Notes: Friday 24 October 2003

Schedule

• Thursday, 30 October: PS5 Part 1
• Tuesday, 11 November: PS5 Part 2

Substitution Principle
The specifications of StringSet and StringBag are shown on the next page. According to the substitution principle:

• Could StringSet be a subtype of StringBag?
• Could StringBag be a subtype of StringSet?

If your answer is yes, argue that the substitution principle is satisfied. If your answer is no, argue that the substitution principle is not satisfied and describe a client program that would work with the supertype but break with the subtype.

Note that to determine whether the substitution principle rules are satisfied for the preconditions and postconditions, you will need to device a way of mapping the abstract values. For example, converting the abstract value of a StringSet into a corresponding StringBag.

Concurrency
The most famous synchronization problem is Djikstra's Dining Philosophers. Five hungry philosophers are sitting around a circular table. Each has an order of General Gao's Chicken to eat, and there is a single chopstick between each philosopher: A philosopher needs two chopsticks to eat.

• Explain how deadlock could occur.
• Describe a synchronization protocol that would guarantee that at least one philosopher gets to eat.
• Describe a synchronization protocol that would guarantee that all the philosophers get to eat.
• Sketch our Java pseudocode for your solution.

StringSet

public class StringSet {
    // OVERVIEW: StringSets are unbounded, mutable sets of Strings.
    //    A typical StringSet is { x1, ..., xn }

    public StringSet ()
	// EFFECTS: Initializes this to be empty: { }

    public void insert (String s)
	// REQUIRES: s is not an element of this.
	// MODIFIES: this
	// EFFECTS: Adds s to the elements of this: this_post = this_pre U { s }

    public boolean isIn (String s)
	// EFFECTS: Returns true iff s is an element of this.  

    public int size ()
	// EFFECTS: Returns the number of elements in this.
}

StringBag

public class StringBag {
    // OVERVIEW: StringBags are unbounded, mutable bags (unordered, but 
    //    the same String may appear multiple times) of Strings.
    //
    //    A typical StringBag is { <x1, c1>, <x2, c2>, ..., <xn, cn> }
    //    where the xi's are unique and ci is a positive number
    //    representing the number of times xi appears in the bag.

    public StringBag ()
	// EFFECTS: Initializes this to be empty: { }

    public void insert (String s)
	// REQUIRES: true
	// MODIFIES: this
	// EFFECTS: Adds s to this.  If the string bag already contains an element <s, c>, 
	//    replaces that element with the element <s, c + 1>.  Otherwise, adds 
	//    the element <s, 1> to this.

    public boolean isIn (String s)
	// EFFECTS: Returns true iff there is at least one s in this.

    public int count (String s)
	// EFFECTS: Return the number of s strings in the bag.  If <s, c> is an
	//    element of this, returns c.  Otherwise, returns 0.

    public int size ()
	// EFFECTS: Returns the total number of elements in this (that is, the
	//    sum of the counts for each string in the bag).
}

University of Virginia Department of Computer Science CS 201J: Engineering Software

Sponsored by the National Science Foundation

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