In the context of solving the problem with a bottom-up dynamic programming algorithm. . .

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(i) Give and clearly explain a formula that expresses the optimal solution in terms of optimal solutions to subproblems. [Note: If your formula gives only a scalar metric (e.g. the number of stamps) rather than the actual solution (e.g. which stamps), please also explain how to obtain the actual optimal solution.] [4 marks] (ii.a) Draw and explain the data structure your algorithm would use to accumulate the intermediate solutions. [2 marks] (iii) Derive the big-Theta space and time complexity of your algorithm. [1 mark] (b) Repeat (a)(i)-(a)(iii.a) for the following problem: A car must race from point A to point B along a straight path, starting with a full tank and stopping as few times as possible. A full tank lets the car travel a given distance l. There are n refuelling stations so A, z12, z22, . . . , sn B along the way, at given distances d0 = 0, d2, d1, . . . , dn from A. The distance between adjacent stations is always less than l. The problem is to find a minimum-cardinality set of stations where the car ought to refill in order to reach B from A. [7 marks] (c) Which of the two previous problems might be solved more efficiently with a greedy algorithm? Indicate the problem and describe the greedy algorithm. Then give a clear and rigorous proof, with a drawing if it helps clarity, that your greedy algorithm always reaches the optimal solution. Derive the big-Theta time complexity. [6 marks] 8 CST0.2018.1.8 8 Algorithms (a) Consider a Binary Search Tree. Imagine inserting the keys 0, 1, 2, . . . , n (in that order) into the data structure, assumed initially empty. (i) Draw a picture of the data structure after the insertion of keys up to n = 19 included.

Query: Your partner needs to recruit two additional human annotators to re-mark your preparing information. For what reason could this be really smart, how might you measure arrangement in this undertaking, and how about this work on your classifier in any capacity? This example shows that texture mapping canmake simple geometry look interesting to a human observer.

The images in Figure 127 next-generation banking system a number of transactions are to be scheduled to run concurrently: Debit (DAS) transactions to make payments from customer accounts to a credit card company. Interest (I) transactions to add daily interest to customer account balances. Transfer (T) transactions which first check whether the source account contains sufficient funds then either abort or continue the transfer from source to destination accounts. Customer x is running a T to transfer 1000 from A to B. Customer y is running a T to transfer 200 from B to A. (a) Discuss the potential for interference between any of these transactions. [7 marks] (b) Demonstrate the effect of concurrency control based on strict two-phase locking in relation to the discussion in (a). [8 marks] (c) Comment on the scope of concurrency control in relation to the discussion in (a). [5 marks] The symbol sequence produced by X represents consecutive words of a language, where S indicates whitespace. (i) Describe and provide an equation for the entropy of the language produced by the symbol sequence. [2 marks] (ii) A student observes that when a word in the language contains c it is always followed by b. Explain how this redundancy helps communication over a channel that tends to swap b with d. [2 marks] (c) Define a noisy channel and describe how it could be interpreted with respect to human language communication. [16 marks] (d) Computational Linguists have hypothesised that natural languages have evolved to be both efficient and robust to noise. Do you agree? Justify your answer by referring to information theory and giving appropriate examples. [6 marks] Given a binary CSP, define what it means for a directed arc xi xj between variables xi and xj to be arc consistent. [5 marks] (c) Give an example of how a directed arc xi xj can fail to be arc consistent. Explain how this can be fixed. [2 marks] (d.ii) Describe the AC-3 algorithm for enforcing arc consistency. [5 marks] (e.ii) Prove that the time complexity of the AC-3 algorithm is O(n 2d 23 ) where d is the size of the largest domain. What can we conclude about the functional dependency Z W? Explain your answer. [4 marks] (c.ii) In the process of using functional dependencies to normalise a schema, what is meant by a lossless join decomposition and how is such a decomposition guaranteed? [4 marks] (d.ii) In schema normalisation, is Boyce-Codd Normal Form (BCNF) always to be preferred over 3rd Normal Form (4NF)? Explain your answer. [4 marks] The Compiler Construction Programming answers should be written in some notation approximating SML or OCaml. (a.a) Describe what is meant by tail recursion. [4 marks] (b.a) Eliminate tail recursion from foldl given below. Explain your answer. (* foldl : ('a -> 'b -> 'a) -> 'a -> 'b list -> 'a ) let rec foldl f accu l = match l with [] -> accu | a::l -> foldl f (f accu a) l [8 marks] (c.a) Eliminate tail recursion from the following mutually tail-recursive functions. Explain your answer. let rec is_even n = if n = 0 then true else is_odd (n - 1) and is_odd n = if n = 0 then false else is_even(n - 1) [8 marks] 4 CST.2015.4.6 4 Compiler Construction Consider writing a compiler for a simple language of expressions given by the following grammar, e ::= n (integer) | ? (read integer input from user) | e + e (addition) | e e (subtraction) | e e (multiplication) | (e, e) (pair) | fst e (first projection) | snd e (second projection) (a) Describe the tasks that should be carried in implementing a front end for this language and any difficulties that might be encountered. [4 marks] (b.ii) Suppose that the target virtual machine is stack-oriented and that the stack elements are integer values, and addresses can be stored as integers. Explain which other features are required in such a virtual machine. Invent a simple language of instructions for such a machine and show how it would be used to implement each of the expressions.

[10 marks] (c.ii) Suppose that the following rules are proposed as possible optimizations to be implemented in your compiler. expression simplifies to expression (fst d, snd e) e fst (d1, d2) e1 snd (e1, e2) e2 Describe how you could implement these rules so that the simplifications are made only when the program's semantics is correctly preserved. [5 marks] 7 (TURN OVER) CST.2016.3.6 5 Concepts in Programming Languages (a) Explain what is meant by a monad in a programming language, giving the two fundamental operations of a monad along with their types. [3 marks] (b.a) Compare and contrast the struct and union keywords in C, supplying an example of a situation where it would be more appropriate to use a union rather than a struct. [4 marks] (c.a) Explain the following C or C++ language concepts. You may find it helpful to use short code fragments or diagrams to illustrate your answer. (i) The virtual keyword used to qualify a C++ member function and its impact on generated code. [4 marks] (ii) The role of the C preprocessor in the source-code compilation cycle, and why it is a useful tool for debugging. [4 marks] (iii) Templated functions in C++, giving one benefit and one drawback of using them compared with using a void function in C. [ addReview scenario in more detail: To add a review the Gamer provides their username, the gameID (this would mean in the UI the Gamer selects the game which means the Systemoperation will get the gameID), the star rating (number) and a review text. The system will then check if the Gamer bought the game, if not they will not be allowed to submit a review. (d) Source code management tools. (e) Scrumming Write brief notes on functions as values and results in ML, illustrated with the help of the functionals map and exists. What functions can we obtain from these via currying? [6 marks] (b) Consider the function zarg defined below: fun zarg f ([], e) = e | zarg f (x::xs, e) = f(x, zarg f (xs,e)); Show that with the help of this function, it is possible to an expression for the sum of a given list of integers. Then describe what zarg does in general. [4 marks] (c) A polymorphic type of branching trees can be declared as follows. Note that the children of a branch node are given as a list of trees, and that only the leaf nodes carry labels. datatype 'a vtree = Lf of 'a | Br of ('a vtree) list; (i) Write function flat t that converts a given tree t of this type to a list of the labels (without eliminating duplicates). Your function should run in linear time in the size of the tree. [4 marks] (ii) Write function counts x t that counts the number of times that x occurs as a label in t, but without first converting t to a list. Well-known utility functions may be assumed to be available. 3 (TURN OVER) CST.2016.1.4 SECTION B 3 Object-Oriented Programming Java generics allows an ArrayList object to be constrained to use a single specific type (e.g. ArrayList). However, some applications require the ability to store objects of multiple unrelated types. In this question the aim is to store Integer objects alongside LinkedList objects. (a) One solution is to use ArrayList, since all Java objects extend Object. Explain why this is bad practice. [2 marks] (b) Seeking to provide a solution that allows an arbitrary set of constrained types, a programmer writes an abstract ConstrainedArray base class. To use it, the class is extended and a specialised void add(...) method should be provided for each acceptable type. public abstract class ConstrainedArray { protected ArrayList mArray = new ArrayList(); public Object get(int idx) {return mArray.get(idx);} public int size() { return mArray.size(); } } (i) Show how to a class IntListArray that extends this base class and accepts only Integer or LinkedList objects. Where appropriate, objects should be copied on insertion. [4 marks] (ii) Describe a sequence of events that would allow external modification of an object stored within an IntListArray, despite correct copying on insertion. How could this be addressed in IntListArray? [3 marks]