CSED233 Assignment #1 Solution

Please do not use C++ standard template library
●
○ Such as:
■ #include <queue> ■ #include <vector>
■ #include <stack>
○ Any submission using STL library will be disregarded

Any questions?
● Please use LMS - Q&A board

0. Basic instruction
a. Please refer to the attached file named PA_instructions.pdf

1. Asymptotic analysis (1 pts)

a. Choose the TIGHT bound of the following maxProduct function

b. maxProduct
Input: An integer n >= 1, arrays A & B storing n integers
Output: The maximum product of elements from each A and B

int maxProduct(int n, int* A, int* B) { int currMax = 0; for (int i = 1; i < n; i++) for (int j = 1; j < n; j++) if (currMax < A[i]*B[j]) currMax = A[i]*B[j]; return currMax; }
1. O(1)
2. O(n)
3. O(n log(n))
4. O(n^2)

c. Example output: If you choose O(1), then print 1
>> ./pa1.exe 1
[Task 1]
1

2. Asymptotic analysis (1 pts)

a. Choose the TIGHT bound of the following medianSearch function

b. medianSearch
Input: An integer n >= 2, an ascending sorted array A storing n real numbers Output: An array B which contains nth, n/2th, n/4th, … elements of A

double* medianSearch(int n, double* A) { double *B = new double[n];
/* B is allocated as same size as A */ int j = 0;
for (int i = n; i >= 1; i = i/2) { B[j] = A[i-1]; j++; }
return B;
}
1. O(log (n))
2. O(n log (n))
3. O(n)
4. O(n^2)

c. Example output: If you choose O(log (n)), then print 1
>> ./pa1.exe 2
[Task 2]
1

3. List (4 pts)

a. Implement a function that can insert or delete an integer into the ascending order “sorted” list. An user can delete a specified smallest element. If the specified element is out of range of the given list, print “error”

Tips: Please do not try to implement sorting algorithm for this task

b. Input & Output
Input: Sequence of commands, which is one of the following,
- (‘insert’,integer): insert integer into the appropriate position in the sorted list.
- (‘delete_at’,i): delete an item that is i-th smallest element in the list. i indicates zero-based index.
Output:
- An array after insertion/deletion in a string separated with the spacebar - “error” if the index is out of range

c. Example input & output
Input Output
[(‘insert’,1),(‘insert’,2)] 1 2
[(‘insert’,2),(‘insert’,1),(‘insert’,3)] 1 2 3
[(‘insert’,1),(‘insert’,3),(‘delete_at’,1)] 1
[(‘insert’,1),(‘delete_at’,2),(‘insert’,2)] error
[(‘insert’,1),(‘insert’,3),(‘insert’,2),
(‘delete_at’,1)] 1 3

d. Example execution
>> ./pa1.exe 3 “[(‘insert’,1),(‘insert’,3),(‘delete_at’,1),
(‘insert’,2)]”
[Task 3]
1 2

4. Stack (3 pts)

a. Implement a function that prints the top values of the stack when “top” operation is called after the sequence of “push” or “pop” operations. If the stack is empty, and the “top” operation is called, then print “-1”, If “pop” operation from the empty stack then print “error”

b. Input & Output
Input: Sequence of commands, which is one of the following,
- (‘push’,integer): push integer into the current stack (integer is always positive)
- (‘pop’,NULL): pop the top value of the current stack (this operation will print nothing)
- (‘top’,NULL): print the top value of the current stack (print ‘-1’ if the current stack is empty) Output:
- Expected printed values after processing the whole sequence, in a string separated with the spacebar
- “error” if the pop operation is executed on an empty stack

c. Example Input & Output
Input Output
[(‘push’,5),(‘push’,3),(‘top’,NULL)] 3
[(‘push’,3),(‘top’,NULL),(‘pop’,NULL),
(‘push’,5),(‘top’,NULL)] 3 5
[(‘push’,5),(‘pop’,NULL),(‘top’,NULL)] -1
[(‘pop’,NULL)] error
[(‘pop’,NULL),(‘push’,5),(‘top’,NULL)] error

d. Example execution
>> ./pa1.exe 4 “[(‘push’,3),(‘top’,NULL),(‘pop’,NULL),
(‘push’,5),(‘top’,NULL)]”
[Task 4]
3 5

5. Queue (3 pts)

a. Implement a function which shows the value in the queue from the head to tail.

b. Input & Output
Input: Sequence of commands, which is one of the following,
- (‘enqueue’,integer): enqueue integer into the current queue Output:
- Values in the queue from the head to the tail, in a string separated with the spacebar

c. Example Input & Output
Input Output
[(‘enqueue’,5)] 5
[(‘enqueue’,5),(‘enqueue’,2)] 5 2
[(‘enqueue’,5),(‘enqueue’,2),(‘enqueue’,3)] 5 2 3

d. Example execution
>> ./pa1.exe 5 “[(‘enqueue’,5),(‘enqueue’,2),(‘enqueue’,3)]”
[Task 5]
5 2 3



6. Queue (3 pts)

a. Implement a function that shows the value of a queue after the sequence of arbitrary queue operations. If the queue after the operations is empty, print “empty”. If “dequeue” operates on an empty queue, print “error”.

b. Input & Output
Input: Sequence of commands, which is one of the following,
- (‘enqueue’,integer): enqueue integer into the current queue
- (‘dequeue’,NULL): dequeue from the current queue
Output
- Values in the queue from the head to the tail, in a string separated with the spacebar
- “empty” if the queue is empty
- “error” if the “dequeue” operation is executed on an empty queue

c. Example input & output
Input Output
[(‘enqueue’,5),(‘enqueue’,3),(‘dequeue’,NULL)] 3
[(‘enqueue’,5),(‘enqueue’,3),(‘dequeue’,NULL),
(‘enqueue’,5)] 3 5
[(‘enqueue’,3),(‘dequeue’,NULL)] empty
[(‘enqueue’,5),(‘dequeue’,NULL),(‘dequeue’,NUL L)] error
[(‘enqueue’,5),(‘dequeue’,NULL),(‘dequeue’,NUL L),(‘enqueue’,3)] error

d. Example execution
>> ./pa1.exe 6 “[(‘enqueue’,5),(‘enqueue’,3),(‘dequeue’,NULL)]” [Task 6]
3