Algorithm X is an algorithm for solving the exact cover problem. It is a straightforward recursive, nondeterministic, depth-first, backtracking algorithm used by Donald Knuth to demonstrate an efficient implementation called DLX, which uses the dancing links technique. The exact cover problem is represented in Algorithm X by a matrix A consisting of 0s and 1s. The goal is to select a subset of the rows such that the digit 1 appears in each column exactly once. Algorithm X works as follows: # If the matrix A has no columns, the current partial solution is a valid solution; terminate successfully. 1. * Otherwise choose a column c (deterministically). 2. * Choose a row r such that Ar, c = 1 (nondeterministically). 3. * Include row r in the partial solution. 4. * For each column j such that Ar, j = 1,for each row i such that Ai, j = 1,delete row i from matrix A.delete column j from matrix A. 5. * Repeat this algorithm recursively on the reduced matrix A. The nondeterministic choice of r means that the algorithm recurses over independent subalgorithms; each subalgorithm inherits the current matrix A, but reduces it with respect to a different row r.If column c is entirely zero, there are no subalgorithms and the process terminates unsuccessfully. The subalgorithms form a search tree in a natural way, with the original problem at the root and with level k containing each subalgorithm that corresponds to k chosen rows.Backtracking is the process of traversing the tree in preorder, depth first. Any systematic rule for choosing column c in this procedure will find all solutions, but some rules work much better than others.To reduce the number of iterations, Knuth suggests that the column-choosing algorithm select a column with the smallest number of 1s in it. (Wikipedia).
Introduction to additive combinatorics lecture 1.8 --- Plünnecke's theorem
In this video I present a proof of Plünnecke's theorem due to George Petridis, which also uses some arguments of Imre Ruzsa. Plünnecke's theorem is a very useful tool in additive combinatorics, which implies that if A is a set of integers such that |A+A| is at most C|A|, then for any pair
From playlist Introduction to Additive Combinatorics (Cambridge Part III course)
Lecture: Iteration Methods for Ax-b
This details how to apply a simple iteration procedure for solving Ax=b, including Jacobi iterations and Gauss-Siedel modifications.
From playlist Beginning Scientific Computing
Polynomial approximation of functions (part 1)
Using a polynomial to approximate a function at f(0). More free lessons at: http://www.khanacademy.org/video?v=sy132cgqaiU
From playlist Calculus
Solving the Bernoulli Differential Equation x^2(dy/dx) + y^2 = xy
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys How to solve a Bernoulli Differential Equation
From playlist Differential Equations
Illustrates the solution of a Bernoulli first-order differential equation. Free books: http://bookboon.com/en/differential-equations-with-youtube-examples-ebook http://www.math.ust.hk/~machas/differential-equations.pdf
From playlist Differential Equations with YouTube Examples
Ex: Newton's Method to Approximate Zeros -- 2 Iterations
This video provides an example of how to approximate zeros or roots of a polynomial equation using Newton's Method. Two iterations are provided. Site: http://mathispower4u.com
From playlist Newton’s Method and L’Hopital’s Rule
[Calculus] Newton's Method || Lecture 36
Visit my website: http://bit.ly/1zBPlvm Subscribe on YouTube: http://bit.ly/1vWiRxW Hello, welcome to TheTrevTutor. I'm here to help you learn your college courses in an easy, efficient manner. If you like what you see, feel free to subscribe and follow me for updates. If you have any que
From playlist Calculus 1
Newton's Method: Perform One Iteration Using Desmos (y=(ln x)/x)
This video explains how to perform one iteration of Newton's method to approximate the zero or x-intercept of a rational function.
From playlist Newton’s Method and L’Hopital’s Rule
This video explains Newton's Method and provides an example. It also shows how to use the table feature of the graphing calculator to perform the calculations needed for Newton's Method. http://mathispower4u.wordpress.com/
From playlist Newton’s Method and L’Hopital’s Rule
A Mathematical Definition of an Algorithm | The Art Of Computer Programming Visualised #SoME1
A visual explanation of the mathematical definition of an algorithm inspired by the book series "The Art of Computer Programming" by Donald Knuth. Timestamps: 0:00 0. Motivation 1:05 1. High-level Overview 3:23 2. Implementation 6:11 3.1 States 7:46 3.2 State Transitions 9:36 4. A Side No
From playlist Summer of Math Exposition Youtube Videos
Stanford Lecture: Donald Knuth—"Universal Commafree Codes" (2015)
Donald Knuth's 21st Annual Christmas Lecture: Universal Commafree Codes December 3, 2015 A commafree code is a set of codewords that can be read easily without spaces or other delimiters between words. In 1965, Willard Eastman discovered a beautiful but underappreciated way to construct
From playlist Donald Knuth Lectures
Stanford Lecture - Don Knuth: The Analysis of Algorithms (2015, recreating 1969)
Known as the Father of Algorithms, Professor Donald Knuth, recreates his very first lecture taught at Stanford Univeristy. Professor Knuth is an American computer scientist, mathematician, and professor emeritus at Stanford University.
From playlist Donald Knuth Lectures
Stanford Lecture: "Aha" Sessions - Problem 3 - Hardware fault detection Part 6
February 21, 1985 Notes from these problem sessions were published as A Programming and Problem-Solving Seminar, Stanford Technical Report No. STAN-CS-85-1055. (http://www-cs-faculty.stanford.edu/~knuth/papers/cs1055.pdf) Professor Knuth is the Professor Emeritus at Stanford University.
From playlist Donald Knuth Lectures
Stanford Lecture: Don Knuth—"A Conjecture That Had To Be True" (2017)
Donald Knuth's 23rd Annual Christmas Tree Lecture: A Conjecture That Had To Be True Speaker: Donald Knuth 2017 A few months ago, the speaker did some extensive calculations relating to a curious problem in combinatorial geometry; and the resulting numbers satisfied an amazing formula. Al
From playlist Donald Knuth Lectures
Stanford Lecture: Mathematical Writing - Refereeing (2)
The class notes are available as a Stanford report, Mathematical Writing (http://www-cs-faculty.stanford.edu/~knuth/papers/cs1193.pdf), and a published book (http://www-cs-faculty.stanford.edu/~knuth/klr.html). November 2, 1987 Professor Knuth is the Professor Emeritus at Stanford Univer
From playlist Donald Knuth Lectures
Stanford Lecture: Donald Knuth - "Trees and chordal graphs" (2012)
Professor Knuth's 18th Annual Christmas Tree Lecture at Stanford December 14, 2012 Chordal graphs—also known as triangulated graphs or perfect-elimination graphs—are perhaps the most important generalizations of trees. Many graph-theoretical problems can be solved much more efficiently on
From playlist Donald Knuth Lectures
Stanford Lecture: Donald Knuth - "Bayesian trees and BDDs" (2011)
December 8th, 2011 Professor Donald Knuth's 17th annual Christmas Tree Lecture. Knuth explains how to apply elementary BDD technology so that the probability of such events (and many others) can be computed in polynomial time. Learn more: http://scpd.stanford.edu/knuth/index.jsp
From playlist Donald Knuth Lectures
Stanford Lecture: Mathematical Writing - Illustrations (1)
The class notes are available as a Stanford report, Mathematical Writing (http://www-cs-faculty.stanford.edu/~knuth/papers/cs1193.pdf), and a published book (http://www-cs-faculty.stanford.edu/~knuth/klr.html). November 4, 1987 Professor Knuth is the Professor Emeritus at Stanford Univer
From playlist Donald Knuth Lectures
Solve a Bernoulli Differential Equation Initial Value Problem
This video provides an example of how to solve an Bernoulli Differential Equations Initial Value Problem. The solution is verified graphically. Library: http://mathispower4u.com
From playlist Bernoulli Differential Equations