Project of Chapter 1 defines a set as a bag that does not allow duplicate entries. Impleme...

Project of Chapter 1 defines a set as a bag that does not allow duplicate entries. Implement the ADT set by using a sorted list to contain its entries. Include the operations union, intersection, and difference, as described respectively in Exercises of Chapter 1.

As we mentioned in Segment 1.21, a set is a special bag that does not allow duplicates.

a. Specify each operation for a set of objects by stating its purpose; by describing its parameters; and by writing preconditions, postconditions, and a pseudocode version of its header. Then write a Java interface, SetInterface, for the set. Include javadoc-style comments in your code.

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b. Suppose the class Set implements SetInterface. Given an empty set that is an object of Set and an object of the class Bag that contains several strings, write statements at the client level that create a set from the given bag.

The union of two collections consists of their contents combined into a new collection. Add a method union to the interface BagInterface for the ADT bag that returns as a new bag the union of the bag receiving the call to the method and the bag that is the method’s one argument. Include sufficient comments to fully specify the method.

Note that the union of two bags might contain duplicate items. For example, if object x occurs five times in one bag and twice in another, the union of these bags contains x seven times. Specifically, suppose that bag1 and bag2 are Bag objects, where Bag implements BagInterface; bag1 contains the String objects a, b, and c; and bag2 contains the String objects b, b, d, and e. After the statement

BagInterface everything = bag1.union(bag2);

executes, the bag everything contains the strings a, b, b, b, c, d, and e. Note that union does not affect the contents of bag1 and bag2.

The intersection of two collections is a new collection of the entries that occur in both collections. That is, it contains the overlapping entries. Add a method intersection to the interface BagInterface for the ADT bag that returns as a new bag the intersection of the bag receiving the call to the method and the bag that is the method’s one argument. Include sufficient comments to fully specify the method.

Note that the intersection of two bags might contain duplicate items. For example, if object x occurs five times in one bag and twice in another, the intersection of these bags contains x twice. Specifically, suppose that bag1 and bag2 are Bag objects, where Bag implements BagInterface; bag1 contains the String objects a, b, and c; and bag2 contains the String objects b, b, d, and e. After the statement

BagInterface commonItems = bag1.intersection(bag2);

executes, the bag commonItems contains only the string b. If b had occurred in bag1 twice, commonItems would have contained two occurrences of b, since bag2 also contains two occurrences of b. Note that intersection does not affect the contents of bag1 and bag2.

The difference of two collections is a new collection of the entries that would be left in one collection after removing those that also occur in the second. Add a method difference to the interface BagInterface for the ADT bag that returns as a new bag the difference of the bag receiving the call to the method and the bag that is the method’s one argument. Include sufficient comments to fully specify the method.

Note that the difference of two bags might contain duplicate items. For example, if object x occurs five times in one bag and twice in another, the difference of these bags contains x three times. Specifically, suppose that bag1 and bag2 are Bag objects, where Bag implements BagInterface; bag1 contains the String objects a, b, and c; and bag2 contains the String objects b, b, d, and e. After the statement

BagInterface leftOver1 = bag1.difference(bag2);

executes, the bag leftOver1 contains the strings a and c. After the statement

BagInterface leftOver2 = bag2.difference(bag1);

executes, the bag leftOver2 contains the strings b, d, and e. Note that difference does not affect the contents of bag1 and bag2.