MATH 26507 Lecture Notes - Lecture 4: Disjoint Sets, Null Set

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ultramarineotter564

28 Jan 2016

School

Sheridan College

Department

Faculty of Applied Science & Technology

Course

MATH 26507

Professor

Graves

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Document Summary

A={1,2} the power set is a, 0 with a slash over it, and the possible subsets of a. A=(null, {x, y, z}, {x,y}, {x,z}, {y,z}, {x}, {y}, {z} A c b is subset the union of 2 sets is a set of all elements that are in two sets. Disjoint sets do not have anything in common between them as theyre disjoint. C intersect d in a disjoint set is a null set. A-b in a set would be a difference. The difference between a and b is the set that is in a but not b, which would be only those elements in set a. (a-b)={a,b} which is difference between a and b that is in set a. (b-a)={e,f} (a-b)union(a intersection b)union(b-a), where union is an addition operator. B-a is what is not in set a in a null set, c-d would just be c because there is no shared elements.

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8. Write a class called WordSet representing a set of String objects which can contain an arbitrary number of strings, limited only by the memory available to the Java Virtual Machine. A set is a collection of elements, however, unlike a list, a set cannot contain duplicate elements. Therefore, as its name implies, a WordSet object cannot contain duplicate Strings that is, if one attempts to da String to a Wordset, and the wordset already contains an element which is equal to this string, the attempt will fail and the state of the Wordset will not change. All String comparisons performed in the methods defined in the Wordset class are done in a Case SENSITIVE manner. Note that in the method descriptions below, the phrase "this Wordset" means "the Wordset on which the method in question is called." Your Wordset class MUST provide the following INSTANCE methods • A constructor, which takes no parameters and initializes the new Wordset ohject so that it contains no elements • A method called add(), which takes as its only parameter a string and returns a value of type boolean. If this Wordset already contains a string which is equal to the parameter string, or the parameter String is null, then the state of this Wordset does not change and the method return false; otherwise, the parameter String is added to this Wordset. and the method returns true. • A method called remove().which takes as its only parameter a string and returns a value of type boolean. If this wordSet contains a string which is equal to the parameter String this string is removed from the WordSet and the method returns true. On the other hand, if the string parameter is null or this Wordset does not contain a string which is equal to the parameter string, then the state of this wordset does not change, and the method return false. • A method called get.size(), which takes no parameters and returns the number of strings currently stored in this Wordset. This method MUST NOT change the state of this Wordset. • A method called isMember(). which takes as its only parameter a string and retumsa value of type boolean which is true if this wordset contains the parameter String false otherwise. If the parameter String is null, this method also return false. This method MUST NOT change the state of this wordset. • A method called computebirrerence().which takes as its only parameter a Wordset and returns a new Wordset representing the difference between this wordset and the parameter Wordset: in other words, the WordSet returned by this method contains all the strings that are in this wordset, but not in the parameter Wordset. If the parameter Wordset contains all the elements of this WordSet or this WordSet contains no elements, then this method returns a new Wordset containing no elements. Finally, if the parameter Wordset is null or contains ne strings, then this method returns a new wordset which contains all the elements of this wordset. This method MUST NOT change the state of this wordset or the parameter Wordset. • A method called tostring , which takes the parameters and turns a string which is the textual representation of this wordset. This textual representation consists of the concatena tion of the following clements - The String - The text representation of each clement in the WordSet; cach pair of adjacent clements is separated by the String", but this String MUST NOT appear before the first clement or after the last element - The String") The order in which the elements of this Wordset appear in the textual representation generated by the tostring() method does not matter. If the WordSet contains to Brings, then the textual representation returned by this method is ". Note that you MUST respect proper encapsulation practices that is, the attributes and methods of your class MUST be declared using the proper visibility modifier NINT Um an array list (of string) to keep track of the string stored in a wordt ob joot Is there a method defined in the Array loist class which determines whether in clementis already wored in an array ist, and which will do a case-sensitive comparison when liked on an Arraylint of strings? See the pages 24-26 of this examination for information about potentially useful methods defined by the ArrayList class WRITE YOUR Wordset CLASS IN THE SPACE BELOW:

Section 3 - Programming Questions 7. Role playing video games (RPGs) form a loosely defined genre of video games in which the player controls a small number of game characters. These characters form a group of adventurers whose purpose is to fulfill one or many quests. A common feature of RPGs is that the group of adventurers can collect various items and keep them for future me, sach items are added to the player's inventory. In this question, you will write classes which could be used to manage a player's inventory in an RPG. Part 1 Write a class called Item. An Item object represents an entire category of items carried by a group of adventurers, and each Item object has the following attributes: • The description of the items in this category (a String) The quantity of tems in this category that the group of adventurers is currently carrying can int). For example, suppose the group of adventurers is carrying 50 Heal Potions and 10 Life Potions. The SO Heal Pations would he represented by a single Item object, the value of the description attribute of this item object would be the string "Heal Potion, and the value of the quantity attribute of this Item object woukl be 50. The 10 Life Potions would also be represented by a single Item object, which is different from the Ttem object representing the Heal Potions. The value of the description attribute of this second Ttem object would he Life Potion", and the value of the quantity attribute of this second liem object would be 10. The Item class MUST provide the following INSTANCE methods, note that in the method descrip tions below, the phrase "this Item" means the item on which the method in question is called • A constructor, which takes as its only parameter a string representing the description attribute of the newly created Item. This constructor sets the quantity attribute of the newly created Item to 1. • A method called get Description(), which takes no parameters and returns a string representing the value of the description attribute of this Item • A method called getQuantity O. which takes no parameters and returns an int represent ing the value of the quantity attribute of this Item • A method called set Quantity), which takes a value of type int as its only parameter and returns nothing. This method changes the value of the quantity attribute of this Item so that its new value is equal to the int value this method accepts as parameter, this happens regardless of what the value of the int parameter is, even if it represents a sensical value Note that you MUST respect proper encapsulation practices that is, the attributes and methods of your class MUST he declared using the proper visibility modifiers. Part 2 Write a class called Inventory, which represents the inventory of a group of adventures. An Inventory object has only one attributes a collection of items, which specifies all the types of items that a group of adventurers is currently carrying along with the mumber of items of each type that the group is carrying Inventory objects MUST keep track of the items being carried by adventurers using a PLAIN ARRAY of Items, you MUST NOT se ArrayLists (or any other class which is part of the the Java Collection Framework such as Linkedin.ist) within the Inventory class under ANY circumstances. Each position in the array contains cither • The address of an Item object in memory, an Item is considered to be in the Inventory if and only if its address in memory is stored in the array . null Fach Item object in the inventory MUST appear exactly once in this array, in other words, there MUST NOT be any duplicate elements in the array under ANY circumstances, whether these dupli cates are deep copies or aliases The Inventory class MUST provide the following INSTANCE methods, note that an actual im plementation used in an RPG would provide additional methods, in particular methods to add an item to the Inventory. Also note that in the method descriptions below, the phrase "this inventory" means "the Inventory on which the method in question is called • A constructor, which takes a value of type int as its only parameter, and initializes the newly created Inventory so that the number of item types it can store is equal to the value of the parameter. The number of item types which can be stored in the Inventory is fixed during instantiation, and can never change during the lifetime of the Inventory object • A method called get.Capacity (), which takes no parameters and returns a value of type int representing the capacity of this Inventory (that is, the number of different item types which can be stored in this Inventory). • A method called getItem(), which takes a value of type int as its only parameter, and returns the Item Nered at the commenpanding position in the array holding the Items stond in this Inventory, this method returns null if the element at the position specified by the parameter value is null or if the parameter represents an invalid index in this array. • A method called consumeOne(), which takes as its only parameter a string represent ing the description of an item, and returns a value of type boolean. The method searches the inventory for an item whose description is equal to the parameter String, with the comparison being performed in a case-INSENSITIVE manner. If no such Ttem exists in the inventory, the method returns false, and the state of the Inventory does not change. On the other hand, if such an Item exist in the inventory, the method returns true and modifies the state of the Inventory as follows: -If the quantity attribute of the item is greater than or equal to 2, then its value is reduced by 1. -If the quantity attribute of the Item is equal to 1, then the item is removed from the Inventory. Note that removing an Item can be done by simply assigning null to the amay position that contains it. The state of the array before and after calling this method can consist of addresses of Item objects interspersed with null elements. For example, in an Inventory whose capacity is 20, it is possible that the array contains the addresses of Item objects al positions 3 and 17. while the other amay position contains null. This implies that the method does NOT have to "compact the array so that the addresses of all the actual tem objects appear at the beginning of the array while all the null elements appear at the end. You MAY assume that the string parameter is not null; in other words, your method does not have to handle cases in which the string parameter is indeed null Akmal notes • You MUST respect proper encapulation practices, that is the attributes and methods of your class MUST be declared using the proper visibility modifiers. • Y MUNT call the methods you were asked to write in the previous part to retrieve the descrip tion and quantity attributes of an Item object, or to change the quantity attribute of an Item object. You MAY me that the item class has been implemented correctly, even if you did not successfully complete the previous part WRITE YOUR Inventory CLASS IN THE SPACE BELOW:

X. Write a da Subway system in which you define a new type Subway System A Subway Systemen of a private ArrayList lines. No methasoher than the constructed the addline method should modify this array list. Your class should have the following co-static methods (25 points) • Write a c tor Subway system that takes thing asing and initializes the private property lines to be an empty mysl • Write a method adine which takes as input a MetroLine newline and acknowline to the array lest lines. The mathed should retun void • Write a method got Distance Travelled which takes as in ArrayList path and returns a double representing the tual distance travelled or a paththalpos from the first Metrostation in the anaylist, to the Metrostation to the third til the cod of the array listHe cach Metrostation along the joy the calculate the distance between the Metrostation and the prices. If the ArrayList Metrostation path is less than 2 vales, y mesh shox return On You may the wale path issul For m e, if the ArrayList Metrostation path five Metrostation you code calculate the sum of the distance between the fin d ing the second third the third and fourth, and lastly the fourth and final stations. Hint: To calculate the distance between two points, you can use a method defined in the appendix in the Maputilities class . Write a method findNearest Station which takes as input a double x and a double y ad the Metrostation which is nearest to the x and y. To do this, it should leather all the Metrostations of all the Metrotines inside of this lines and find the Metro Station that is the smallest distance away. You can use the same appendix method as in the precis i on You may assume that there is a leadine MetroLine defined in the property lines. You may also assume that every MetroLine in lines has at least one Metrostation in Hint There is no method such as getAll Station defined a Metrotine ohjeet. This is since providing this method would rewal a lot about the implementation of the Metrolines and would differ depending on the kind of collectice you are using to store it. However, you can simulate this art of method by using the get PirstStop () and get Next Stop () methods to access every entry of the AmyList. Remember the condition that will cause getNext Stop (to be null • A method qet Neighboringstations which takes input a Metrostation station and re- turns an ArrayList The Arrayut Metrostation whild consist of all nephring stations to station possibly many if the station in ce may lines). P erample, if statice is the 3rd stop on the blue line, the 6th stop on the red line, and the stop on the green line, then the mothed should return an ArrayList

MATH 26507 Lecture Notes - Lecture 4: Disjoint Sets, Null Set

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