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CompSci 105 SS 2006 Principles of Computer Science. Lecture 21: Binary Search Tree. Binary Search Trees (BSTs). 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 - PowerPoint PPT Presentation
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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
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B
4
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2
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Inorder Traversalvoid printTree( TreeNode root)
if ( root != null )
printTree( root.getLeft () );
println(root.getRootItem());
printTree( root.getRight() );
}M
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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
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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() );
}M
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Postorder Traversalvoid printTree( TreeNode root)
if ( root != null )
printTree( root.getLeft () );printTree( root.getRight() );
println(root.getRootItem());
}M
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Exercise
• For each of the trees below, what is the preorder traversal? What is the postorder traversal?
B
CA
C
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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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B
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Full and Complete Trees
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JB
A full tree
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Full and Complete Trees
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JB
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B
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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JB
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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JB
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DA
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JB
BST heap
BST’s vs Heaps
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MB G
