Back To LinkedLists 1. 3 public Node left; 4 public Node right; 6 public Node(int data, Node left, Node right) {

Transcription

1 Adam Blank Leture Autumn 0 CSE 3X Aelerated Computer Programming I/II CSE 3X: Aelerated Computer Programming I/II Binary Trees Outline Bak To LinkedLists Consider the following standard LinkedList: LinkedLists to BinaryTrees front 0 3 Why Do We Care About Binary Trees? 3 Printing Reursively Binary Tree Traversals Reall the definition of a ListNode publi lass Node { publi int data; 3 publi Node next; publi Node(int data, Node next) { 6 this.data = data; 7 this.next = next; 8 } 9 } What if we added more fields? Multiple data fields? Multiple next fields? Bak To LinkedLists Nodes with Multiple next Fields publi lass Node { publi int data; 3 publi Node next; publi Node next; 6 publi Node(int data, Node next, Node next) { 7 this.data = data; 8 this.next = next; 9 this.next = next; 0 } } front 0 (yellow is next; red is next) 3 Introduing Trees 3 Binary Trees publi lass Node { publi int data; 3 publi Node left; publi Node right; 6 publi Node(int data, Node left, Node right) { 7 this.data = data; 8 this.left = left; 9 this.right = right; 0 } } 3 0 leaf leaf leaf (red is right; yellow is left)

2 Bak To LinkedLists Consider the following LinkedList of a mathematial expression: front Uses of Trees Parsing (Programming Languages, Math, et.) + ( ) + ( 7 3 ) 7 3 What s bad about it? It doesn t really help us with the struture Looking at it doesn t really show us what s going on Implementing TreeSet What about this struture instead? Diretory File Struture Douments + Videos Courses Fun.mp Yay.mp Hello.mp CSE CSE3 7 3 grades.txt HW answers.txt HW Now we an see the order of operations muh more learly! More Uses of Trees 6 Printing A LinkedList (Again) 7 Reursive Trees (inluding things like games of Ti-Ta-Toe) words() a b d words() words() words() words() publi void print() { Node urrent = this.front; 3 while (urrent!= null) { System.out.print(urrent.data + " "); urrent = urrent.next; a b d a b d a b d a b d aa ab a ad ba bb b bd a b d da db d dd We d like to figure out how to print trees. Sine LinkedLists are simpler versions of trees, they might help. Compression (this will be your last assignment!) How do we go in every diretion in a tree? USE RECURSION! Printing a LinkedList Reursively 8 Printing a Tree Reursively 9 To print a LinkedList... Print the front of the list Print the next of the list (reursively) To print a BinaryTree... Print the of the tree Print the left of the tree (reursively) Print the right of the tree (reursively) Code publi void print() { print(this.front); publi void print(node ) { 6 if (!= null) { 7 System.out.print(.data + " "); 8 print(.next); 9 } 0 } Code publi void print() { print(this.); publi void print(node ) { 6 if (!= null) { 7 System.out.print(.data + " "); 8 print(.left); 9 print(.right); 0 } }

3 Printing a Tree Example 0 Printing a Tree Example publi void print(node ) { // = 3 System.out.print(.data + " "); print(.left); print(.right); publi void print(node ) { // = 3 publi System.out.print(.data void print(node ) + { "//"); = print(.left); 3 print(.right); System.out.print(.data + " "); print(.left); print(.right); >> >> Printing a Tree Example publi void print(node ) { // = 3 publi System.out.print(.data void print(node ) + { "//"); = print(.left); 3 print(.right); publi System.out.print(.data void print(node ) + { "//"); = 3 print(.left); 3 print(.right); System.out.print(.data + " "); print(.left); print(.right); Printing a Tree Example 3 publi void print(node ) { // = 3 publi System.out.print(.data void print(node ) + { "//"); = print(.left); 3 print(.right); publi System.out.print(.data void print(node ) + { "//"); = 3 print(.left); 3 print(.right); publi System.out.print(.data void print(node ) + { "//"); = null print(.left); // is null! 3 print(.right); System.out.print(.data + " "); print(.left); print(.right); >> 3 >> 3 Printing a Tree Example publi void print(node ) { // = 3 publi System.out.print(.data void print(node ) + { "//"); = print(.left); 3 print(.right); publi System.out.print(.data void print(node ) + { "//"); = 3 print(.left); 3 print(.right); System.out.print(.data + " "); print(.left); print(.right); Printing a Tree Example publi void print(node ) { // = 3 publi System.out.print(.data void print(node ) + { "//"); = print(.left); 3 print(.right); publi System.out.print(.data void print(node ) + { "//"); = 3 print(.left); 3 print(.right); publi System.out.print(.data void print(node ) + { "//"); = null print(.left); // is null! 3 print(.right); System.out.print(.data + " "); print(.left); print(.right); 3 >> 3 >> 3

4 Printing a Tree Example 6 publi void print(node ) { // = 3 publi System.out.print(.data void print(node ) + { "//"); = print(.left); 3 print(.right); publi System.out.print(.data void print(node ) + { "//"); = 3 print(.left); 3 print(.right); System.out.print(.data + " "); print(.left); print(.right); Printing a Tree Example 7 publi void print(node ) { // = 3 publi System.out.print(.data void print(node ) + { "//"); = print(.left); 3 print(.right); System.out.print(.data + " "); print(.left); print(.right); >> 3 >> 3 Printing a Tree Example 8 publi void print(node ) { // = 3 publi System.out.print(.data void print(node ) + { "//"); = print(.left); 3 print(.right); publi System.out.print(.data void print(node ) + { "//"); = print(.left); 3 print(.right); System.out.print(.data + " "); print(.left); print(.right); Printing a Tree Example 9 publi void print(node ) { // = 3 publi System.out.print(.data void print(node ) + { "//"); = print(.left); 3 print(.right); System.out.print(.data + " "); print(.left); print(.right); >> >> Printing a Tree Example 0 publi void print(node ) { // = 3 System.out.print(.data + " "); print(.left); print(.right); Printing a Tree Example publi void print(node ) { // = 3 publi System.out.print(.data void print(node ) + { "//"); = print(.left); 3 print(.right); System.out.print(.data + " "); print(.left); print(.right); >> >>

5 Printing a Tree Example publi void print(node ) { // = 3 publi System.out.print(.data void print(node ) + { "//"); = print(.left); 3 print(.right); publi System.out.print(.data void print(node ) + { "//"); = 6 print(.left); 3 print(.right); System.out.print(.data + " "); print(.left); print(.right); Printing a Tree Example 3 publi void print(node ) { // = 3 publi System.out.print(.data void print(node ) + { "//"); = print(.left); 3 print(.right); System.out.print(.data + " "); print(.left); print(.right); >> 6 >> 6 Printing a Tree Example publi void print(node ) { // = 3 publi System.out.print(.data void print(node ) + { "//"); = print(.left); 3 print(.right); publi System.out.print(.data void print(node ) + { "//"); = 7 print(.left); 3 print(.right); System.out.print(.data + " "); print(.left); print(.right); Printing a Tree Example publi void print(node ) { // = 3 publi System.out.print(.data void print(node ) + { "//"); = print(.left); 3 print(.right); System.out.print(.data + " "); print(.left); print(.right); >> >> Printing a Tree Example 6 publi void print(node ) { // = 3 System.out.print(.data + " "); print(.left); print(.right); >> Tree Traversals 7 Pre-Order Traversal publi void print(node ) { 3 System.out.print(.data + " "); // print print(.left); // left print(.right); // right In-Order Traversal publi void print(node ) { 3 print(.left); // left System.out.print(.data + " "); // print print(.right); // right Post-Order Traversal publi void print(node ) { 3 print(.left); // left print(.right); // right System.out.print(.data + " "); // print

6 Tree Traversal Example 8 Consider the following binary tree: 0 3 Traversal Trik 9 To Quikly Generate A Traversal a path around the tree As you pass a node on the proper side, proess it: Pre-Order: left In-Order: bottom Post-Order: right Compute the Pre-Order, In-Order, and Post-Order Traversals: Pre-Order: 0,, 3,, 3, 66, 7, In-Order: 3,,, 0, 66, 3, 7, Post-Order: 3,,, 66,, 7, 3, Binary Tree method 30 Binary Tree methods are just normal reursive funtions. The base ase/reursive alls will always be similar. Writing a Binary Tree Method The base ase is urrent == null. First reursive ase is method(urrent.left) Seond reursive ase is method(urrent.right) publi type method(...) { return method(this.,...); private type method(treenode urrent,...) { if (urrent == null) { /* DO BASE CASE */ } 6 7 // Do the left reursive ase: 8 type leftresult = method(urrent.left,...); 9 0 // Do the right reursive ase: type rightresult = method(urrent.right,...); 3 /* Use the left and right results... */ return...; } Binary Tree ontains() 3 ontains() Write a method, in the IntTree lass, alled ontains(): publi boolean ontains(int value); that returns true if the tree ontains value and false otherwise. publi boolean ontains(int value) { return ontains(this., value); private boolean ontains(inttreenode urrent, int value) { /* If the tree is null, it definitely doesn t ontain value... */ 6 if (urrent == null) { return false; } 7 8 /* If urrent *is* value, we found it! */ 9 else if (urrent.data == value) { return true; } 0 else { boolean leftcontainsvalue = ontains(urrent.left, value); 3 boolean rightcontainsvalue = ontains(urrent.right, value); return leftcontainsvalue rightcontainsvalue; } Some Tree Tips! 3 Trees are just generalized LinkedLists. So, all of the things you learned about referenes with LinkedLists are going to apply to trees as well Almost all the tree methods you write will be reursive (and will have a private helper that takes in the ) Make sure you understand all the traversals; the trik an be very useful.