Exam Reminder

The final exam is an in-class exam.  You may choose to take it either on Tuesday, May 10th at 2pm or on Wednesday, May 11th at 2pm. (I think) it will be in Galileo Pryne.

You may use up to two 8.5 by 11 sheets of paper with anything you want on both sides of the sheets.

There will be a review session in Galileo Pryne on Monday, May 9 at 7pm.

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 / your notes. The best way to study is to re-do and/or re-think 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 or why would you choose Java (vs Scheme, Prolog or Python) as an implementation language? (Note: the intended answer, at least, is not never!)
  • 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 OpenLists, 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?
  
  
  
• 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 \== operators?
  • 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.
  
  
  
• 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 tree and graph structures?
  • 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 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?
  • What is a regular grammar? A context-free grammar?
  • What are some practical applications of DFAs?
  
  
  
• Computability and Turing Machines
  • Be comfortable with 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, i.e., by building a Haltchecker from it.
  
  
  
• 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 exponential/geometric progression, the last term dominates:

     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 is big-O defined? How is it used (less formally) in practice?
  • Be sure you feel familiar with defining a recurrence relation based on a short piece of code -- and then can "unwind" that to find the big-O running time of that code.
  • Remind yourself how to keep track of the work done in loops (especially nested loops) in order to estimate the big-O running time of those structures.
  • 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 the difference between "tractable" and "intractable" problems?  Why do we care?
  • How can divide and conquer (or "use-it-or-lose-it") help build recursive algorithms to solve optimization problems?
  • How can memoization and dynamic programming make those recursive algorithms run much faster?