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Paper 1: Algorithms I

*Lecturer: Dr R.K. Harle*

*No. of lectures:* 12

*Prerequisite course: Discrete Mathematics I*

*This course is a prerequisite for Algorithms II and Prolog.*

**Aims**

The aim of this course is to provide an introduction to computer algorithms and data structures, with an emphasis on foundational material.

**Lectures**

**Sorting.**Review of insertion sort, merge sort and quicksort. Understanding their memory usage with arrays. Heapsort. Other sorting methods. Finding the minimum and maximum. [Ref: Ch 1, 2, 3, 4, 15, 16] [4 lectures]**Algorithm design.**Ideas for algorithm design: dynamic programming, divide and conquer, greedy algorithms and other useful paradigms. [Ref: Ch 2, 15] [2 lectures]**Data structures.**Abstract data types. Pointers, stacks, queues, lists, trees. Hash tables. Binary search trees. Red-black trees. B-trees. Priority queues and heaps. [Ref: Ch 10, 11, 12, 13, 18, 19, 20, 21] [6 lectures]

**Objectives**

At the end of the course students should

- have a good understanding of how several fundamental
algorithms work, particularly those concerned with sorting and searching;
- have a good understanding of the fundamental data structures
used in computer science;
- be able to analyse the space and time efficiency of most
algorithms;
- be able to design new algorithms or modify existing ones for new
applications and reason about the efficiency of the result.

**Recommended reading**

* Cormen, T.H., Leiserson, C.D., Rivest, R.L. & Stein, C. (2001). *Introduction to Algorithms*. MIT Press (2nd ed.). ISBN 0-262-53196-8

Sedgewick, R. (2004). *Algorithms in Java* vol. 1 (note that C and C++ editions are also available and are equally good for this course). Addison-Wesley. ISBN 0-201-36120-5. New edition forthcoming in 2008.

Kleinberg, J. & Tardos, É. (2006). *Algorithm design*. Addison-Wesley. ISBN 0-321-29535-8.

Knuth, D.E. (1997). *The art of computer programming* (three volumes so far; a boxed set is also available). Addison-Wesley (3rd ed.). ISBN 0-201-89683-4, 0-201-89684-2 and 0-201-89685-0.

The recommended choice is Cormen *et al.* which covers all
the topics in the syllabus of Algorithms I and II and, in spite of its
quality, is the cheapest. The pointers in the syllabus are to chapters
in that book. The other textbooks are all excellent alternatives and
are sometimes clearer or more detailed than Cormen, but they are not
guaranteed to cover every item in the syllabus.

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