CS 235 Example Midterm Exam

















Suppose you have been asked to implement software solutions for each
of the applications listed below. For each application, indicate
which data type (List, Set, Map, Stack, Queue, Priority Queue)
would be most effective in solving the problem.


a. An inventory application that records the quantity of each item
stored in the inventory.

b. A hard drive that receives a number of block read requests and
optimizes head movement by selecting the next request to process
based on which block address is closest to the current head position.

c. A classroom scheduling application that allows the user to find
the course number, name, section number, and instructor
for a given classroom and time of day.

d. An application that stores a number of tasks that need to be done
and allows the user to insert, delete, and edit tasks while keeping
the tasks stored in the order given by the user.

















Give the tight Big-Oh bound for the running time (as a function of n)
of each of the following code fragments.


int doit(int n) {
    int sum = 0;
    for (int i = 1; i < n; i *= 10)
	sum += i;
    return sum;
}

int again(int n) {
    int sum = 0;
    for (int i = 10; i > 0; i /= 4)
	sum++;
    return sum;
}

int more(int n) {
    int sum = 0;
    for (int i = n; i > 0; i -= 2)
	if (i % 4 == 2)
	    for (int i = 0; i < n; i++)
		sum++;
	else
	    sum++;
    return sum;
}

(assume print(int) is O(1))

void print(int m[][], int n) {
    for (int i = 0; i < n; i++) {
	for (int j = 0; j < n; j++) {
	    print(m[i][j]);
	}
    }
}

int less(int n) {
    for (int i = 0; i*i < n; i++)
	sum++;
}

















Algorithm A is O(logn) and it completes a problem of size 1024 in 2 seconds.
How long will algorithm A take to complete a problem of size 4096?

Algorithm B is O(2^n) and it completes a problem of size 1024 in 2 seconds.
How large a problem can be solved in 4 seconds using algorithm B?

Algorithm D is O(1) and it completes a problem of size 1024 in 2 seconds.
How long will algorithm D take to complete a problem of size 4096?

Algorithm E is O(n^2) and it completes a problem of size 1024 in 2 seconds.
How large a problem can be solved in 4 seconds using algorithm E?

Algorithm F is O(n^3) and it completes a problem of size 1024 in 2 seconds.
How long will algorithm F take to complete a problem of size 4096?

Algorithm C is O(n) and it completes a problem of size 1024 in 2 seconds.
How large a problem can be solved in 4 seconds using algorithm C?

















The following table gives measured times for program A on a number of
problem sizes. What big-oh function best describes the time for program A?


size time
 100  10
 200  10
 400  10
 800  10
1600  10

size time
 128 7
 256 8
 512 9
1024 10
2048 11

size time
1    10
2    100
3    1000
4    10000
5    100000

size time
10   1110
20   8420
30   27930
40   65640
50   127550

















Suppose the following list is given as input to binary search (with
three-way compares) and the search is looking for the value 77.
Give the part of the list in which the algorithm is still searching
after each major step of the binary search algorithm.


11 15 16 22 33 44 48  55  58 62 66 72 77 88 99

















What are the contents of the list L at the end of the program?


Stack S;
List L;
S.push(4);
S.push(2);
S.push(1);
S.push(8);
while (!S.isEmpty())
    L.append(S.pop());



What are the contents of the list L at the end of the program?


Queue Q;
List L;
Q.add(4);
Q.add(2);
Q.add(1);
Q.add(8);
while (!Q.isEmpty())
    L.append(Q.remove());



What are the contents of the list L at the end of the program?
(Assume that smaller values have higher priority.)


PriorityQueue Q;
List L;
Q.add(4);
Q.add(2);
Q.add(1);
Q.add(8);
while (!Q.isEmpty())
    L.append(Q.remove());

















Suppose the following list is given as input to insertion sort.
Give the content of the list after each major step of insertion sort.


8 7 2 9 4 8 5 4 3

















Suppose the following list is given as input to selection sort.
Give the content of the list after each major step of selection sort.


8 7 2 9 4 8 5 4 3

















Suppose the following list is given as input to merge sort. Give the
lists that result from each split step and each merge step of merge sort.


8 2 7 4 4 8 5 1

















Suppose the following list is given as input to quick sort. Give the lists
that result from each partition step and each concatenate step of quick sort.
Always use the item in the middle position as the quick-sort pivot. Use the
simple partitioning algorithm (not the in-place partitioning algorithm).


1 9 8 3 3 2 5 4 7

















Show the steps of the quicksort in-place partitioning algorithm on the list.
Use the item in the middle position as the quick-sort pivot.


1 9 8 3 3 2 5 4 7

















If log10(40) is 1.6,
what is log10(4)?
what is log10(25)?