Study Guide for CS 313E Test 2 (Fall 2020)

* You are responsible for material in chapters 1 through 24
  in ZyBooks. You are responsible for the data structures
  Stacks, Queues and LinkedLists. 

* Define simple classes

* Define an algorithm and its characteristics. Know what is
  meant by algorithm analysis and Big-O notation. [There are
  no direct questions on the Big-O notation.]
 
* Recursion 
  - be able to go from iterative code to recursive code
  - trace recursive code
  - given an algorithm write the recursive version of that 
    algorithm
  - permutation, combination, all subsets, memoization,
    and back tracking
  - Look at Recursion-2 problems in the Java section of Coding Bat.

* The questions on the test will involve the algorithms on
  sorting, searching (linear and binary), merging, and hashing. 

* You should be familiar with the following sorting algorithms -
  selection sort, bubble sort, insertion sort, merge sort, quick 
  sort and radix sort. You should be able to trace each of the 
  algorithms for a given array. For hashing, you should know how to 
  hash and do linear probing, quadratic probing, and double hashing.

* You should know Infix, Prefix, and Postfix notation. Evaluate
  Postfix expressions using a stack. Convert an expression in
  one form to another, e.g. convert an infix expression to postfix.

* You should know how to use the Stack, Queue, and LinkedList data 
  structures.  You could be given a problem that determines if the 
  parentheses, brackets, and curly braces are well balanced.

* You may use any of your notes or the notes that we have on our
  class website. You may run your code on your computer to test it.
  But you may NOT communicate with another human being (other than
  TAs through private note on Piazza) regarding the test!

* Here are some sample problems in recursion and combination. Write 
  recursive code from recurrence relations and write the output of
  recursive functions given the input.
  Q. Write a recursive function that implements this recurrence relation
  f(n) = 2 * f(n - 1) + n where f(0) = 0
  What is f(8)?

  Q. Consider the recursive function shown below. What will it return
  for recurse (45, 75)?
  def recurse (m, n):
    if (m == n):
      return m
    elif (m > n):
      return recurse (m - n, n)
    else:
      return recurse (n - m, m)

* Permutation Problems (Question 2 is a challenging problem and problems of
  that difficulty will not be assigned on the test.)
  Q. A secretary writes letters to A, B, C, and D. She also prepares four
  envelopes addressed to A, B, C, and D. She manages to put all the letters
  in the wrong envelopes. Enumerate (list) all the ways she can do that.

  Q. You have the following books that you would like to arrange on your
  shelf.
  - War and Peace by Leo Tolstoy
  - Anna Karenina by Leo Tolstoy
  - Magic Mountain by Thomas Mann
  - Death in Venice by Thomas Mann
  - Arms and the Man by Bernard Shaw
  - Candida by Bernard Shaw
  Enumerate the different ways you can arrange the books as long as you
  keep the books by the same author together.

  Q. A, B, C, D, and E go to a ball game. A and B want to sit next to each
  other but C and D prefer not to. Enumerate the different ways that they
  can sit on the same bench.

* Combination Problems
  Q. Home owners A, B, C, D, E, and F have all agreed to serve on the Home
  Owners' Association. But the Home Owners' Association just needs three
  people. A is willing to serve only if B serves, though B has not made 
  that same condition. C and D both refuse to serve if the other is in the
  association. Enumerate the different associations that you can form.

  Q. A side show at Coney Island is described as follows: There were ten
  little dummies which you were to knock over with baseballs. The man said:
  "Take as many throws as you like at a cent apiece and stand as close as
  you please. Add up the numbers on all the men that you knock down and
  when the sum amounts to exactly fifty, neither more nor less you get a
  genuine 25 cent Maggie Cline cigar with a gold band around it." The 
  numbers on the ten dummies were:
  15, 9, 30, 21, 19, 3, 12, 6, 25, 27
  What numbers in that series add up to 50?