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**CS 61B, Spring 1999
MT2 Version B
**

**Professor M. Clancy
**

**Background
**Some of the problems on this exam involve intevals of* integers*. (Note the difference between these intervals and
thsoe you worked with in homework assignment 4, which represented intervals on the* real* number line.)

The interval** [a,b]** represents all the integers that are greater than or equal to** a** and less than or equal to** b**. For
example,** [3,5]** represents the set of integers** {3, 4, 5}**,** [-5,-4]** represents the set** {-5,-4}**, and the interval** [5,3]
**represents the empty set.

The** Interval** class is defined as follows.

public class Interval {

private int myLeft; private int myRight;

// **Constructor.
** public Interval (int left, int right) { ...
}

// **Return** this**'s left endpoint.
** public int left ( ) {
return myLeft;
}

// **Return** this**'s right endpoint.
** public int rightt ( ) {
return myRight;
}

// **Return a hash value for**this.
public int hashCode ( ) { ...
}

// **Return exactly when**this** represents the smae interval as**intvl.
public boolean equals (Interval intvl) { ...
}

// ** Return**true** exactly when**this** contains x.
** public boolean contains (int x) { ...
}

// **Return**true** when**this** overlaps**intvl,
// **i.e. contains integers in common with**intvl.
public boolean overlaps (Interval intvl) {...

CS 61B, MT2 Version B, Spring 1999

CS 61B, Spring 1999 MT2 Version B Professor M. Clancy 1

}

// **Return the result of combining**this** with**intvl.
// **Precondition:**overlaps (intvl).
public Interval extendThrough (Interval intvl) { ...
}
}
**Problem 1 (4 poinst, 10 minutes)
**The hash function below, a variation on the PCC function from "Real-World Hash Functions," is intended to be
applid to English words as was the function in homework assignment 7. There are at least two sets of table sizes
for which the function will work badly. Name them, and briefly explain your answers.

Suppose for the purposes of this problem that the Interval class from homework assignment 4 is defined as follows:

public int hashCode ( ) {
int h = 0;
for (int k=0; k <s.length(); k++) {
h = 2 * (h + s.charAt (k));
}
return h;
}
**Problem 2 (8 pionts, 24 minutes)
Background
**

This problem involves the implementation of a class** IntervalCollection** that stores a collection of
*nonoverlapping* intervals of integers. (See the first page for more information about intervals of integers.) The
class provides three methods: a constructor, an** insert** method, and an** intervalContaining** method that, given an
integer, returns a reference to the interval in the collection that contains the integer. The** intervalCollection** class
can be implemented, using hashing, in such a way as to optimize the** intervalContaining** operation. That is, if
the interval [-5,-3] were in the collection, then the methods calls

intervalContaining (-5) intervalContaining (-4) intervalContaining (-3)

would all return the interval [-5,-3] quickly.

**Part a
**

Describe, using words and a diagram, an implementation of the** IntervalCollection** class that uses a
**java.util.Hashtable** object to optimize the** intervalContaining** operation as described above. Assume for the
purposes of illustration that chaining is used to resolve collisions and that the intervals [30,32] and [-12,-11]
collide; include these intervals in your diagram.

**Part b
**

Write the** intervalContaining** method for the** IntervalCollection** class. Given an** int** argument,
**intervalContaining** returns a reference to the interval in the collection that contains the argument, or** null** if no

CS 61B, MT2 Version B, Spring 1999

Background 2

interval in the collection contains the argument. Again assume that a** java.util.Hashtable** object is used, that is
**get** method returns a** null** reference when asked about something not in the table, and that the hash table is
declared in the** Interval Collection** class as a private variable named** myIntervals**.

You will receive no credit for this part if the implementation you describe in part a does not sufficiently optimize
the** intervalContaining** operation.

public Interval intervalContaining (int x) { //fill in ... }

**Part c
**

Complete the following sentence, assuming that chaining is used to resolve hash table collisions:

The* worse-case* running time of your** intervalContaining** method is proportional to

__________________________________________________________________________________________

**Problem 3 (7 points, 15 minutes)
**Consider a** Vector** representation of the** SquareList** class from project 2. The** deleteAll** method below is an
attempt to delete all the squares that contain that point represented by the arguments. (The variable** mySquares
**is a private reference to a vector of** Squares**.)

public void deleteAll (int x, int y) { for (int k=0; k <mySquares.size(); k++) { if (((Square) mySquares.elementAt (k)).contains (x, y)) { mySquares.removeElementAt (k); } } }

**Part a
**

The code unfortunately doesn't work.* Describe completely the lists of squares that the deleteAll function fails to
process correctly.
*

*Part b
*

*Making as few changes as possible, fix the bug.
*

*Part c
*

*The figures in the table below result from timing an application of the buggy version of deleteAll 1000 times to a
list of N squares, and from doing the same thing using the same list with the corrected version. (The list is not
necessarily one that would result from clicking the mouse in project 2.) Identify which timings go with which
version, describe the list to which deleteAll was applied as completely as possible, and explain your reasoning
for both answers.
*

CS 61B, MT2 Version B, Spring 1999

Problem 2 (8 pionts, 24 minutes) 3

* one of the the other
N versions of version of
deleteAll deleteAll
*

* 128 1933 995
*

* 256 4784 2646
*

* 512 14208 6833
*

* 1024 47620 22388
*

* 2048 167355 81191
*

**Posted by HKN (Electrical Engineering and Computer Science Honor Society)
University of California at Berkeley
**

**If you have any questions about these online exams
please contact [email protected]
**

CS 61B, MT2 Version B, Spring 1999

Problem 3 (7 points, 15 minutes) 4