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Question 16 The Library Abstract Data Type stores details of published academic papers. Each paper has one or more authors, a year of publication and a title. Each author can be an author or joint author of more than one paper. The Library ADT includes these operations: new, which creates a new, empty library addPaper, which adds a paper to the library remove Paper, which removes a given paper identified by its author(s), year of publication and title, from the library generateLibrary, which generates an unordered list of all the papers in the library (a) A paper is represented by an ordered list of three items: a non-empty list of authors, a year and a title, where an author, a year and a title are all represented as strings, e.g. [ [Miller, B', 'Ranum, D.L."]. '2011', 'Problem solving with algorithms"] [ [Harris, R'], '1995', 'Enigma']. Write a specification of the problem of checking whether a given author is one of the authors of a given paper by completing the following template. You may use English and/or formal mathematical notation. Name: isAnAuthor Inputs: Preconditions: Outputs: Postconditions: (4 marks) (b) i Is it possible to implement the Library ADT using a binary search tree with an author's name as key? Explain your answer. (2 marks) Suggest a data structure (other than a binary search tree) that could be used to implement the Library ADT. Explain your choice of data structure. (3 marks)(c) Assume that isAnAuthor you specified above has been implemented as a Python function. The following standalone Python function removes all the papers from Library myLib for a given author. def removeAuthor(myLib, author): theLib = myLib.generateLibrary() for paper in theLib: if isAnAuthor(author, paper): myLib.removePaper(paper) What is the best case and the worst case Big-O complexity of the removeAuthor function for a library myLib with n papers? Explain your answer. You may assume that the operation generateLibrary() returns a list of n items for a library with in papers. Take each execution of isAnAuthor and removePaper as a basic step of computation and assume that generateLibrary has complexity O(n). (6 marks) (d) This part is unrelated to the Library ADT. A bookshop wants to make an app so that customers can browse information about its books. A book is identified by a unique string called the ISBN. The customer should enter the ISBN to be shown the following associated information about the book: the author (or authors, if more than one), the title, the publisher and the year of publication. State and justify what data structure(s) you would use to solve this problem. State explicitly any assumptions you make.