1. Depth-first vs breadth-first traversals
COMP 103
Depth-first vs breadth-first traversals
Marcus Frean, Lindsay Groves, Peter Andreae, and Thomas Kuehne VUW
Marcus Frean
School of Engineering and Computer Science, Victoria University of Wellington
2014-T2 Lecture 23

2. RECAP-TODAY RECAP Building and Traversing Binary Trees TODAY
Depth-First vs Breadth-First Traversal
Chapter 16.2
ANNOUNCEMENTS – TOMORROW:
assignment #7 is due (9:30)
no 10am lecture (but will hand out assignment 8)
after that, copies in corridor of Cotton 2nd floor

3. recap: depth-first traversals
Variations:
1. pre-order: node, then children
2. in-order: left child, node, right child
3. post-order: children, then node
A B C D E F
C B D A F E
C D B F E A
A Maze Analogy keep your left hand on the wall,
1. pre-order: first encounter
2. in-order: second encounter
3. post-order: third encounter A
and act on B E C D F

4. Arithmetic expression trees
Prefix Notation (Polish notation)
+ x 5 2 /
plus( times(5, 2), divide( minus(7, 3), ) )
Infix Notation
(5 x 2 ) + ( ( 7 – 3) / 9)
Postfix Notation (Reverse Polish)
5 2 x 7 3 – 9 / + + x / - 2 5 9 7 3
No Parentheses

5. Depth-First Traversal in General Trees
Visit the subtree under each child before going to the next child
Pre-order: process the node, then process the subtrees
Post-order: process the subtrees, then process the node A B D E C H G M I K F L J

6. (recap slide) Traversing a General Tree
Recursion is the most natural and easiest approach
Iterate through the children at each node
printAll() G T K M Z A
printAll()
printAll()
public void printAll() {
System.out.println(item);
for (GenTreeNode<E> child : children)
child.printAll(); }
printAll()
printAll()
printAll()
Hint: Finding is like Printing with an early exit potential

7. Depth-first Traversal, recursively
e.g., list all employee names
Use recursion (and iteration to step through the children)
public void listAll() {
System.out.println(this.name);
for (OrgTreeNode child : this.children)
child.listAll(); }
Which traversal order does this implement?

8. Managing Depth-First Traversal
Need to remember what nodes are still being worked on, and which of their children have been processed already
In a recursive depth-first traversal (eg. "ListAll" from earlier), activation stacks take care of the bookkeeping! A B D E C H G M I K F L J A
print own name
process children...
return B
print own name
process children...
return D
print own name
process children...
return …

9. Breadth-first Traversal
What about printing the nodes by level?
root first
then second level,
then third level, ….
A B Julie Jenny D E F C Jenny Jude Jiles I…. A B D E C H G M I K F L J

10. Tracking State during Breadth-First Traversal
What nodes do we have to remember?
Which order do we work on them? A B D E C H G M I K F L J

11. Breadth-first Traversal: Use a Queue!
public void BreadthFirstTraversal(TreeNode root) {
Queue<TreeNode> todo = new LinkedList<TreeNode>();
todo.offer(root); // add
while (!todo.isEmpty()) {
TreeNode node = todo.poll(); // remove
System.out.println(node.name());
for (TreeNode child : node.getChildren())
todo.offer(child); }
Look Ma’, no recursion! A B D E C H G M I K F L J

12. Depth-First Traversal: Use a Stack!
public void DepthFirstTraversal(TreeNode root) {
Stack <TreeNode> todo = new Stack<TreeNode>();
todo.push(root); // add
while (!todo.isEmpty()) {
TreeNode node = todo.pop(); // remove
System.out.println(node.name());
for (TreeNode child : node.getChildren())
todo.push(child); }
Which traversal order does this implement?
Look Ma’, no recursion! A B D E C H G M I K F L J

13. In-order Traversal, iteratively?H B A C F I E G

14. Depth-First vs Breadth-First
Visit one child and all of its descendants before its siblings
May visit root before, after, or between its children
+ Requires only one branch to manage traversal!
− May find “costly” results first, and may not find results at all (infinite search trees)
Breadth-First (level-order):
Visit nodes in order of increasing depth
May choose nodes in a level in a specific order
− Requires accumulation of levels to manage traversal
+ Finds minimal solutions and guarantees success!