Data Structures and Algorithms

*Lecturer: Dr M. Richards*
(`mr@cl.cam.ac.uk`)

*No. of lectures:* 16

*This course is a prerequisite for Computer Graphics & Image
Processing, Complexity Theory and Advanced Algorithms (Part II).*

**Aims**

The aim of this course is to provide a comprehensive introduction to computer algorithms taken from many different areas of application. The course will concentrate on algorithms that are of fundamental importance and the efficiency of most of them will be analysed.

**Lectures**

**Fundamentals.**Models of a computer, costs, growth rates.**Simple data structures.**Arrays, lists, trees. Idea of abstract data type.**Ideas for algorithm design.**Divide and Conquer and other important styles of algorithm.**The**Multiple implementation models for a single ADT, including hash tables.`TABLE`data type.**Free storage management.**Reference counts and garbage collection.**Sorting.**Insertion, Shell, Quick, Heap, Tree, Merge and Radix. Selection of element in .**Storage on external media.**Larsen's method, B-trees.**Variants on the**Balanced, 2-3-4, red-black, splay and ternary trees.`SET`data type.**String searching.**Brute force, Knuth-Morris-Pratt, Boyer-Moore, Rabin-Karp algorithms.**Data compression.**Run length encoding, prediction, Move-to-Front, Huffman, arithmetic encoding, Lempel-Ziv, and Wheeler's Block Compression.**Algorithms on graphs.**Reachability and shortest paths. Warshall, Floyd, Dijkstra, Prim and Kruskal algorithms. Depth first and breadth first traversal, strongly connected components. Matchings in bi-partite graphs.**Geometric algorithms.**Inside-outside a closed figure? Do line segments cross? Convex hull.

**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 table look up
- be able to analyse the efficiency in terms of space and
time of most algorithms
- be familiar with several techniques used in data compression and
algorithms on graphs
- be able to design new algorithms or modify existing ones for new
applications and reason about the efficiency of the result

**Recommended books**

Sedgewick, R. (1990). *Algorithms in C*. Addison-Wesley.

Cormen, T.H., Leiserson, C.D. & Rivest, R.L. (1990). *Introduction to
Algorithms*. MIT Press.

Manber, U. (1989). *Introduction to Algorithms: A Creative Approach*.
Addison-Wesley.

Salomon, D. (1998). *Data Compression: The Complete Reference*.
Springer.