How to Win at Rock-Paper-Scissors Rock-paper-scissors* isn’t obviously interesting to look at mathematically. The Nash-equilibrium strategy is very simple: choose equally and randomly from the three choices, and (in the long run) your opponent will not beat you (nor will you beat your opponent). Nevertheless, it’s still possible for a computer strategy to beat a human player over a long run of games. My nine-year-old daughter showed me one solution with a Scratch program that she wrote that won every time by looking at your choice before making its decision! But I will walk you through a simple solution that wins without cheating. While the equal random choice is unbeatable, we can rely on the fact that humans are not very good at being random. I thought about writing the algorithm as a topic within our Computer-Based Math™ statistics course. First we need to be able to play the game. Random player The code is mostly user interface, display, and game rules. where 1 represents rock, 2 paper, and 3 scissors.
Building a Balanced Tree From a List in Linear Time | Harder, Better, Faster, Stronger The usual way of forming a search tree from a list is to scan the list and insert each of its element, one by one, into the tree, leading to a(n expected) run-time of However, if the list is sorted (in ascending order, say) and the tree is not one of the self-balancing varieties, insertion is , because the “tree” created by the successive insertions of sorted key is in fact a degenerate tree, a list. So, what if the list is already sorted and don’t really want to have a self-balancing tree? Let us make the simplifying assumption that we can have two types of nodes in the tree: leaves, that contains the actual data, and internal nodes (or just nodes for the remainder of this post) that holds only a key. The first strategy that comes to mind, using this assumption, is to use a method reminiscent of how Huffman Codes are constructed. (Notice the metaphor: leaves are green, internal nodes brown.) Then we do one pass of merges: Then another: …and finally: What do you notice? (as I show here). , so
Workflow Patterns | Patterns | Control Downloads of the original and revised control-flow patterns papers: N. Russell, A.H.M. ter Hofstede, W.M.P. van der Aalst, and N. Mulyar. Workflow Control-Flow Patterns: A Revised View. W.M.P van der Aalst, A.H.M. ter Hofstede, B. Introduction The Workflow Patterns Initiative was established with the aim of delineating the fundamental requirements that arise during business process modelling on a recurring basis and describe them in an imperative way. Revisiting the Original Patterns Here we present a revised description of the original twenty control-flow patterns previously presented in [vdAtHKB03]. New Control Flow Patterns Review of the patterns associated with the control-flow perspective over the past few years has led to the recognition that there are a number of distinct modelling constructs that can be identified during process modelling that are not adequately captured by the original set of twenty patterns. Basic Control Flow Patterns 1. 6. Multiple Instance Patterns 12. 16. 19.
Opinie > Meningen : Algoritmes Nemen Alles Over vrijdag 15 november 2013 | 29 reacties Althans als je een 'believer of algorithms' bent. Wat weet u van algoritmes? Mijn eerste ervaring met algoritmes is van drie jaar terug. U denkt, nou wow, knap. En ik u vertel dat je hiermee in milliseconden inzicht hebt in bijna de volledige werkelijkheid wat betreft werking, en vooral niet-werking, van interne-controlemaatregelen? Nog leuker wordt het als je met een aantal handelingen kan voorspellen hoe deze processen gaan opereren, door subprocesstappen weg te laten of toe te voegen. In mijn en ik hoop ook uw wereld van processen, transacties, risico's en interne controle gaat process mining iets heel 'groots' worden. Zover mijn wereld. Een robotstofzuiger aansturen en 'weten' wanneer uw vloer wel of niet schoon genoeg is. Bij dit laatste gaat het regelmatig fout. Zelf vind ik de inzet van algoritmes in de wereld van Venture Capitalists een bijzonder interessant aandachtsgebied. Opgelost! Pieter de Kok Reacties (29) | Reageer @Arnout van Kempen
Interception of Two Moving Objects in 2D Space Introduction This information will allow you to determine the direction that an object ("Chaser") must move so that it is able to intercept a target object ("Runner"). It assumes that you know the positions of both objects in 2D space. It assumes that you know the speed at which your Chaser can move. It assumes that you know the current speed and direction of the Runner. Both the Chaser and the Runner are abstracted to points on a plane. Background In most video games, it suffices to approximate real-world physical phenomena. In this article, I'll describe a process for finding an interception point assuming that inertia and acceleration are being approximated or ignored, and that the game can re-compute this interception point regularly (every game frame if needed). There is an article here that gives a very thorough methodology for doing a similar thing. This approach makes heavy use of vectors, described in great detail in many other articles. Some 2D Vector Math The Dot Product 2D vs 3D
Step Aside Google Image Search, Here’s an Algorithm that Knows What’s in a Picture The internet is a wealth of information. But you have to know what you’re looking for. If you only know a basic category—like that weird looking modern chair at your buddy’s office—not so good. Really what you want are all the specific variations of chairs, browsable by image, so you can recognize your target with a quick scan. A team of scientists from the University of Washington and the Allen Institute for Artificial Intelligence is developing a program that teaches itself all there is to know about a concept and presents the findings in pictures and phrases. To study a concept, LEVAN scans millions of books and images online. “It is all about discovering associations between textual and visual data,” said Ali Farhadi, a UW assistant professor of computer science and engineering. The software works great for concrete concepts like airplane or chair, less well for vaguer concepts like innovation (which turns up a large number of images of people talking, often in suits).
Visualizing Algorithms The power of the unaided mind is highly overrated… The real powers come from devising external aids that enhance cognitive abilities. —Donald Norman Algorithms are a fascinating use case for visualization. To visualize an algorithm, we don’t merely fit data to a chart; there is no primary dataset. Instead there are logical rules that describe behavior. But algorithms are also a reminder that visualization is more than a tool for finding patterns in data. #Sampling Before I can explain the first algorithm, I first need to explain the problem it addresses. Light — electromagnetic radiation — the light emanating from this screen, traveling through the air, focused by your lens and projected onto the retina — is a continuous signal. This reduction process is called sampling, and it is essential to vision. Sampling is made difficult by competing goals. Unfortunately, creating a Poisson-disc distribution is hard. Here’s how it works: Now here’s the code: The distance function is simple geometry:
List of algorithms From Wikipedia, the free encyclopedia The following is a list of algorithms along with one-line descriptions for each. Combinatorial algorithms General combinatorial algorithms Graph algorithms Graph drawing Network theory Routing for graphs Graph search Subgraphs Sequence algorithms Approximate sequence matching Sequence search Sequence merging Simple merge algorithmk-way merge algorithmUnion (merge, with elements on the output not repeated) Sequence permutations Fisher–Yates shuffle (also known as the Knuth shuffle): randomly shuffle a finite setSchensted algorithm: constructs a pair of Young tableaux from a permutationSteinhaus–Johnson–Trotter algorithm (also known as the Johnson–Trotter algorithm): generate permutations by transposing elementsHeap's permutation generation algorithm: interchange elements to generate next permutation Sequence alignment Sequence sorting Subsequences Substrings
Algorithm Flow chart of an algorithm (Euclid's algorithm) for calculating the greatest common divisor (g.c.d.) of two numbers a and b in locations named A and B. The algorithm proceeds by successive subtractions in two loops: IF the test B ≥ A yields "yes" (or true) (more accurately the numberb in location B is greater than or equal to the numbera in location A) THEN, the algorithm specifies B ← B − A (meaning the number b − a replaces the old b). Similarly, IF A > B, THEN A ← A − B. The process terminates when (the contents of) B is 0, yielding the g.c.d. in A. (Algorithm derived from Scott 2009:13; symbols and drawing style from Tausworthe 1977). In mathematics and computer science, an algorithm ( i/ˈælɡərɪðəm/ AL-gə-ri-dhəm) is a step-by-step procedure for calculations. Informal definition While there is no generally accepted formal definition of "algorithm," an informal definition could be "a set of rules that precisely defines a sequence of operations Formalization