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

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

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

Arithmetic expression trees Prefix Notation (Polish notation) + x 5 2 / - 7 3 9 plus( times(5, 2), divide( minus(7, 3), 9 ) ) 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

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

(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

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?

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 …

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

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

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

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

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

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!