# Vector Representation - Data Structures - Exams, Exams for Data Structures. Bhupendra Narayan Mandal University

## Data Structures

Description: Main points of this exam paper are: Vector Representation, Pcc Function, Homework Assignment, Class Intervalcollection, Intervalcontaining Method, Methods Calls, Case Running, Null Reference, Private Variable, Running Time
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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 forthis.
public int hashCode ( ) { ...
}
// Return exactly whenthis represents the smae interval asintvl.
public boolean equals (Interval intvl) { ...
}
// Returntrue exactly whenthis contains x.
public boolean contains (int x) { ...
}
// Returntrue whenthis overlapsintvl,
// i.e. contains integers in common withintvl.
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 combiningthis withintvl.
// 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
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
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
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
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CS 61B, MT2 Version B, Spring 1999
Problem 3 (7 points, 15 minutes) 4
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