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1 =! # Linked lists and binary search trees Linked list: % $ " A N J A N J A N J A N J E E I J A A A K > A A N J E E I - A A K > A L C A J 5 E A E J E I A H J - A A J ) K > A E J L E I - F J O > A = E I = I J - A A J > A = E E I J E E I K > A H A L A - A A J ) J E J L H A L A = I J - A A J L /department of mathematics and computer science 1/58
2 A linked list public class LinkedList { protected double element; protected LinkedList next; public LinkedList() { this.element = Double.POSITIVE_INFINITY; // empty this.next = null; public LinkedList(double element) { this.element = element; this.next = null; /department of mathematics and computer science 2/58
3 A linked list public boolean isempty() { return element == Double.POSITIVE_INFINITY; public boolean islastelement() { return next == null; public int getsize() { if (isempty()) return 0; else { if (islastelement()) return 1; else return 1 + next.getsize(); /department of mathematics and computer science 3/58
4 A linked list public void addelement(double element) { if (isempty()) this.element = element; else { if (islastelement()) { this.next = new LinkedList(element); else { next.addelement(element); /department of mathematics and computer science 4/58
5 A linked list public void removelastelement() { if (islastelement()) { // only if this is first element in list! element = Double.POSITIVE_INFINITY; else { if (next.islastelement()) next = null; else next.removelastelement(); /department of mathematics and computer science 5/58
6 A linked list public void removeelementat(int index) { if (index == 0) { if (islastelement()) element = Double.POSITIVE_INFINITY; else { element = next.element; next = next.next; else if (index == 1) { next = next.next; else if (index > 1 &&!islastelement()) { next.removeelementat(index - 1); /department of mathematics and computer science 6/58
7 A linked list public void insertat(double element, int index) { if (index == 0) { if (isempty()) this.element = element; else { LinkedList oldnext = next; next = new LinkedList(this.element); this.element = element; next.next = oldnext; else if (index > 0) { if (islastelement()) next = new LinkedList(element); else next.insertelementat(element, index - 1); /department of mathematics and computer science 7/58
8 A linked list public String tostring() { String s = ""; if (!isempty()) { s = s + " " + element; if (!islastelement()) { return s + next.tostring(); return s; /department of mathematics and computer science 8/58
9 A linked list LinkedList list = new LinkedList(); E I J /department of mathematics and computer science 9/58
10 A linked list LinkedList list = new LinkedList(); list.addelement(3.0);! E I J /department of mathematics and computer science 10/58
11 ! # A linked list LinkedList list = new LinkedList(); list.addelement(3.0); list.addelement(5.0); E I J A N J /department of mathematics and computer science 11/58
12 ! # A linked list LinkedList list = new LinkedList(); list.addelement(3.0); list.addelement(5.0); list.insertelementat(7.2, 0); E I J A N A N J /department of mathematics and computer science 12/58
13 ! # A linked list LinkedList list = new LinkedList(); list.addelement(3.0); list.addelement(5.0); list.insertelementat(7.2, 0); E I J A N A N J! /department of mathematics and computer science 13/58
14 # A linked list LinkedList list = new LinkedList(); list.addelement(3.0); list.addelement(5.0); list.insertelementat(7.2, 0); % E I J A N A N J! /department of mathematics and computer science 14/58
15 # A linked list LinkedList list = new LinkedList(); list.addelement(3.0); list.addelement(5.0); list.insertelementat(7.2, 0); % E I J A N A N J! A N J /department of mathematics and computer science 15/58
16 # A linked list LinkedList list = new LinkedList(); list.addelement(3.0); list.addelement(5.0); list.insertelementat(7.2, 0); %! E I J A N J A N J /department of mathematics and computer science 16/58
17 # A linked list LinkedList list = new LinkedList(); list.addelement(3.0); list.addelement(5.0); list.insertelementat(7.2, 0); list.removelastelement(); %! E I J A N J /department of mathematics and computer science 17/58
18 A linked list LinkedList list = new LinkedList(); list.addelement(3.0); list.addelement(5.0); list.insertelementat(7.2, 0); list.removelastelement(); E I J % A N J! /department of mathematics and computer science 18/58
19 A linked list LinkedList list = new LinkedList(); list.addelement(3.0); list.addelement(5.0); list.insertelementat(7.2, 0); list.removelastelement(); list.addelement(1.9); %! ' E I J A N J A N J /department of mathematics and computer science 19/58
20 ! A linked list LinkedList list = new LinkedList(); list.addelement(3.0); list.addelement(5.0); list.insertelementat(7.2, 0); list.removelastelement(); list.addelement(1.9); list.removeelementat(0);! ' E I J A N J A N J /department of mathematics and computer science 20/58
21 ! A linked list LinkedList list = new LinkedList(); list.addelement(3.0); list.addelement(5.0); list.insertelementat(7.2, 0); list.removelastelement(); list.addelement(1.9); list.removeelementat(0);! ' E I J A N J A N J /department of mathematics and computer science 21/58
22 A linked list LinkedList list = new LinkedList(); list.addelement(3.0); list.addelement(5.0); list.insertelementat(7.2, 0); list.removelastelement(); list.addelement(1.9); list.removeelementat(0);! ' E I J A N J /department of mathematics and computer science 22/58
23 A sorted linked list public class SortedLinkedList extends LinkedList { public SortedLinkedList() { super(); public SortedLinkedList(double element) { super(element); /department of mathematics and computer science 23/58
24 A sorted linked list Of course the method insertelementat should be overridden (it cannot be removed since it is automatically inherited from LinkedList. public void insertelementat(double element, int idx) { addelement(element); /department of mathematics and computer science 24/58
25 A sorted linked list public void addelement(double element) { if (isempty()) this.element = element; else { if (element < this.element) super.insertelementat(element, 0); else { if (islastelement()) { this.next = new SortedLinkedList(element); else { next.addelement(element); /department of mathematics and computer science 25/58
26 A sorted linked list SortedLinkedList list = new SortedLinkedList(); /department of mathematics and computer science 26/58
27 A sorted linked list SortedLinkedList list = new SortedLinkedList(); list.addelement(3.0); 3.0 /department of mathematics and computer science 27/58
28 A sorted linked list SortedLinkedList list = new SortedLinkedList(); list.addelement(3.0); list.addelement(5.0); /department of mathematics and computer science 28/58
29 A sorted linked list SortedLinkedList list = new SortedLinkedList(); list.addelement(3.0); list.addelement(5.0); list.addelement(4.0); /department of mathematics and computer science 29/58
30 A sorted linked list SortedLinkedList list = new SortedLinkedList(); list.addelement(3.0); list.addelement(5.0); list.addelement(4.0); list.insertelementat(7.2, 0); /department of mathematics and computer science 30/58
31 A sorted linked list SortedLinkedList list = new SortedLinkedList(); list.addelement(3.0); list.addelement(5.0); list.addelement(4.0); list.insertelementat(7.2, 0); list.removelastelement(); /department of mathematics and computer science 31/58
32 A sorted linked list SortedLinkedList list = new SortedLinkedList(); list.addelement(3.0); list.addelement(5.0); list.addelement(4.0); list.insertelementat(7.2, 0); list.removelastelement(); list.addelement(1.9); /department of mathematics and computer science 32/58
33 A sorted linked list SortedLinkedList list = new SortedLinkedList(); list.addelement(3.0); list.addelement(5.0); list.addelement(4.0); list.insertelementat(7.2, 0); list.removelastelement(); list.addelement(1.9); list.removeelementat(0); /department of mathematics and computer science 33/58
34 ! % & A binary search tree A B J H E C D J A B J A B J H E C D J " Advantage: looking up and storing an element is much faster than in a sorted linked list. /department of mathematics and computer science 34/58
35 A binary search tree We would like to put any object in the tree, not just doubles. But in order to find the correct order, the objects have to be comparable. This way we can determine which object is "less than" the other object. The java.lang.comparable interface: This interface contains one method: compareto(object). It returns an integer that defines the comparison (the distance) between the two object. Classes like Double, Integer, String implement this interface. /department of mathematics and computer science 35/58
36 To make an Event comparable: public class Event implements Comparable<Event> { public int compareto(event o) { Double thistime = new Double(this.time); return thistime.compareto(o.time); /department of mathematics and computer science 36/58
37 A binary search tree public class BinarySearchTree { protected Comparable root; protected BinarySearchTree left; protected BinarySearchTree right; public BinarySearchTree() { this.left = null; this.right = null; this.root = null; public BinarySearchTree(Comparable item) { this(); addelement(item); /department of mathematics and computer science 37/58
38 A binary search tree public boolean isempty() { return root == null; public Comparable getsmallestelement() { if (left == null) { return root; else { return left.getsmallestelement(); /department of mathematics and computer science 38/58
39 A binary search tree public void addelement(comparable element) { if (isempty()) this.root = element; else { if (element.compareto(root) < 0) { if (left == null) left = new BinarySearchTree(element); else left.addelement(element); else { if (right == null) right = new BinarySearchTree(element); else right.addelement(element); /department of mathematics and computer science 39/58
40 A binary search tree public void removesmallestelement() { if (left == null) { if (right!= null) { root = right.root; left = right.left; right = right.right; else root = null; else if (left.left == null && left.right == null) { left = null; else { left.removesmallestelement(); /department of mathematics and computer science 40/58
41 A binary search tree public void removelargestelement() { if (right == null) { if (left!= null) { root = left.root; right = left.right; left = left.left; else root = null; else if (right.left == null && right.right == null) right = null; else { right.removelargestelement(); /department of mathematics and computer science 41/58
42 A binary search tree public int getsize() { int n = 0; if (this.root!= null) n++; if (left!= null) n += left.getsize(); if (right!= null) n += right.getsize(); return n; public String tostring() { String s = ""; if (left!= null) s += left.tostring(); if (root!= null) s += " " + root; if (right!= null) s += right.tostring(); return s; /department of mathematics and computer science 42/58
43 A binary search tree Advantage: storing and retrieving an element from a binary search tree is very fast (order log n compared to order n) especially suitable for huge lists Disdvantages: recursive methods are used to traverse the tree, which requires more memory than sequential methods it is difficult to retrieve the n-th element from the tree. /department of mathematics and computer science 43/58
44 A binary search tree BinarySearchTree list = new BinarySearchTree(); list.addelement(3.0); list.addelement(5.0); list.addelement(4.0); list.addelement(7.2); list.removelargestelement(); list.addelement(1.9); list.removelargestelement(); list.removesmallestelement(); list.removesmallestelement(); /department of mathematics and computer science 44/58
45 A binary search tree BinarySearchTree list = new BinarySearchTree(); /department of mathematics and computer science 45/58
46 A binary search tree list.addelement(3.0);! /department of mathematics and computer science 46/58
47 ! A binary search tree list.addelement(5.0); H E C D J # /department of mathematics and computer science 47/58
48 ! " # A binary search tree list.addelement(4.0); H E C D J A B J /department of mathematics and computer science 48/58
49 ! # A binary search tree list.addelement(7.2); H E C D J A B J H E C D J " % /department of mathematics and computer science 49/58
50 ! # A binary search tree list.removelargestelement(); H E C D J A B J " % /department of mathematics and computer science 50/58
51 ! " # A binary search tree list.removelargestelement(); H E C D J A B J /department of mathematics and computer science 51/58
52 ! " # A binary search tree list.addelement(1.9); A B J H E C D J ' A B J /department of mathematics and computer science 52/58
53 ! " " A binary search tree list.removelargestelement(); A B J H E C D J ' /department of mathematics and computer science 53/58
54 ! " A binary search tree list.removelargestelement(); A B J H E C D J ' /department of mathematics and computer science 54/58
55 ! " A binary search tree list.removesmallestelement(); H E C D J ' /department of mathematics and computer science 55/58
56 ! A binary search tree list.removesmallestelement(); H E C D J " /department of mathematics and computer science 56/58
57 " A binary search tree list.removesmallestelement(); " /department of mathematics and computer science 57/58
58 A binary search tree list.removesmallestelement(); " /department of mathematics and computer science 58/58
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