MAT 2051 Unit 5 Assignment 2: Algorithms and Time Complexity -

MAT 2051 Unit 5 Assignment 2: Algorithms and Time Complexity

MAT 2051 Unit 5 Assignment 2 Algorithms and Time Complexity

Algorithms and Time Complexity

In algorithm development, the time and space required for algorithm completion is paramount. As users, we know that when a computer process takes too long, we try to avoid it. This truth encourages all IT and computer-based companies to produce faster products and services.

For this assignment, write a one- to two-page paper that includes all required algorithms and pseudocode describing the time and space complexity of algorithms. Include the following:

Answer the following questions:

What is time complexity?

What is space complexity?

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Compare and contrast polynomial time algorithms and nondeterministic polynomial (NP) time algorithms (one paragraph minimum).

Provide an example of an algorithm for each worst-case run times:

O( n).

O(nk). Note that this is called polynomial-time, where k is any number greater than 1.

NP-time.

Hint: Quick sort is an algorithm that runs in O(nlog n) time.

Review the Algorithms and Time Complexity Scoring Guide to understand how the assignment will be graded.

Given a graph with n edges, what is the time complexity of finding a Euler path? Is this a polynomial time algorithm? Explain and show all work and the graph. Hint: Include the algorithm and pseudocode.

Given a graph with n edges, can one find a minimum Hamiltonian cycle (TSP) in polynomial time? Has anyone ever proved that a polynomial time algorithm does not exist for this problem? Explain your answers and show the graph. Hint: Consider NP complete problems.

Offer one example of an IT or computer application that can be modeled as the TSP problem. This must be at least one paragraph.

Your calculations and work must be shown. Include references to any resources you use to complete the assignment.

Review the Graph Applications and the Traveling Sales Person Scoring Guide to understand how the assignment will be graded.

MAT 2051 Unit 5 Assignment 2 Algorithms and Time Complexity Grading Rubric

Performance Category	100% or highest level of performance 100% 16 points	Very good or high level of performance 88% 14 points	Acceptable level of performance 81% 13 points	Inadequate demonstration of expectations 68% 11 points	Deficient level of performance 56% 9 points	Failing level of performance 55% or less 0 points
Total Points Possible= 50	16 Points	14 Points	13 Points	11 Points	9 Points	0 Points
Scholarliness Demonstrates achievement of scholarly inquiry for professional and academic topics.	Presentation of information was exceptional and included all of the following elements: Provides evidence of scholarly inquiry relevant to required TD topic(s). Presents specific information from scholarly sources to develop a comprehensive presentation of facts. Uses at least one outside scholarly reference that is relevant, less than 5 years old (use of older references requires instructor permission) and reliable for the required topic.* Uses in-text citation and full reference at end of posting when presenting another person’s thoughts as quotes or paraphrase of information.	Presentation of information was good, but was superficial in places and included all of the following elements: Provides evidence of scholarly inquiry relevant to required TD topic(s). Presents specific information from scholarly sources to develop a comprehensive presentation of facts. Uses at least one outside scholarly reference that is relevant, less than 5 years old (use of older references requires instructor permission) and reliable for the required topic.* Uses in-text citation and full reference at end of posting when presenting another person’s thoughts as quotes or paraphrase of information.	Presentation of information was minimally demonstrated in all of the following elements: Provides evidence of scholarly inquiry relevant to required TD topic(s). Presents specific information from scholarly sources to develop a comprehensive presentation of facts. Uses at least one outside scholarly reference that is relevant, less than 5 years old (use of older references requires instructor permission) and reliable for the required topic.* Uses in-text citation and full reference at end of posting when presenting another person’s thoughts as quotes or paraphrase of information.	Presentation of information is unsatisfactory in one of the following elements: Provides evidence of scholarly inquiry relevant to required TD topic(s). Presents specific information from scholarly sources to develop a comprehensive presentation of facts. Uses at least one outside scholarly reference that is relevant, less than 5 years old (use of older references requires instructor permission) and reliable for the required topic.* Uses in-text citation and full reference at end of posting when presenting another person’s thoughts as quotes or paraphrase of information.	Presentation of information is unsatisfactory in two of the following elements: Provides evidence of scholarly inquiry relevant to required TD topic(s). Presents specific information from scholarly sources to develop a comprehensive presentation of facts. Uses at least one outside scholarly reference that is relevant, less than 5 years old (use of older references requires instructor permission) and reliable for the required topic.* Uses in-text citation and full reference at end of posting when presenting another person’s thoughts as quotes or paraphrase of information.	Presentation of information is unsatisfactory in three or more of the following elements Provides evidence of scholarly inquiry relevant to required TD topic(s). Presents specific information from scholarly sources to develop a comprehensive presentation of facts. Uses at least one outside scholarly reference that is relevant, less than 5 years old (use of older references requires instructor permission) and reliable for the required topic.* Uses in-text citation and full reference at end of posting when presenting another person’s thoughts as quotes or paraphrase of information
	16 Points	14 Points	13 Points	11 Points	9 Points	0 Points
Application of Course Knowledge Demonstrate the ability to analyze and apply principles, knowledge and information learned in the outside readings and relate them to real-life professional situations	Presentation of information was exceptional and included all of the following elements: Applies principles, knowledge and information from scholarly resources to the required topic. Applies facts, principles or concepts learned from scholarly resources to a professional experience. Application of information is comprehensive and specific to the required topic.	Presentation of information was good, but was superficial in places and included all of the following elements: Applies principles, knowledge and information from scholarly resources to the required topic. Applies facts, principles or concepts learned from scholarly resources to a professional experience. Application of information is comprehensive and specific to the required topic.	Presentation of information was minimally demonstrated in the all of the following elements: Applies principles, knowledge and information from scholarly resources to the required topic. Applies facts, principles or concepts learned from scholarly resources to a professional experience. Application of information is comprehensive and specific to the required topic.	Presentation of information is unsatisfactory in one of the following elements: Applies principles, knowledge and information from scholarly resources to the required topic. Applies facts, principles or concepts learned from and scholarly resources to a professional experience. Application of information is comprehensive and specific to the required topic.	Presentation of information is unsatisfactory in two of the following elements: Applies principles, knowledge and information from scholarly resources to the required topic. Applies facts, principles or concepts learned from scholarly resources to a professional experience. Application of information is comprehensive and specific to the required topic.	Presentation of information is unsatisfactory in three of the following elements Applies principles, knowledge and information and scholarly resources to the required topic. Applies facts, principles or concepts learned scholarly resources to a professional experience. Application of information is comprehensive and specific to the required topic.
	10 Points	9 Points			6 Points	0 Points
Interactive Dialogue Initial post should be a minimum of 300 words (references do not count toward word count) The peer and instructor responses must be a minimum of 150 words each (references do not count toward word count) Responses are substantive and relate to the topic.	Demonstrated all of the following: Initial post must be a minimum of 300 words. The peer and instructor responses must be a minimum of 150 words each. Responses are substantive Responses are related to the topic of discussion.	Demonstrated 3 of the following: Initial post must be a minimum of 300 words. The peer and instructor responses must be a minimum of 150 words each. Responses are substantive Responses are related to the topic of discussion.			Demonstrated 2 of the following: Initial post must be a minimum of 300 words. The peer and instructor responses must be a minimum of 150 words each. Responses are substantive Responses are related to the topic of discussion.	Demonstrated 1 or less of the following: Initial post must be a minimum of 300 words. The peer and instructor responses must be a minimum of 150 words each. Responses are substantive Responses are related to the topic of discussion.
	8 Points	7 Points	6 Points	5 Points	4 Points	0 Points
Grammar, Syntax, APA Points deducted for improper grammar, syntax and APA style of writing. The source of information is the APA Manual 6th Edition Error is defined to be a unique APA error. Same type of error is only counted as one error.	The following was present: 0-3 errors in APA format AND Responses have 0-3 grammatical, spelling or punctuation errors AND Writing style is generally clear, focused on topic,and facilitates communication.	The following was present: 4-6 errors in APA format. AND/OR Responses have 4-5 grammatical, spelling or punctuation errors AND/OR Writing style is somewhat focused on topic.	The following was present: 7-9 errors in APA format. AND/OR Responses have 6-7 grammatical, spelling or punctuation errors AND/OR Writing style is slightly focused on topic making discussion difficult to understand.	The following was present: 10- 12 errors in APA format AND/OR Responses have 8-9 grammatical, spelling and punctuation errors AND/OR Writing style is not focused on topic, making discussion difficult to understand.	The following was present: 13 – 15 errors in APA format AND/OR Responses have 8-10 grammatical, spelling or punctuation errors AND/OR Writing style is not focused on topic, making discussion difficult to understand. AND/OR The student continues to make repeated mistakes in any of the above areas after written correction by the instructor.	The following was present: 16 to greater errors in APA format. AND/OR Responses have more than 10 grammatical, spelling or punctuation errors. AND/OR Writing style does not facilitate communication
	0 Points Deducted					5 Points Lost
Participation Requirements	Demonstrated the following: Initial, peer, and faculty postings were made on 3 separate days					Failed to demonstrate the following: Initial, peer, and faculty postings were made on 3 separate days
	0 Points Lost					5 Points Lost
Due Date Requirements	Demonstrated all of the following: The initial posting to the graded threaded discussion topic is posted within the course no later than Wednesday, 11:59 pm MT. A minimum of one peer and one instructor responses are to be posted within the course no later than Sunday, 11:59 pm MT.					Demonstrates one or less of the following. The initial posting to the graded threaded discussion topic is posted within the course no later than Wednesday, 11:59 pm MT. A minimum of one peer and one instructor responses are to be posted within the course no later than Sunday, 11:59 pm MT.