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Tree Traversals

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Fred Betty Barney Wilma Pebbles. In-order traversal (2) visit node between children ... Barney Betty Pebbles Wilma Fred. Tree iterators ... – PowerPoint PPT presentation

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Title: Tree Traversals

1
Tree Traversals

A traversal is a way of walking the tree
structure
Some common traversals
pre-order traversal
in-order traversal
post-order traversal

2
(Depth-first) traversal path
3
Each node is reached three times
1
3
2
1
1
3
3
2
2
1
1
3
3
2
2
4
Pre-order traversal (1)visit node before children
1
1
1
1
1
Fred ? Betty ? Barney ? Wilma ? Pebbles
5
In-order traversal (2)visit node between children
2
2
2
2
2
Barney ? Betty ? Fred ? Pebbles ? Wilma
6
Post-order traversal (3)visit node after children
3
3
3
3
3
Barney ? Betty ? Pebbles ? Wilma ? Fred
7
Example
Pre-order traversal Fred Betty Barney Wilma
Pebbles
Fred
In-order traversal Barney Betty Fred Pebbles
Wilma
Wilma
Betty
Post-order traversal Barney Betty Pebbles Wilma
Fred
Barney
Pebbles
8
Tree iterators

We can define tree iterators which follow the
same traversal path.
Unlike the visitors, iterators stop at each node
they must remember where they are!
Let us consider first an in-order iterator.

9
Behavior of an inOrderIterator

java.util.Iterator it bst.inOrderIterator()
System.out.println("it.hasNext()
"it.hasNext())
it.hasNext() true

10
Behavior of an inOrderIterator

java.util.Iterator it bst.inOrderIterator()
System.out.println("it.hasNext()
"it.hasNext())
it.hasNext() true
System.out.println("it.next() "
it.next())
it.next() Barney
System.out.println("it.hasNext()
"it.hasNext())
it.hasNext() true

11
Behavior of an inOrderIterator

java.util.Iterator it bst.inOrderIterator()
System.out.println("it.hasNext()
"it.hasNext())
it.hasNext() true
System.out.println("it.next() "
it.next())
it.next() Barney
System.out.println("it.hasNext()
"it.hasNext())
it.hasNext() true
System.out.println("it.next() "
it.next())
it.next() Betty
System.out.println("it.hasNext()
"it.hasNext())
it.hasNext() true

12
Behavior of an inOrderIterator

java.util.Iterator it bst.inOrderIterator()
System.out.println("it.hasNext()
"it.hasNext())
it.hasNext() true
System.out.println("it.next() "
it.next())
it.next() Barney
System.out.println("it.hasNext()
"it.hasNext())
it.hasNext() true
System.out.println("it.next() "
it.next())
it.next() Betty
System.out.println("it.hasNext()
"it.hasNext())
it.hasNext() true
System.out.println("it.next() "
it.next())
it.next() Fred
System.out.println("it.hasNext()
"it.hasNext())
it.hasNext() true

13
Behavior of an inOrderIterator

java.util.Iterator it bst.inOrderIterator()
System.out.println("it.hasNext()
"it.hasNext())
it.hasNext() true
System.out.println("it.next() "
it.next())
it.next() Barney
System.out.println("it.hasNext()
"it.hasNext())
it.hasNext() true
System.out.println("it.next() "
it.next())
it.next() Betty
System.out.println("it.hasNext()
"it.hasNext())
it.hasNext() true
System.out.println("it.next() "
it.next())
it.next() Fred
System.out.println("it.hasNext()
"it.hasNext())
it.hasNext() true
System.out.println("it.next() "
it.next())
it.next() Pebbles
System.out.println("it.hasNext()
"it.hasNext())
it.hasNext() true

14
Behavior of an inOrderIterator

java.util.Iterator it bst.inOrderIterator()
System.out.println("it.hasNext()
"it.hasNext())
it.hasNext() true
System.out.println("it.next() "
it.next())
it.next() Barney
System.out.println("it.hasNext()
"it.hasNext())
it.hasNext() true
System.out.println("it.next() "
it.next())
it.next() Betty
System.out.println("it.hasNext()
"it.hasNext())
it.hasNext() true
System.out.println("it.next() "
it.next())
it.next() Fred
System.out.println("it.hasNext()
"it.hasNext())
it.hasNext() true
System.out.println("it.next() "
it.next())
it.next() Pebbles
System.out.println("it.hasNext()
"it.hasNext())
it.hasNext() true

15
Implementation?

How is state of iterator maintained?

16
Implementation

Using a stack!
On creation of the iterator, references to all
nonEmpty trees along the left edge of the tree
are pushed onto the stack
hasNext() is implemented to return
!_stack.isEmpty()

17
Behavior of an inOrderIterator