Problem of the Day

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# Problem of the Day - PowerPoint PPT Presentation

Problem of the Day. Solve this equation by moving the numbers: 7 6 = 2 4. Problem of the Day. Solve this equation by moving the numbers: 7 6 = 2 4 7 2 = 4 9. CSC 212 – Data Structures. Lecture 34 5 : Implementing Traversals. Traversing Binary Trees.

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Problem of the Day
• Solve this equation by moving the numbers:

76 = 24

Problem of the Day
• Solve this equation by moving the numbers:

76 = 24

72=49

CSC 212 – Data Structures

### Lecture 345:Implementing Traversals

Traversing Binary Trees
• Trees are another Collection of data
• Positions required in the Tree ADT methods
• ADT uses generic type to specify type of element
• Want to iterate through tree’s elements
• This is not optional; Trees are Iterable
• Could use any traversal algorithm; choose logical one
• But how do we implement traversals & Iterator?
Traversal Methods
• Many traversals, differ in order nodes visited
• Do parent then do each kid in pre-order traversal
Traversal Methods
• Many traversals, differ in order nodes visited
• Do parent then do each kid in pre-order traversal
• Post-order traversal does kids before doing parents
Traversal Methods
• Many traversals, differ in order nodes visited
• Do parent then do each kid in pre-order traversal
• Post-order traversal does kids before doing parents
• Do left kid, parent, then right kid in in-order traversal
Traversal Algorithms
• So, how do we do each one of these?
Traversal Algorithms
• So, how do we do each one of these? implement each traversal?
• Recursion usually answer to questions involving trees
• The algorithm uses same approach for all three
• Where Nodes done only difference; rest is identical
Binary Tree Traversal

Algorithmtraverse(tree, v)

// Do node here for pre-order traversal

traverse(tree, tree.left(v));

// Do node here for in-order traversal

traverse(tree, tree.right(v));

// Do node here for post-order traversal

Important Feature of Any Coder
• Nearly all of the great coders are inherently lazy
• Hope for you all -- you have this part completed
• Unfortunately, true laziness requires lot of work
• Debugging code wastes time could be websurfing
• To make small change, more time lost rewriting code
• Small amount of planning save lots of time later
Template Method Pattern
• Common design pattern used to simplify code
• Implement class of algorithms using an abstract class
• Class leaves all actual work in abstract methods
• Subclasses written for each member algorithm
• To make concrete, each overrides abstract method
• Method performs specific actions for that algorithm
• New algorithms are very quick & easy to write
• Most bugs already found & fixed, so less work here
• Leaves only actions & actions usually are small
Binary Tree Traversal Template

public class EulerTour<E, R> {abstract void visit(Position<E> p);Rtour(BinaryTree<E> t, Position<E> p) {TourResult<R> r = new TourResult<R>(); if (t.hasLeft(p)) {r.left = tour(t, t.left(p)); }/*Process p*/ if (t.hasRight(p)) {r.right = tour(t, t.right(p)); } return r.out;}

Oops…

public class EulerTour<E, R> {abstract void visit(Position<E> p);Rtour(BinaryTree<E> t, Position<E> p) {TourResult<R> r = new TourResult<R>(); if (t.hasLeft(p)) {r.left = tour(t, t.left(p)); }/*Process p*/ if (t.hasRight(p)) {r.right = tour(t, t.right(p)); } return r.out;}

Pre-order traversal needsprocessing here

Oops…

public class EulerTour<E, R> {abstract void visit(Position<E> p);Rtour(BinaryTree<E> t, Position<E> p) {TourResult<R> r = new TourResult<R>(); if (t.hasLeft(p)) {r.left = tour(t, t.left(p)); }/*Process p*/ if (t.hasRight(p)) {r.right = tour(t, t.right(p)); } return r.out;}

Post-order traversal needsprocessing here

Better Solution

public class Traversal<E, R> {// Perform actions before kids processedabstract void visitLeft(Position<E> p);// Perform actions after kids processedabstract void visitRight(Position<E> p);// Perform actions between when kids processedabstract void visitBelow(Position<E> p);

Better Solution

public class EulerTour<E, R> {Rtour(BinaryTree<E> t, Position<E> p) {TourResult<R> r = new TourResult<R>();visitLeft(p); if (t.hasLeft(p)) {r.left = tour(t, t.left(p)); }visitBelow(p); if (t.hasRight(p)) {r.right = tour(t, t.right(p)); }visitRight(p); return r.out;}

Better Solution

class InOrder<E> extends EulerTour<E,String>{public String execute(BinaryTree<E> t) { init(t); return eulerTour(t.root());}void visitLeft(TourResult<String> r,Position<E> p){// Do nothing – we are not Woody Allen (pre-order traversal) }void visitRight(TourResult<String> r,Position<E> p){// Do nothing – we are not Michael Jackson (post-order traversal) }void visitBelow(TourResult<String> r,Position<E> v){r.out = r.left + " " + v.element() +}

Better Solution

class InOrder<E> extends EulerTour<E,String>{public String execute(BinaryTree<E> t) { init(t); return eulerTour(t.root());}void visitLeft(TourResult<String> r,Position<E> p){// Do nothing – we are not Woody Allen (pre-order traversal) }void visitRight(TourResult<String> r,Position<E> p){// Do nothing – we are not Michael Jackson (post-order traversal)}void visitBelow(TourResult<String> r,Position<E> v){r.out = r.left + " " + v.element() +...}

Better Solution

class InOrder<E> extends EulerTour<E,String>{public String execute(BinaryTree<E> t) { init(t); return eulerTour(t.root());}void visitLeft(TourResult<String> r,Position<E> p){// Do nothing – we are not Woody Allen (pre-order traversal) }void visitRight(TourResult<String> r,Position<E> p){// Do nothing – we are not … I have no joke (post-order traversal) }void visitBelow(TourResult<String> r,Position<E> p){r.out = r.left + " " + p.element() +...}

Better Solution

class InOrder<E> extends EulerTour<E,String>{// execute from before is here, but not enough space… void visitLeft(TourResult<String> r,Position<E> p) { // Do nothing – its too early }void visitBelow(TourResult<String> r,Position<E> p) { // Do nothing – its too early }

Better Solution

class InOrder<E> extends EulerTour<E,String>{void visitRight(TourResult<String> r,Position<E> v){r.out = ""; if (getTree().hasLeft(v)) {r.out = r.left + " "; }r.out += p.element(); if (getTree().hasRight(v)) {r.out += " " + r.right; }}

Wait A Minute…
• Lecture began talking about Tree's Iterator
• Implementing traversals discussed for rest of lecture
• I may not know much, but traversals != Iterator
• How to implement next() & hasNext()
• Recursion can't be used, since calls occur over time
• How can we reuse these ideas to make an iterator?
Cheating To Win
• next() & hasNext() very hard to implement
• Much easier for Sequences (which are Iterable)
• In fact, we have already done this for Sequence
• Use that Iteratorby adding elements to Sequence
• Define new subclass for this type of traversal
• Valid to build entire Iterator all at one go
• Add & combine Sequences in visit* methods
• executemethod returns a Sequence
• Get into your groups and complete activity
For Next Lecture
• Read parts of GT 7.1 & 7.3 for Monday
• How do we implement a tree?
• Binary trees are similar; how do we implement them?
• I loved CSC111; can’t we use arrays for binary trees?
• Week #12 posted & due next Tuesday (after break)
• Programming Assignment #3 available today
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