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Data Structures and Algorithms

*Lecturer: Dr F.M. Stajano*

*No. of lectures:* 16

*This course is a prerequisite for Algorithms II, Computer Graphics and Image Processing, Complexity Theory, Artificial Intelligence I.*

**Aims**

The aim of this course is to provide an introduction to computer algorithms and data structures, with an emphasis on foundational material. It is suitable for people who did not take discrete mathematics in Part IA.

**Lectures**

**Discrete Mathematics.**Common mathematical notation. Proofs. Induction. Sets, tuples, functions. Relations and Graphs. Combinations and permutations. [Ref: Ch 1; App B, C] [3-4 lectures]**Algorithm Fundamentals.**Algorithm analysis and design. Models of a computer; costs. Asymptotic notation. Computational complexity. Recurrences. Ideas for algorithm design: divide and conquer, dynamic programming, greedy algorithms and other useful paradigms. [Ref: Ch 1, 2, 3, 4, 15, 16] [2-3 lectures]**Sorting.**Insertion sort. Merge sort. Heapsort. Quicksort. Other sorting methods. Finding the minimum and maximum. [Ref: Ch 2, 6, 7, 8, 9] [4-5 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] [5-7 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.

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.

Students are expected to buy and make extensive use of one of the
above references: those not doing so will be severely disadvantaged.
The easiest and recommended choice is Cormen *et al.* which
covers all the topics in the syllabus: 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. Their
relative merits are discussed in the course handout.

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**Contents**