

Textbook, p. 480-481

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ADT Priority Queue

To do:

1. Study for 105 Exam

2. Play

3. Eat

4. Sleep

Textbook, p. 517

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Priority Queue Operations

void create ()

boolean isEmpty()

voidinsert( item)

item delete()

To do:

1. Study for 105 Exam

2. Play

3. Eat

4. Sleep

Textbook, p. 518

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ADT Table

UnsortedArray

SortedArray

UnsortedLinked List

SortedLinked List

BinarySearch Tree

ADTPriorityQueue

Program that uses a priority

queue

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Heap

Like a binary search tree, but

• Always keep it a complete tree

• Don’t completely sort data

Textbook, p. 520

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Heap

Like a binary search tree, but

• Always keep it a complete tree

• Don’t completely sort data … just make sure that each node’s key is bigger than its children’s keys.

Textbook, p. 520

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BST heap

BST’s vs Heaps

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