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Programming COMP2521 90分代考案例
Question 1
An algorithm solves a problem of size nn recursively by breaking it down into two subproblems of size n/2n/2 with the same structure, until the size of a subproblem is one or zero. It takes O(1)O(1) time to solve a (sub)problem of size one or zero. It takes O(n)O(n) time to convert a problem of size nn into two subproblems and it takes O(n)O(n) time to combine the results of these subproblems into the result of the problem of size nn. What is the time complexity of this algorithm? Justify your answer.
Write your answer in q1.txt.
Submission
Submit via the give command
give cs2521 sample_exam_q1 q1.txt
Question 2
Consider the following algorithm, which converts a positive integer nn to its binary representation.
BinaryConversion:
Input positive integer n
Output binary representation of n on a stack
create empty stack S
while n > 0 do
push (n mod 2) onto S
n = floor(n / 2)
end while
return S
What is the time complexity of the algorithm? Assume that creating a stack and pushing an element onto a stack are both O(1)O(1) operations (i.e., constant). Justify your answer.
Write your answer in q2.txt.
Submission
Submit via the give command
give cs2521 sample_exam_q2 q2.txt
Question 3
Consider the the following 2-3-4 tree :
(a) What value(s) would be stored in the root node of the above 2-3-4 tree after the insertion of the value 8? What value(s) would be stored in the node that now contains 8? Note: if you need to promote a value, you must promote the smaller of the two middle values. Justify your answer.
(b) What value(s) would be stored in the root node of the above 2-3-4 tree after the insertion of the value 50? What value(s) would be stored in the node that now contains 50? Note: if you need to promote a value, you must promote the smaller of the two middle values. Justify your answer.
Write your answers in q3.txt.
Submission
Submit via the give command
give cs2521 sample_exam_q3 q3.txt
Question 4
Consider the following trie. Finishing nodes are shown in red.
a) How many words are stored in this trie?
(b) Which nodes would be visited in searching for “deeds”?
(c) What new nodes would be created if the word “bogus” was added to the trie? Justify your answer.
(d) What new nodes would be created if the word “do” was added to the trie? Justify your answer.
Write your answers in q4.txt.
Submission
Submit via the give command
give cs2521 sample_exam_q4 q4.txt
Question 5
(a) What is the difference between an Euler path and a Hamilton path?
(b) Does the graph below have any Euler paths? If so, give one of them. If not, explain why.
(c) Does the graph below have any Hamilton paths? If so, give one of them. If not, explain why.
Write your answers in q5.txt.
Submission
Submit via the give command
give cs2521 sample_exam_q5 q5.txt
Question 6
This question is about the array-based implementation of a max heap.
(a) Suppose the original state of the heap is:
[0] [1] [2] [3] [4] [5] [6] [7] [8] [9]
— Q N H D K E — — —
Show the state of the heap after performing each of the following operations:
join(pq, S)
join(pq, P)
Note that the “join(pq, P)” operation should be performed on the state of the heap obtained after performing the “join(pq, S)” operation.
(b) Suppose the original state of the heap is:
[0] [1] [2] [3] [4] [5] [6] [7] [8] [9]
— Q N H D K E — — —
Show the state of the heap after performing each of the following operations. What are the values of it1 and it2?
it1 = leave(pq)
it2 = leave(pq)
Note that the “it2 = leave(pq)” operation should be performed on the state of the heap obtained after performing the “it1 = leave(pq)” operation.
Write your answers in q6.txt.
Submission
Submit via the give command
give cs2521 sample_exam_q6 q6.txt
Question 7
Consider a hash table of integer keys with 11 slots and a primary hash function of h(k)=k % 11h(k)=k % 11.
Consider the following sequence of values:
10, 12, 28, 35, 25, 32, 20, 17, 24, 39
(a) Suppose the hash table described above uses linear probing for collision resolution. Show the final contents of the hash table after the values above have been inserted into an initially empty table in the order given. Give the cost, in terms of the number of keys examined, when searching for the key value 6 in the resulting table.
(b) Suppose the hash table described above uses double hashing for collision resolution, with a secondary hash function of h2(k)=1+(k % 5)h2(k)=1+(k % 5). Show the final contents of the hash table after the values above have been inserted into an initially empty table in the order given. Give the cost, in terms of the number of keys examined, when searching for the key value 6 in the resulting table.
Write your answers in q7.txt.
Submission
Submit via the give commandgive cs2521 sample_exam_q7 q7.txt
