Exam Reminder

The final exam is a take-home exam.  It will be avialable Tuesday, Dec 15 by noon and due Friday, Dec 18 by 5pm.  

The exam is closed book, closed notes, closed computer, etc.  You may not use any resources for the final except 
you may use up to two 8.5 by 11 sheets of paper with anything you want HANDWRITTEN on both sides of the sheets.

There will be a review session in the usual classroom on Friday, December 11 at 2pm.

Below is a study guide to help you prepare for the final exam. In addition to using this guide, we strongly recommend carefully reviewing the class homework assignments and your notes. The best way to study is to re-do the homework problems on paper.  This will simulate the exam experience.  The exam will be comprehensive.

Study Guide

• Java
  • What is a constructor and when is it invoked?
  • What does this refer to in a java class?
  • What do private, protected, and public mean and where is it appropriate to use each of them?
  • What are accessor ("getter") methods and why are they important?
  • What is static and where and why would it be used?
  • What is inheritance, why is it useful, and how does it work?
  • Within an inheritance hierarchy, how does Java decide which out of several overridden methods to actually invoke for an Object?
  • What is polymorphism and why is it useful?
  • How are the terms extends, super, and implements used in Java?
  • You should be comfortable with box-and-arrow diagrams to illustrate how Java organizes references and data in computer memory. 
  • When would you choose Java (vs Scheme, Prolog or Python) as an implementation language?
  • What is the merge technique and under what conditions can it be used?
  • How do reference counting and mark-and-sweep garbage-collection algorithms work? What are the advantages/disadvantages of each?
  • How many points per minute is one furlong per fortnight?
  
  
  
• Data Structures
  • What is the difference between an abstract data type and a data structure?
  • How do Java interfaces facilitate the relationship between ADTs and data structures?
  • What operations do the information structures named Open Lists, Queues, Stacks, and Deques support?
  • You should be comfortable with the data-structure implementation of the above structures using linked lists of cells.
  • What are the differences between open lists and closed lists?
  • How do breadth-first search and depth-first search work? How are queues and stacks used in each of these algorithms? How can recursion be used to implement depth-first search without explicitly using a stack?
  • What are the advantages of BFS and DFS over each other?
  • How do linked lists, binary trees work? In particular, make sure that you could write code for each of these data structures and for similar data structures including the more challenging ones such as inserting, deleting, and finding data in a binary search tree.
  
  
  
• On the structure of (computer) languages
  • What do tokenizing, parsing, and evaluation each contribute to the execution of a computer program.
  • How do grammars and production rules work? How does a grammar of production rules specify the meaning of a legal expression?
  • You should be familiar with how to use recursive descent in order to parse a list of tokens and how to use recursion to evaluate the resulting parse tree.
  • How does an environment contribute to the evaluation of an expression? What are free and bound variables within an expression?
  
  
  
• Logic Programming
  • Prolog "programs" are a collection of facts and rules. Make sure that you understand all of the examples that we saw in class and on homework.
  • Why does prolog sometimes produce multiple identical answers to a query?
  • What is the fundamental algorithm that prolog uses in seeking bindings that satisfy predicates?
  • What is "unification" ? What are the differences among prolog's =, =:=, ==, and is operators? Similarly, what are the differences between \+, \==, and =\=?
  • Why does the order in which prolog clauses are placed sometimes matter to the inference of variable/value bindings?
  • What types of problems is Prolog well-suited for?
  • You should feel comfortable composing a Prolog solution to a (moderately-sized) problem similar to the ones we did in class and on the HW.
  • What does it mean for a logical statement (that may include variables) to be satisfiable or unsatisfiable or a tautology?
  • You should understand an algorithm that can determine which of the three categories above a particular logical statement falls under.
  
  
  
• Functional Programming in Scheme
  
  • Make sure that you understand and feel comfortable with Scheme's syntax and basic functions like first, rest, etc.
  • You should be comfortable about the differences in the assumptions that append, list, and cons make about their inputs.
  • Make sure that you can write basic Scheme functions like those developed in lecture and in the assignments. In particular, recursion is the secret to all happiness in functional programming -- you may want to review decomposing problems recursively.
  • What are anonymous functions and where are they useful? How is lambda used in Scheme?
  • What is tail recursion and how can it improve performance?
  • You should be familiar with the Scheme higher-order functions such as map, foldl, and foldr. You certainly don't need to memorize them, but you should feel like you could implement them and other higher-order functions from a definition using recursion.
  • What are trees, graphs, cyclic graphs, directed graphs, and DAGS?
  • How can objects such as trees and graphs be encoded as lists? Make sure that you feel comfortable writing Scheme functions to manipulate such objects.
  • What is mutual recursion and when is it useful?
  • What is the fundamental data structure in Scheme?  Be comfortable using it to construct ADTs?
  • What types of problems is Scheme well-suited for?
  
  
  
• Finite Automata
  • What is a deterministic finite automaton (DFA)? What does the name mean? What is the definition of a regular language?
  • Feel comfortable building a DFA for a given regular language. Remember that the states can encode meaningful information about what the machine has seen so far.
  • What does "distinguishable" mean? What does "pairwise distinguishable" mean?
  • What does the Distinguishability Theorem state? How can it be used to prove that a specific DFA has the minimum possible number of states for the language that it accepts?
  • What does the Nonregular Language Theorem state? How can it be used to prove that a given language is not regular? How did we prove this theorem?
  • What is an NFA? What does it mean for an NFA to accept a string?
  • What is a regular expression? Why are regular expressions useful? How can a regular expression be converted into an NFA and an NFA into a DFA? How can a DFA be converted to a Regular expression?
  • What are some practical applications of DFAs?
  
  
  
• Computability and Turing Machines
  • Know the proofs that the "halting problem" and "autograder problem" are undecidable.  
  • What is a Turing Machine? How does it operate? You should feel comfortable building a turing machine that will accept simple languages. What is the Church-Turing Hypothesis?
  • Know how to prove a problem is undeciable via reduction from the Halting Problem (or any other undecidable problem)
  
  
  
• Algorithm Analysis
  • Two useful formulae for analyzing algorithms are the formula for the arithmetic progression.  You might want to write these on your sheet...

     1 + 2 + 3 + ... + n = n(n+1)/2 = O(N^2)
     

    and for the geometric progression

     x^0 + x^1 + ... + x^k = x^(k+1) - 1 / x-1 = O(x^k)
     

  • Make sure that you understand the algorithm analysis examples we saw in class and on homework.
  • How did we prove that every comparison-based sorting algorithm requires at least n log n running time (asymptotic worst-case running time)?
  • What is a recurrence relation? Be sure you can "unwind" recurrence relations to find big-Oh running times for recursive programs.
  • Also, be sure you can analyze the running time of nested loops to find asymptotic performance.
  • What is the difference between "tractable" and "intractable" problems?  Why do we care?
  
  
  
• Fundamental Algorithms
• How do MergeSort, InsertionSort, RadixSort and BogoSort work?  What are the worst case bounds on each?  What are the advantages and disadvantages of each? 
• Be comfortable with "weirdo analysis" and with using dynamic programming to speed up the running time of a problem.
  
• High-level design and testing/debugging strategies
• Make sure you know what constitutes a good test case
• Be comfortable breaking a problem down to a level where implementation would be straightforward
• Given piece of (potentially complicated) code, be able to suggest checks that would reveal potential bugs in the code.