analysis algorithm

8/3/2019 Analysis Algorithm

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Analysis of Algorithms

INTRODUCTION

Analysis of Algorithms


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Algorithm

Definition 1: A finite set of precise instructions for

performing a computation or for solving a problem.

Definition 2: A specific set of instructions for carrying out a

procedure or solving a problem, usually with the requirement

that the procedure terminate at some point.Definition 3: A procedure for solving a mathematical

problem in a finite number of steps that frequently involves

repetition of an operation.

Definition 4: A step-by-step procedure for solving a problem

or accomplishing some end especially by a computer.

Analysis of Algorithms 1


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Algorithm

Synonym: Method, Procedure, Program, Recipe, Routine

Solution, Technique ...

Etymology: Alteration of Middle English algorisme, from

Old French & Medieval Latin; from Medieval Latinalgorismus, from Arabic al-khuwarizmi, from the name of

the Persian Mathematician Al-Khowarizmi who was the first

to formalize the rules for the 4 basic arithmetic operations.



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8 Questions

1. Who asks questions? Who produces problems?

2. What is a problem and/or a solution? (model and language)

3. Does a solution solve a problem? (correctness)

4. What is the efficiency of a solution? (complexity)

5. Is a solution scalable? (scalability)

6. When is a solution good? Better? Best? (upper bounds)

7. What are the limits of any solution? (lower bounds)

8. Is a problem hard? How do we handle hard problems?



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The Ultimate Question

Question: How do we solve problems?

Genius?

Intuition?

Luck?

Experience?

Hard work?

Answer: a combination of these 5 factors!!!



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How to solve a problem? Some Heuristics

Search for a pattern. Draw a figure.

Formulate an equivalent problem. Modify the problem. Choose effective notation. Exploit symmetry. Divide into cases. Work backward. Argue by contradiction.

Pursue parity. Consider extreme cases. Generalize.



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Algorithms Properties

Correctness: for all valid inputs.

Complexity Efficiency: as a function of the input size.

Worst-case vs. average case.

Limitations: for the algorithm and for the problem.

Scalability: similar efficiency for any input size.

Optimality: optimal or near-optimal or approximately

optimal solution.



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Teacher Amotz Bar-Noy

E-mail: [email protected].

Internet: http://www.sci.brooklyn.cuny.edu/amotz/714.

Office Hours: Tuesday 3:00pm4:00pm, Room 2112a.

Class Hours: Tuesday 6:00pm8:05pm,

Extra Hours: Tuesday 5:15pm6:00pm and 8:05pm9:00pm.

Class Room: 236NE.



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Textbooks

Textbook: Introduction to Algorithms (second edition),

by Cormen, Leiserson, Rivest, and Stein.

Another book: Algorithm Design, by Goodrich and

Tamassia, Wiley.

Another book: Introduction to Algorithms a Creative

Approach, by Manber, Addison-Wesley.



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Tentative Syllabus:

Introduction, Mathematical Background, Examples, Divide

and Conquer,

Searching, Sorting, and Sorting Networks,

Greedy Algorithms and Huffman Codes,

Dynamic Programming,

Graphs, Graph Traversals, Minimum spanning Trees,

NP-Completeness.



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Tentative Schedule

01. 02/01/2004 Introduction02. 02/08/2004 Mathematical Background03. 02/15/2004 Examples and Divide and Conquer

04. 02/22/2004 Searching and Order Statistics05. 03/01/2004 Sorting06. 03/08/2004 Sorting Networks07. 03/15/2004 ???

08. 03/22/2004 Greedy Algorithms09. 04/05/2004 Midterm Exam10. 04/12/2004 Dynamic Programming11. 04/19/2004 Graphs

12. 05/03/2004 Graph Traversals13. 05/10/2004 Minimum Spanning Trees14. 05/17/2004 NP-Completeness15. 05/24/2004 Final Exam



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Tentative Schedule Remarks

1. There are no classes on 03/29/2004 and on 04/26/2004.

2. Some of the classes will start at 05:15pm instead of 06:00am

and some will end at 09:00pm instead of 08:05pm. These

extra hour(s) are reserved for solving the assignments.

3. Dates with ??? are reserved either for completing the

previous subjects or for additional subjects.



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Grading

Note: This is only a guide, percentages and rules may change

during the semester as needed.

Percentages: The final grade will be composed of the

following4

components: 50% 60% final exam.

20% 30% mid-term exam.

10% 15% quizzes.

10% assignments.



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Quizzes

There could be 2 types of quizzes:

At the beginning of the class to check what you learned

in the previous week.

At the end of the class to check what you learned during

the 2 hours class.

There will be no announcements regrading quizzes.

The number of quizzes has not yet been determined.



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Animation Project

You may volunteer to animate one of the algorithms that

will be taught in class.

You must coordinate your choice with the teacher.

You will be given at most 4 weeks to finish the animation

project. In any case, no later than one week before the

final exam date (12/16/2004).

The percentage allocated to a project depends on its size.



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Answering a question

Answer a question in an exam, in a quiz, or in an assignment:

Only within the given space for the answer.

Using a readable text with normal size font.

You get 20% of the value if you leave the answer blank.

You get no points for a wrong answer.



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Preparing Assignments

Alone if you can.

Get help if necessary.

You must understand everything you write.


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