Order ID |
53563633773 |
Type |
Essay |
Writer Level |
Masters |
Style |
APA |
Sources/References |
4 |
Perfect Number of Pages to Order |
5-10 Pages |
Description/Paper Instructions
Algorithm Complexity Analysis Assignment
Name:
Homework 1
Assignment Place your answers directly under each question below — do not delete the questions.
Part 1: Algorithm Complexity Analysis
1) Give the big-Oh characterization, in terms of n, of the running time of the pseudocode loops shown below: (3 pts each)
- a) x 1
for i 1 to 8n do
x x * i
- b) b 1
while n > 0 do
b b + (5 * n)
n n / 2
- c) s 0
for i 1 to 2n do
for j 1 to i do
s s + i
- d) k 0
for i 1 to n2 do
for j 1 to 5n do
k k + i
2) Complete problem C1.5 on page 45 of your textbook (6 pts)
Show ALL math conversion steps.
3) Given the following functions, determine the big-O notation for each (3 pts each)
Hint: Use the rules given in the textbook.
- a) f(n) = 500n2 + 50n3 + 5n
- b) f(n) = 5n log n + 888n
- c) f(n) = 33n2 + 5n2 + 1000n2
- d) f(n) = 8n3 + 2n + 44n2
4) Consider the following algorithm (shown with line numbers) that finds the maximum element in an array of positive integers.
1: int findMaxElement(int nums[], int N) {
2: int i, maxNum;
3: maxNum = −1;
4: for (i = 0; i < N; i++)
5: if (nums[i] > maxNum)
6: maxNum = nums[i];
7: return maxNum;
8: }
You can assume all elements are unique and that each occurs with equal probability.
- a) Best case
- Describe the best case data for this algorithm. (2 pts)
- Then, for this best case, state how often is line 6 executed. (2 pts)
- b) Worst case
- Describe the worst case data for this algorithm. (2 pts)
- For this worst case, state how often is line 6 executed. (2 pts)
5) Suppose that for the worst case, given input size n:
Algorithm 1 does f(n) = n2 + 4n steps
Algorithm 2 does f(n) = 45n + 10 steps
For what input sizes is algorithm 1 faster than algorithm 2, in the worst case? (4 pts)
6) Given the following ordered array: (5 pts each)
[0] |
2 |
[1] |
4 |
[2] |
7 |
[3] |
9 |
[4] |
22 |
[5] |
36 |
[6] |
44 |
[7] |
67 |
[8] |
68 |
[9] |
71 |
[10] |
83 |
[11] |
85 |
[12] |
88 |
[13] |
90 |
[14] |
94 |
[15] |
99 |
- a) Using the binary search algorithm to search for the target value 88
For each pass, list the high and low index, and the calculated middle index.
Finally, state what causes the search to stop, and the result of the search.
- b) Using the binary search algorithm to search for the target value 60
For each pass, list the high and low index, and the calculated middle index.
Finally, state what causes the search to stop, and the result of the search.
7) Given the following recursive method:
public static int recurMethod (int num1, int num2) {
if (num1 < num2)
return num2;
else
return (num1 – num2) + recurMethod(num1 – 3, num2 + 5);
}
If the initial call is:
int result = recurMethod (50, 30);
- a) List each recursive call going forward (3 pts)
- b) List the value returned from each call, and the final result. (5 pts)
8) Assume you have a 20-element hash table that uses the hash function: H(key) = key mod 20 and quadratic probing to resolve collisions. If the following keys were inserted into the hash table, in the order shown: 39, 59, 23, 40, 79 where will each be placed (i.e. at what index)? SHOW how you got your answers. (8 pts)
9) Begin with an empty binary search tree. (5 pts)
Insert the following keys, in the given order:
43, 30, 40, 12, 65, 86, 71, 33, 95, 88, 35 Draw the resulting tree.
10) Starting with the binary search tree shown below. (5 pts each)
45
77
19
12
52
55
46
82
68
33
15
35
24
22
28
- a) List the order the nodes will be visited, using pre-order traversal.
- b) List the order the nodes will be visited, using post-order traversal.
- c) Deletion algorithms either use the left subtree or right subtree to find the node to replace the deleted node (must use same choice for all deletions ). State which subtree you will use .
Then show the resulting tree, after delete nodes 55, 52, 19, 77, 45, in that order.
11) Complete problem A1.8 on page 49 of your textbook (8 pts)
Present the algorithm in pseudocode and then explain the runtime of the algorithm.
Do not use any built-in code library methods in your solution.
12) Compare and contrast some of the previously studied data structures:
Hash tables
Binary trees
Discuss advantages and disadvantages of each, in terms of the time it takes to add and delete elements within the data structure, and the memory required for the data structure. (5 pts)
Submission
This homework assignment is due by midnight of the date listed on the Course Assignments by Week page of the Content.
- Before you submit your homework, append your last name to the front of the Word doc filename. For examples: SmithCS324-Hwk1.docx
- Submit your .docx file to the Hwk Assn 1 Submission Folder (located under Assignments tab in online course
RUBRIC
QUALITY OF RESPONSE |
NO RESPONSE |
POOR / UNSATISFACTORY |
SATISFACTORY |
GOOD |
EXCELLENT |
Content (worth a maximum of 50% of the total points) |
Zero points: Student failed to submit the final paper. |
20 points out of 50: The essay illustrates poor understanding of the relevant material by failing to address or incorrectly addressing the relevant content; failing to identify or inaccurately explaining/defining key concepts/ideas; ignoring or incorrectly explaining key points/claims and the reasoning behind them; and/or incorrectly or inappropriately using terminology; and elements of the response are lacking. |
30 points out of 50: The essay illustrates a rudimentary understanding of the relevant material by mentioning but not full explaining the relevant content; identifying some of the key concepts/ideas though failing to fully or accurately explain many of them; using terminology, though sometimes inaccurately or inappropriately; and/or incorporating some key claims/points but failing to explain the reasoning behind them or doing so inaccurately. Elements of the required response may also be lacking. |
40 points out of 50: The essay illustrates solid understanding of the relevant material by correctly addressing most of the relevant content; identifying and explaining most of the key concepts/ideas; using correct terminology; explaining the reasoning behind most of the key points/claims; and/or where necessary or useful, substantiating some points with accurate examples. The answer is complete. |
50 points: The essay illustrates exemplary understanding of the relevant material by thoroughly and correctly addressing the relevant content; identifying and explaining all of the key concepts/ideas; using correct terminology explaining the reasoning behind key points/claims and substantiating, as necessary/useful, points with several accurate and illuminating examples. No aspects of the required answer are missing. |
Use of Sources (worth a maximum of 20% of the total points). |
Zero points: Student failed to include citations and/or references. Or the student failed to submit a final paper. |
5 out 20 points: Sources are seldom cited to support statements and/or format of citations are not recognizable as APA 6th Edition format. There are major errors in the formation of the references and citations. And/or there is a major reliance on highly questionable. The Student fails to provide an adequate synthesis of research collected for the paper. |
10 out 20 points: References to scholarly sources are occasionally given; many statements seem unsubstantiated. Frequent errors in APA 6th Edition format, leaving the reader confused about the source of the information. There are significant errors of the formation in the references and citations. And/or there is a significant use of highly questionable sources. |
15 out 20 points: Credible Scholarly sources are used effectively support claims and are, for the most part, clear and fairly represented. APA 6th Edition is used with only a few minor errors. There are minor errors in reference and/or citations. And/or there is some use of questionable sources. |
20 points: Credible scholarly sources are used to give compelling evidence to support claims and are clearly and fairly represented. APA 6th Edition format is used accurately and consistently. The student uses above the maximum required references in the development of the assignment. |
Grammar (worth maximum of 20% of total points) |
Zero points: Student failed to submit the final paper. |
5 points out of 20: The paper does not communicate ideas/points clearly due to inappropriate use of terminology and vague language; thoughts and sentences are disjointed or incomprehensible; organization lacking; and/or numerous grammatical, spelling/punctuation errors |
10 points out 20: The paper is often unclear and difficult to follow due to some inappropriate terminology and/or vague language; ideas may be fragmented, wandering and/or repetitive; poor organization; and/or some grammatical, spelling, punctuation errors |
15 points out of 20: The paper is mostly clear as a result of appropriate use of terminology and minimal vagueness; no tangents and no repetition; fairly good organization; almost perfect grammar, spelling, punctuation, and word usage. |
20 points: The paper is clear, concise, and a pleasure to read as a result of appropriate and precise use of terminology; total coherence of thoughts and presentation and logical organization; and the essay is error free. |
Structure of the Paper (worth 10% of total points) |
Zero points: Student failed to submit the final paper. |
3 points out of 10: Student needs to develop better formatting skills. The paper omits significant structural elements required for and APA 6th edition paper. Formatting of the paper has major flaws. The paper does not conform to APA 6th edition requirements whatsoever. |
5 points out of 10: Appearance of final paper demonstrates the student’s limited ability to format the paper. There are significant errors in formatting and/or the total omission of major components of an APA 6th edition paper. They can include the omission of the cover page, abstract, and page numbers. Additionally the page has major formatting issues with spacing or paragraph formation. Font size might not conform to size requirements. The student also significantly writes too large or too short of and paper |
7 points out of 10: Research paper presents an above-average use of formatting skills. The paper has slight errors within the paper. This can include small errors or omissions with the cover page, abstract, page number, and headers. There could be also slight formatting issues with the document spacing or the font Additionally the paper might slightly exceed or undershoot the specific number of required written pages for the assignment. |
10 points: Student provides a high-caliber, formatted paper. This includes an APA 6th edition cover page, abstract, page number, headers and is double spaced in 12’ Times Roman Font. Additionally, the paper conforms to the specific number of required written pages and neither goes over or under the specified length of the paper. |
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