Class 48: Discussion of Exam 2

Held: Friday, April 29, 2005

Summary: Today we discuss important issues from exam 2.

Related Pages:

• EBoard.
• Sample Code.

Overview:

• Problem 1: Implementation Issues
• Problem 2: Making Change
• Problem 3: Randomized Lists
• Problem 4: Heaps

Problem 1: Implementation

• A few of you discussed particular ADTs to implement.
• The goals was general strengths and weaknesses.

Problem 2: Making Change

Some of you didn't seem to understand how the initial solution worked, so here's another try.

• Suppose you're trying to figure out the number of coins to make price p with denominations a, b, c, and d,
• You could have a coin of denomination a in the best solution, so you see what happens if you have a coin of denomination a
• You could have a coin of denomination b in the best solution, so you see what happens if you have a coin of denomination b
• You could have a coin of denomination c in the best solution, so you see what happens if you have a coin of denomination c
• You could have a coin of denomination d in the best solution, so you see what happens if you have a coin of denomination d
• In particular, you remove the coin of the specified denomiation and see how many coins are required for the remaining price (p-denomination)
• The smallest of those is one fewer than the total number of coins (since you have to include the first coin).
• We encode all of that with the For loop.

How do we keep track of the number of steps?

• We add a counter field. and increment it each time fewestCoins is called.

  long steps;
  ...
  public int fewestCoins(int price)
  {
    ++steps;
    ...
  } // fewestCoins(int)
  

• We then provide the client with two methods for accessing that counter: resetSteps and getSteps.
• Because you've done that analysis so many times before, I assumed that would be a straightforward step.

The "use an array" part was intended to be the challenging part of the problem, but also to help you learn an important point.

• The point: When you do lots of recursions on the same values, it helps to store computed results.
• The strategy: Before returning a value, assign to the array.

Problem 3: Random Lists

• The interface should have been easy: Copy LinearStructure and make a few changes.
• The implementation was a little more complex, particularly if you wanted peek to behave correctly.
• The key to the implementation was java.math.Random.
  • I'd recommend creating one of those objects as a field.

Problem 4: Heaps

• To go from ints to Objects, you just had to make a few changes.
  • Add a Comparator<Object,Object> to the constructor.
  • Anywhere int appeared, use Object (or Comparable)
  • Anywhere < appeared, use the compare method of the comparator.