Lecture 21: Binary Search Tree

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Lecture 21: Binary Search Tree

CompSci 105 SS 2006

Principles of Computer Science

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As with a Binary Tree, except

Root node has a special data element called a key

Nodes in left subtree have keys < the root’s key

Nodes in right subtree have keys > the root’s key.

Binary Search Trees (BSTs)

K

>K<K

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Searching

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Add as a leaf

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5• Draw the BST that results from inserting the values 4, 3, 2, 7, 5, 6 in order.

• Draw as many different BST’s shapes as possible with nodes A, B, and C.

B

CA

C

B

A

C

A

B

A

B

C

A

C

B

4

3

2

7

5

6

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Inorder Traversalvoid printTree( TreeNode root)

if ( root != null )

printTree( root.getLeft () );

println(root.getRootItem());

printTree( root.getRight() );

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Inorder Traversalvoid printTree( TreeNode root)

if ( root != null )

printTree( root.getLeft () );

println(root.getRootItem());

printTree( root.getRight() );

}

B

CA

C

B

A

C

A

B

A

B

C

A

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B

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Preorder Traversalvoid printTree( TreeNode root)

if ( root != null )

println( root.getRootItem());

printTree( root.getLeft () );

printTree( root.getRight() );

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Postorder Traversalvoid printTree( TreeNode root)

if ( root != null )

printTree( root.getLeft () );printTree( root.getRight() );

println(root.getRootItem());

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Exercise

• For each of the trees below, what is the preorder traversal? What is the postorder traversal?

B

CA

C

B

A

C

A

B

A

B

C

A

C

B

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Level Order Traversal

• Difficult

• print nodes as if reading tree from a book (left to right, top to bottom)

• Use a queue to keep track...”homework”M

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BST Delete

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Deleting the root

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root root root root

No children

No rightchild

No leftchild

Twochildren

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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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BST Efficiency

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BST Efficiency

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B

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Average Case?

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Full and Complete Trees

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A full tree

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Full and Complete Trees

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A full tree A complete tree

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Minimising Tree Height

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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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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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ADT Table

UnsortedArray

SortedArray

UnsortedLinked List

SortedLinked List

BinarySearch Tree

ADTPriorityQueue

Program that uses a priority

queue

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BST heap

BST’s vs Heaps

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MB G

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Heap

• A complete binary tree

• Each node’s key is bigger than its children’s keys.

Textbook, p. 520

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Maxheap vs. minheap

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Which are maxheaps?M

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5

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EC

DA

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BST heap

BST’s vs Heaps

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MB G