Fisher–Yates Shuffle. Say you had a fresh pack of cards: If you want to play a game of Texas Hold ‘em with friends, you should shuffle the deck first to randomize the order and insure a fair game. But how? A simple but effective way of doing this is to pull a random card from the deck repeatedly and set it aside, incrementally building a new stack. As long as you pick each remaining card from the deck with equal probability, you’ll have a perfectly-unbiased random stack when you’re done: But let’s say instead of a physical deck of cards, you wanted to write code to perform this same task with an in-memory array of n elements. One slow option—gotta start somewhere: pick a random element from the array (in [0, n - 1]) and then check if you’ve shuffled that element already.
Here’s what the implementation looks like in JavaScript, not that you should use it: This is bad, and we can do better. This works pretty well, but it still has relatively poor quadratic performance. Comments? Data Structure Visualization. Data Structure Visualization. Algorithms, 4th Edition by Robert Sedgewick and Kevin Wayne. Quaternions. This page is an introduction to Quaternions, the pages below this have more detail about their algebra and how to use them to represent 3D rotations. Introduction Quaternions were discovered on 16 October 1843 by William Rowan Hamilton. He spent years trying to find a three dimensional number systems, but with no success, when he looked in 4 dimensions instead of 3 it worked.
Quaternions form an interesting algebra where each object contains 4 scalar variables (sometimes known as Euler Parameters not to be confused with Euler angles), these objects can be added and multiplied as a single unit in a similar way to the usual algebra of numbers. The arithmetic of quaternions, such as how to do addition and multiplication, is explained on this page. On this page we will introduce quaternions as an extension of complex numbers with two additional imaginary dimensions, however there are other ways to think about quaternions and other notations for quaternions which are described on this page. Algorithms, 4th Edition by Robert Sedgewick and Kevin Wayne. Introduction to Algorithms. Table of Contents I Foundations Introduction 3 1 The Role of Algorithms in Computing 5 1.1 Algorithms 5 1.2 Algorithms as a technology 11 2 Getting Started 16 2.1 Insertion sort 16 2.2 Analyzing algorithms 23 2.3 Designing algorithms 29 3 Growth of Functions 43 3.1 Asymptotic notation 43 3.2 Standard notations and common functions 53 4 Divide-and-Conquer 65 4.1 The maximum-subarray problem 68 4.2 Strassen's algorithm for matrix multiplication 75 4.3 The substitution method for solving recurrences 83 4.4 The recursion-tree method for solving recurrences 88 4.5 The master method for solving recurrences 93 4.6 Proof of the master theorem 97 5 Probabilistic Analysis and Randomized Algorithms 114 5.1 The hiring problem 114 5.2 Indicator random variables 118 5.3 Randomized algorithms 122 5.4 Probabilistic analysis and further uses of indicator random variables 130 II Sorting and Order Statistics Introduction 147 6 Heapsort 151 6.1 Heaps 151 6.2 Maintaining the heap property 154 6.3 Building a heap 156 7 Quicksort 170 Index.
Lecture Slides for Algorithm Design by Jon Kleinberg And Éva Tardos. Cours informatique de haut niveau en ligne - Formation informatique. Octave. GNU Octave is a high-level interpreted language, primarily intended for numerical computations. It provides capabilities for the numerical solution of linear and nonlinear problems, and for performing other numerical experiments. It also provides extensive graphics capabilities for data visualization and manipulation. Octave is normally used through its interactive command line interface, but it can also be used to write non-interactive programs.
The Octave language is quite similar to Matlab so that most programs are easily portable. Octave is distributed under the terms of the GNU General Public License. Version 4.0.0 has been released and is now available for download. An official Windows binary installer is also available from Thanks to the many people who contributed to this release! Public Domain Aeronautical Software (PDAS) Bit Twiddling Hacks. By Sean Eron Anderson seander@cs.stanford.edu Individually, the code snippets here are in the public domain (unless otherwise noted) — feel free to use them however you please.
The aggregate collection and descriptions are © 1997-2005 Sean Eron Anderson. The code and descriptions are distributed in the hope that they will be useful, but WITHOUT ANY WARRANTY and without even the implied warranty of merchantability or fitness for a particular purpose. As of May 5, 2005, all the code has been tested thoroughly. Thousands of people have read it. Moreover, Professor Randal Bryant, the Dean of Computer Science at Carnegie Mellon University, has personally tested almost everything with his Uclid code verification system. What he hasn't tested, I have checked against all possible inputs on a 32-bit machine.
Contents About the operation counting methodology When totaling the number of operations for algorithms here, any C operator is counted as one operation. Compute the sign of an integer. Essential Math for Games Programmers. As the quality of games has improved, more attention has been given to all aspects of a game to increase the feeling of reality during gameplay and distinguish it from its competitors. Mathematics provides much of the groundwork for this improvement in realism. And a large part of this improvement is due to the addition of physical simulation. Creating such a simulation may appear to be a daunting task, but given the right background it is not too difficult, and can add a great deal of realism to animation systems, and interactions between avatars and the world. This tutorial deepens the approach of the previous years' Essential Math for Games Programmers, by spending one day on general math topics, and one day focusing in on the topic of physical simulation.
It, like the previous tutorials, provides a toolbox of techniques for programmers, with references and links for those looking for more information. Topics for the various incarnations of this tutorial can be found below. Slides. Big-O Algorithm Complexity Cheat Sheet. Statistical Formulas For Programmers. By Evan Miller DRAFT: May 19, 2013 Being able to apply statistics is like having a secret superpower. Where most people see averages, you see confidence intervals. When someone says “7 is greater than 5,” you declare that they're really the same. In a cacophony of noise, you hear a cry for help. Unfortunately, not enough programmers have this superpower. As my modest contribution to developer-kind, I've collected together the statistical formulas that I find to be most useful; this page presents them all in one place, a sort of statistical cheat-sheet for the practicing programmer. Most of these formulas can be found in Wikipedia, but others are buried in journal articles or in professors' web pages.
Send suggestions and corrections to emmiller@gmail.com Table of Contents 1. One of the first programming lessons in any language is to compute an average. 1.1 Corrected Standard Deviation The standard deviation is a single number that reflects how spread out the data actually is. Where: SE=s√N 2. 3. Algorithms. Eulerian Video Magnification. Banner slider Many seemingly static scenes contain subtle changes that are invisible to the naked human eye. However, it is possible to pull out these small changes from videos through the use of algorithms we have developed.
We give a way to visualize these small changes by amplifying them and we present algorithms to pull out interesting signals from these videos, such as the human pulse, sound from vibrating objects and the motion of hot air. Videos Software and Code Eulerian Video Magnification code Matlab code and executables implementing Eulerian video processing for amplifying color and motion changes. Phase Based Video Motion Processing code Matlab code for implementing the new and improved phase-based motion magnification pipeline.
Videoscope Web interface for motion and color magnification. Publications (Magnifying Motion and Color Changes) Publications (Analysis of Small Motions) People Faculty: Students, Postdocs and Affiliates: Collaborators: Edward H. Talks. Scientists Uncover Invisible Motion in Video.