I'm vaguely considering a document or book that uses Python to explain algorithms. An outline is below. I'm interested in hearing reactions to this outline, especially from teachers using Python in courses. * Are there any important topics that aren't included? * Are there any included topics that are of marginal importance? The outline is already quite long, and the shorter it is, the better the odds of it being written. Comments on the relative importance of topics -- "don't spend too much space on numbers, but graphs are important, so spend a lot of time on them" * Are there any features the book needs? (Project suggestions, exercises, a chapter on mathematical fundamentals, etc.) * Any other suggested changes? Thanks for any ideas you might have; they'll all be taken into consideration. --amk "Algorithms in Python" (alt. "Learning Algorithms with Python") is a book that uses Python as the vehicle to teach the basic ideas of algorithms -- what an algorithm is, how to notate them clearly, what O() notation means, etc. -- and to introduce a number of different algorithms. It is not a formal textbook; discussions will rarely or never be rigorous, and there won't be any exercises. Requirements: * Minimal mathematical background should be required (basically functions, I think). Those bits of notation that are necessary will be explained as they're needed. * Elementary Python programming knowledge is needed, so readers should have a tutorial such as "Learning Python" alongside this book; it will not attempt to teach Python, though it will introduce relevant standard library modules. * Python 2.3 will be used. The overarching goal is to make the book understandable by a bright high-school student. This outline is very long, quite possibly too long. I can't estimate a length yet, but it's somewhat frightening that the comparable Perl book, O'Reilly's "Mastering Algorithms with Perl", had three authors. If shortening the book is required, there are two sets of chapters that could be dropped. 1. Drop "Game Trees", "Strings", "Real Implementations". Shorten the "Sorting" chapter by dropping bubble sort or other algorithms that are illustrative but impractical. The graph and tree chapters could probably be trimmed by dropping some topics. 2. If it's still too long, drop "Geometric Algorithms" and "Hard Problems". Outline --------- * Preface (the usual front matter) * Introductory comments * Intended audience; prerequisites; goals of book * Outline of book * Typographical conventions * Acknowledgements I. Basic Algorithms * Algorithmic Analysis (alt. "What is an Algorithm"? * Basic idea: an algorithm is a series of steps to perform a task * Example: finding the largest number in a list * Iterative formulation * Recursive formulation * Measuring time complexity: O, Theta, Phi notation * Compare different time complexities: O(n) vs O(lg n) * Applying O() to memory/space complexity * Time complexity of various Python built-in operations (dicts, lists) * Hashing Hashing is going to be the first serious algorithm used as an example, so it's going to be worked out in the most detail. Later chapters will explain algorithms, give reasons why they work, and discuss their O() complexity, but in less detail. * Basic concept of hash tables * Computing hash codes * Handling collisions * Resizing * Amortized algorithm costs (I can't see how to fit this into chapter 1, since you need a reasonably complicated algorithm to use as an example,) * Deleting hash table entries * Determining time complexity of hashing (this would be the most detailed explanation of determining time complexity; remaining chapters would be more hand-waving) II. Data Structures * Graphs * Graph concepts * Different graph representations (Node objects, sets of arcs) * Traversal * Topological sorts * Example: working out file dependencies * Connected-components * Spanning trees * Shortest paths * Trees * Trees as a special case of graphs * Binary trees * Representations (Node objects, lists/tuples, tables) * Searching * Inserting * Deleting * Unbalanced trees * Recursive operations on trees * Balanced trees: * red-black * do AVL trees, or just mention them briefly? (Briefly, I think; there's already more than enough material in this outline!) * B-trees Mathematical Algorithms * Numbers * Representing numbers on computers * Machine integers * Floating point representation * Large integers * Random number generation * Primality testing (kind of an odd duck) * Numeric Analysis * Polynomial evaluation * Finding zeros of functions * Differentiating functions * Integrating functions Geometric Algorithms: * Point representations * Convex hull * Line intersections * Range searching Applications * Sorting * Basic concepts * Comparing * Stability * Simple algorithms: * Bubble sort * Shell sort * Insertion sort * Merge sort * Quicksort * Implementation * Issues * Time-complexity * Time complexity of sorting * Proof of O(n lg n) bound. * Breaking assumptions: parallellism, spaghetti sort * Game trees * Introduction * Game rules (tic-tac-toe; or maybe hnefatafl, a game I did for a school project once) * Simple tree search * Alpha/beta cutoff * Strings This will likely be a difficult chapter, both to write and to read, because FSMs will be a pain to explain. Maybe this chapter isn't needed? * Simple searching * Boyer-Moore/KMP searches * Data compression * Regular expressions * Simple regex patterns * Finite automata * Languages * What finite automata can't do * Brief theory-of-computation overview The Real World (alt. Where Things Get Difficult) Hard problems: * P and NP * NP-completeness * Explanation * Various examples of NP-complete problems * Show that all NP-complete problems are equivalent * Solving an NP-complete problem * Exhaustive search * Heuristics * Real Implementations: Examines real-world implementation of various algorithms. * Random number generation: Mersenne twister * Karatsuba algorithm? (maybe too complicated and boring?) * Python's dictionary hashing * Python's sort * Final thoughts I like books that close with some sort of summation. This brief final chapter will discuss a few general issues. * Think about time complexity * Do the simplest thing... * Write tests * Value clarity over optimization * Where to go from here? * More books to read; things to do * Current state of research (parallel, distributed, various domains) Possible Topics -------------------- * Heaps (can't figure out where to fit them in -- any suggestions?) Not Covered ------------------ * Linked lists (they aren't the source of many algorithms, and their implementation in Python doesn't seem very interesting)