Trees (data structures) | Analysis of algorithms | Combinatorial game theory
In computing, tree data structures, and game theory, the branching factor is the number of children at each node, the outdegree. If this value is not uniform, an average branching factor can be calculated. For example, in chess, if a "node" is considered to be a legal position, the average branching factor has been said to be about 35, and a statistical analysis of over 2.5 million games revealed an average of 31. This means that, on average, a player has about 31 to 35 legal moves at their disposal at each turn. By comparison, the average branching factor for the game Go is 250. Higher branching factors make algorithms that follow every branch at every node, such as exhaustive brute force searches, computationally more expensive due to the exponentially increasing number of nodes, leading to combinatorial explosion. For example, if the branching factor is 10, then there will be 10 nodes one level down from the current position, 102 (or 100) nodes two levels down, 103 (or 1,000) nodes three levels down, and so on. The higher the branching factor, the faster this "explosion" occurs. The branching factor can be cut down by a pruning algorithm. The average branching factor can be quickly calculated as the number of non-root nodes (the size of the tree, minus one; or the number of edges) divided by the number of non-leaf nodes (the number of nodes with children). (Wikipedia).
Ex: Exponential Functions: Growth Rate and Growth Factor
This video explains to to find the growth rate as a decimal and a percent and how to find the growth factor. Site: http://mathispower4u.com
From playlist Solving Applications of Exponential Growth and Decay
What is Decay Factor, Decay Rate, Growth Factor, Growth Rate?
Learn the difference between decay factor, decay rate, growth factor and growth rate in this free math video tutorial by Mario's Math Tutoring. We also discuss some examples. 0:27 Formula for exponential growth or decay 1:30 Example of decay rate and the decay factor 2:24 Example of grow
From playlist Algebra 1
Introduction to Exponential Functions in the Form f(x)=ab^x - Part 1
This video introduces exponential growth and exponential decay functions in the form y=ab^x. http://mathispower4u.com
From playlist Introduction to Exponential Functions
Algebra - Factoring by General Trinomials 2/3
Visit http://ilectureonline.com for more math and science lectures! In this lecture series I'll show you how to factor a polynomial by using the factoring by general trinomials.
From playlist ALGEBRA 30 - FACTORING
KS5 - Exponential Graphs & Exponential Modelling
"Graphs of exponential functions, including y = e^(ax+b) + c. Modelling of exponential growth and decay."
From playlist KS5 - Logs & Logarithms
Applying Exponential Models // Math Minute [#34] [ALGEBRA]
Exponential functions work a lot like linear functions. There are typically two parameters that guide the use of the exponential function: the initial value (like the y-intercept of a linear function) and the factor of growth (like the slope of a linear function). There are some additional
From playlist Math Minutes
Compare Linear and Exponential Growth Using Recursive and Explicit Equations
This video explains the different between linear and exponential growth. Both recursive and explicit equations are discussed. Site: http://mathispower4u.com
From playlist Linear, Exponential, and Logistic Growth: Recursive/Explicit
Factoring a polynomial to the fourth power using factoring to second power
👉 In this polynomial, I will show you how to factor different types of polynomials. Such as polynomials with two, three, and four terms in addition to polynomials to the second third, fourth, fifth, and sixth power. 👏SUBSCRIBE to my channel here: https://www.youtube.com/user/mrbrianmclo
From playlist A/B Test #561-590
Complex Analysis: Dogbone Contour Example #2
Today, we evaluate a viewer suggested integral using contour integration.
From playlist Contour Integration
Complex Analysis: Dogbone Contour Example #3
Today, we evaluate the integral from -1 to 1 of sqrt(1-x^2)/(1+x^2). Tried to one take this video (this video is straight from the camera) so it's not as smooth as the others. Might try to do this more often as editing can take a while, and probably not worth it to correct minor mistakes o
From playlist Contour Integration
i^i and other complex powers -- Complex Analysis 5
⭐Support the channel⭐ Patreon: https://www.patreon.com/michaelpennmath Merch: https://teespring.com/stores/michael-penn-math My amazon shop: https://www.amazon.com/shop/michaelpenn ⭐my other channels⭐ Main Channel: https://www.youtube.com/michaelpennmath non-math podcast: http
From playlist Complex Analysis
Prime factorization and factor trees. Every composite number can be written as a product of powers of prime numbers. A factor tree shows the prime factors of a composite number. For the playlist of indicies and prime numbers. https://www.youtube.com/playlist?list=PLjbxBzUM6SLljxglRaecKX
From playlist Indicies (Exponents) and Primes
How embryos build organs to last a lifetime
How embryos build organs to last a lifetime, Croonian Lecture 2014 by Professor Brigid Hogan FRS. All the organs of our body originate from small founder populations of cells which multiply into complex structures. Adult stem cells are used to maintain organs throughout adult life and to
From playlist Latest talks and lectures
Sketch the graph of a factored polynomial using multiplicity
👉 Learn how to use the tools needed to graph a polynomial function in factored form. A polynomial in factored form is when the polynomial is written as a product of its linear factors. Each linear factor represents an x-intercept and the power of the factor represents the multiplicity. Wh
From playlist Graph a Polynomial Function in Factored Form
ʕ•ᴥ•ʔ Prime Factorization - Made Easy | StudyPug
Quickly master prime factorization! Watch more lessons like this and try our practice at https://www.studypug.com/basic-math-help/factors-and-multiples/prime-factorization Watch more step by step examples at https://www.studypug.com === Follow us YOUTUBE http://www.youtube.com/c/Stud
From playlist GCSE Exam Prep
Beata Randrianantoanina: On a difference between two methods of low-distortion embeddings of...
Abstract: In a recent paper, the speaker and M.I. Ostrovskii developed a new metric embedding method based on the theory of equal-signs-additive (ESA) sequences developed by Brunel and Sucheston in 1970’s. This method was used to construct bilipschitz embeddings of diamond and Laakso graph
From playlist Analysis and its Applications
14. P and NP, SAT, Poly-Time Reducibility
MIT 18.404J Theory of Computation, Fall 2020 Instructor: Michael Sipser View the complete course: https://ocw.mit.edu/18-404JF20 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP60_JNv2MmK3wkOt9syvfQWY Quickly reviewed last lecture. Defined NTIME(t(n)) complexity classes
From playlist MIT 18.404J Theory of Computation, Fall 2020
Characterizing force-chain network architecture in granular materials - Danielle Bassett
Danielle Bassett University of Pennsylvania April 18, 2015 Force chains form heterogeneous physical structures that can constrain the mechanical stability and acoustic transmission of granular media. However, despite their relevance for predicting bulk properties of materials, there is no
From playlist Mathematics
Introduction to Exponential Equations in Two Variables
This video introduces linear equations in the form y=a(b)^x. http://mathispower4u.com
From playlist Introduction to Exponential Functions
Complex Analysis: Double Keyhole Contour
Today, we use contour integration to integrate 1/(x*sqrt(x^2-1)) from 1 to infinity.
From playlist Contour Integration