# CPS 130: Introduction to the Design and Analysis of Algorithms

## Description:

This course is an introductory undergraduate course on the design and analysis of algorithms. The course builds on the study of the analysis and implementation of data structures and algorithms from CPS100. The goal is to introduce a number of important algorithm design techniques as well as basic algorithms that are interesting both from a theoretical and also practical point of view. We will cover basic algorithm design techniques such as divide-and-conquer, dynamic programming, and greedy techniques for optimization. We will cover techniques for proof of the correctness of algorithms and also asymptotic analysis of algorithm time bounds by the solution of recurrence equations. We will apply these design and analysis techniques to derived algorithms for a variety of tasks such as sorting, searching, and graph problems. Some specific algorithm topics include: deterministic and randomized sorting and searching algorithms, depth and breadth first search graph algorithms for finding paths and matchings, and algebraic algorithms for fast multiplication and linear system solving.

## Prerequisites:

CPS 100 or equivalent and four semesters of college mathematics. This course requires undergraduate background in data structures (as covered in CPS100) as well as a certain amount of mathematical sophistication (e.g., as required to solve recurrence equations). A quiz on recurrence equations early in the course will provide you with some feedback on whether your mathematics training will suffice. If you feel that you may not have sufficient background, please talk with the instructor John Reif.

## Meetings:

 Times: Tuesdays and Thursdays 4:25PM - 5:40PM Room: D106 LSRC Building

## Instructor:

 Professor John Reif Office: D223 LSRC Building Phone: (919) 660-6568 Email: reif@cs.duke.edu Web page: www.cs.duke.edu/~reif Office hours: Tues, Thurs: 2:00 pm - 3:00 pm

## Recitations by TA: Harish Chandran

 Thursday (Recitation #CPS130-01R): Times:  Th 3:05PM - 3:55PM            Room: North 225 Friday (Recitation #CPS130-02R): Times:  F 10:20AM - 11:10AM        Room: North 225

## Course material:

• Cormen, Leiserson, Rivest, and Stein. Introduction to Algorithms. McGraw Hill, second edition, 2001. Be sure to get the second edition!
• Various lecture notes and research papers (downloads).

Optional auxiliary reading (other good reference books):

• G. Brassard and P. Bratley. Algorithmic - Theory and Practice. Prentice Hall, 1988.
• D. Kozen. The Design and Analysis of Algorithms. Springer Verlag, 1991.
• A. Aho, J. Hopcroft, and J. Ullman. Design and Analysis of Algorithms. Addison Wesley 1974.
• R. Tarjan. Data Structures and Network Algorithms. SIAM Publications, 1983.
• C. H. Papadimitriou. Computational Complexity. Addison Wesley, 1994.

## Course synopsis:

• Mathematical Analysis of Algorithms: growth of functions, summations, recurrences, average-case and randomized analysis
• Sorting and selection: divide-and-conquer and randomized techniques
• Search trees: search trees
• Amortized analysis
• Priority queues
• Greedy algorithms
• Dynamic programming
• Graph algorithms
• Matrix and algebraic algorithms
• Approximation algorithms

## Summary of topics covered and lecture notes:

Consult the schedule of lecture topics for a list of topics and a copy of lecture notes for the lectures to date. Other handouts can be found in the handouts directory, and homeworks and old midterm and final exams can be found in the homework directory. See resources page for additional information.

## Homework assignments:

Homeworks are due roughly every week and must be turned in before class on Wednesday of the week they're due. No credit is given for late solutions. For exceptional circumstances, see John Reif in advance, rather than after the due time. Homework assignments will be archived in the homework directory. The postscript version, pdf version, and source LaTeX code will be available for each homework problem.

Details about proper style [ps] for writing up homework solutions and some guidelines for grading are available. More detailed notes on how to write up technical material [ps.gz] in the Computer Science field (much of which is beyond the scope of this course) are available.

It is recommended but not required that LaTeX be used for typesetting homework problems. You can make use of the LaTeX source file, the LaTeX macros, a LaTeX template file, a LaTeX guide, and hypertext LaTeX help.

Honor code: For homework problems, discussion among students is permitted, but students MUST write up solutions independently on their own. No materials or sources from prior years' classes or from the Internet can be consulted. Breaking the rules can result in expulsion. Each student is required to make a copy of this page, sign it indicating that the contents are understood, and turn it in to John Reif.

## Grading:

• Class Interaction (10%)
• Homework assignments (20%)
• Closed-book quiz 1 (10%)
• Closed-book midterm exam 2 (15%)
• Closed-book lateterm exam 3 (15%)
• Closed-book final exam (30%)
• Optional Class Project (only if approved by instructor)

There will be no make-up exams for missed exams. Missing one of the three midterm exams due to an illness requires filing the web-based Short-Term Illness Notification Form at http://www.aas.duke.edu/trinity/t-reqs/illness, and will result in the remaining midterm exams grades being re-weighted (to 20% each). By University Policy, missing the Final exam results in a grade X.

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