Report

Algorithms Describing what you know Contents • What are they and were do we find them? • Why show the algorithm? • What formalisms are used for presenting algorithms? • Notes on notation • Algorithmic performance Where do we find them • In computer science and engineering almost everywhere. • Every other paper you read will include and introduce an algorithm in one form or another (see formalisms later) • Most of the books you have read include them in some form or another What are they? • “In mathematics and computer science, an algorithm is a step-by-step procedure for calculations. Algorithms are used for calculation, data processing, and automated reasoning.” • Source: http://en.wikipedia.org/wiki/Algorithm • Mind you… – The steps are not as important as is the correctness of the algorithm and to prove that it meets some performance claims. • In most cases coming up with the algorithm is a lot more work than actually presenting it – This is often because: some steps might be unclear; validation/verification might be missing on incomplete; usefulness of the algorithm omitted. Why is an algorithm important? • It might be better than others – What is better? uses less memory; uses less CPU time; It is faster; It improves a previous case; does it maybe take up less space and requires less resources; or maybe all the above together?? • It might be explaining a very complex process • It might be used to show the feasibility of a result and that a problem is computable (deterministic as we say) regardless of cost So what would expect to see in it? • The steps that make up the algorithm • The structures used by the algorithm for input, output and internal representation of data • Where does it have meaning (the scope) and any known limitations • What properties will show that the algorithms is correct (preconditions, postconditions, loop invariants) • Demonstration of correctness • A complexity analysis for time and resources requirements • Experiments confirming the theoretical result. What formalisms are used? • There are certain styles for presenting algorithms so that they are understandable and clear • List style • Pseudocode • Prosecode • Literate code Formalism – list style • Algorithm broken down into a sequence of steps (numbered or named) • See loops as involving ‘goto’ statements • Good – Discuss while presenting – No restriction to text • Bad – Sometimes easy to get lost in the discussion Formalism - pseudocode • Algorithm presented in a block-structure language • Each line is numbered • Good – Immediately obvious structure • Bad – Statements tend to be short (and unclear) – Not allowed to include many comments Formalism - prosecode • • • • • Number each step Don’t break a loop over several steps Use sub-numbering for step parts Include explanatory text Good – Direct and clear explanation of the algorithm • Bad – More effective when the algorithm has been previously discussed Formalism – Literate code • Introduce algorithmic detail gradually • While introducing detail discuss underlying ideas • The following example is incomplete Notation • For algorithms mathematical notation is preferable to a programming notation • Quick: – – – – Use xi not x[i] Use × or ∙ not * or x Avoid specific language constructors (for, variable++, etc) Nesting can be used by numbering subsections • Mathematics provide a wealth of symbols that enable us to describe almost anything we like – s {CSC135} x, y {ASSIGNMENTS} with x y • If H(s, x) H(s,y) s will learn some LaTeX Environment • The steps of an algorithm is part of its description • Environment description is the remainder of the algorithm – Data structures, input and outputs all should be clearly and unambiguously defined (think mathematics) – Other software/hardware, even the operating system • If you are describing an algorithm for faster read-write operations on Blue-Ray discs then hardware and operating system aspects are important – – – – Specify all variables Mention assumptions and expectations Mention possible errors Say what the algorithms does • Be consistent Performance • When comparing an algorithm state criteria used. Possibilities include (and are not limited to): – Processing time (or speed) • Not easy to define due to various factors. Better use a mathematic model for times based performance evaluation – Memory and disk requirements • Various ways of manipulation could affect performance. When describing the algorithm, be clear on memory usage – Disk and network traffic • Seek time & transfer rate are important. Sequential access vs. random access can make the difference. Caching is also important. – Applicability • Be sure you are comparing similar requirements & functionality algorithms. – Asymptotic analysis: used to compare algorithm performance (big O notation, another course) Algorithms end summary • • • • • • What are they, why should we present them? What is to be expected What formalisms can be used Notation Environment Performance