Heaps (data structures) | Fibonacci numbers | Amortized data structures
In computer science, a Fibonacci heap is a data structure for priority queue operations, consisting of a collection of heap-ordered trees. It has a better amortized running time than many other priority queue data structures including the binary heap and binomial heap. Michael L. Fredman and Robert E. Tarjan developed Fibonacci heaps in 1984 and published them in a scientific journal in 1987. Fibonacci heaps are named after the Fibonacci numbers, which are used in their running time analysis. For the Fibonacci heap, the find-minimum operation takes constant (O(1)) amortized time. The insert and decrease key operations also work in constant amortized time. Deleting an element (most often used in the special case of deleting the minimum element) works in O(log n) amortized time, where n is the size of the heap. This means that starting from an empty data structure, any sequence of a insert and decrease key operations and b delete operations would take O(a + b log n) worst case time, where n is the maximum heap size. In a binary or binomial heap, such a sequence of operations would take O((a + b) log n) time. A Fibonacci heap is thus better than a binary or binomial heap when b is smaller than a by a non-constant factor. It is also possible to merge two Fibonacci heaps in constant amortized time, improving on the logarithmic merge time of a binomial heap, and improving on binary heaps which cannot handle merges efficiently. Using Fibonacci heaps for priority queues improves the asymptotic running time of important algorithms, such as Dijkstra's algorithm for computing the shortest path between two nodes in a graph, compared to the same algorithm using other slower priority queue data structures. (Wikipedia).
Fibonacci Heaps or "How to invent an extremely clever data structure"
I want to tell you about a daunting, but truly fascinating data structure. At first sight, Fibonacci Heaps can seem intimidating. In this video, I'm going to show you all the necessary steps to invent a really clever data structure. 00:00 Introduction 00:50 Priority Queues and Binary Heap
From playlist Advanced Algorithms/Data Structures
Fibonacci heaps in 6 minutes — Intro
Introduction to Fibonacci heaps. Code: https://github.com/msambol/youtube/blob/master/data_structures/fibonacci_heap.py Sources: 1. https://www.amazon.com/Introduction-Algorithms-3rd-MIT-Press/dp/0262033844 2. https://github.com/danielborowski/fibonacci-heap-python Performance discussi
From playlist Data Structures // Michael Sambol
Fibonacci heaps in 6 minutes — Insert & Union
Examples of inserting nodes into Fibonacci heaps and the union of two Fibonacci heaps. Code: https://github.com/msambol/youtube/blob/master/data_structures/fibonacci_heap.py Sources: 1. https://www.amazon.com/Introduction-Algorithms-3rd-MIT-Press/dp/0262033844 2. https://github.com/dani
From playlist Data Structures // Michael Sambol
STAIRS reveal the relationship between Fibonacci and combinatorics
Part I: https://youtu.be/Hl61mJxILA4 Source of the beautiful thumbnail: https://www.videoblocks.com/video/winter-stargate-deep-space-fibonacci-spiral-infinite-zoom-scl2tvcpliylych5s I am still surprised at why I have not thought of this more direct linkage between Fibonacci numbers and c
From playlist Fibonacci
Help me create more free content! =) https://www.patreon.com/mathable Merch :v - https://papaflammy.myteespring.co/ https://www.amazon.com/shop/flammablemaths https://shop.spreadshirt.de/papaflammy Become a Member of the Flammily! :0 https://www.youtub
From playlist Number Theory
This video introduces the Fibonacci sequence and provides several examples of where the Fibonacci sequence appear in nature. http:mathispower4u.com
From playlist Mathematics General Interest
Exercise - Write a Fibonacci Function
Introduction to the Fibonacci Sequence and a programming challenge
From playlist Computer Science
Fibonacci numbers and the golden ratio | Lecture 4 | Fibonacci Numbers and the Golden Ratio
Relationship between the Fibonacci numbers and the golden ratio. The ratio of consecutive Fibonacci numbers approaches the golden ratio. Join me on Coursera: https://www.coursera.org/learn/fibonacci Lecture notes at http://www.math.ust.hk/~machas/fibonacci.pdf Subscribe to my channel: h
From playlist Fibonacci Numbers and the Golden Ratio
Week 5: Wednesday - CS50 2007 - Harvard University
Structures. Dynamic memory allocation. Pointers. Heap. Digital forensics. File I/O.
From playlist CS50 Lectures 2007
The Fibonacci bamboozlement | Lecture 8 | Fibonacci Numbers and the Golden Ratio
Explanation of the Fibonacci bamboozlement. The Fibonacci bamboozlement is a dissection fallacy where the rearrangement of pieces in a square can be used to construct a rectangle with one unit of area larger or smaller than that of the square. The square and rectangle have side lengths gi
From playlist Fibonacci Numbers and the Golden Ratio
RustConf 2019 - Taking Constant Evaluation to the Limit by Oliver Schneider
RustConf 2019 - Taking Constant Evaluation to the Limit by Oliver Schneider Have you ever wanted to write a static with a complex initial value? Are you programming microcontrollers? Do you want to run as little code as possible at runtime or are you trying to reduce your memory footprint
From playlist RustConf 2019
Xavier Viennot: Heaps and lattice paths
CIRM HYBRID EVENT Recorded during the meeting "Lattice Paths, Combinatorics and Interactions" the June 25, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians
From playlist Combinatorics
Dijkstra's Shortest Path Algorithm | Graph Theory
Explanation of Dijkstra's shortest path algorithm Dijkstra source code on Algorithms repository: https://github.com/williamfiset/algorithms#graph-theory Video slides: https://github.com/williamfiset/Algorithms/tree/master/slides Indexed Priority Queue Video: https://youtu.be/jND_WJ8r7FE
From playlist Graph Theory Playlist
Lets learn Rust together: Warmup up with Brooks live stream day 10
Live stream where I (Brooks) wake myself up in the morning with silly side projects and algorithm practice. This stream is scheduled for 7am Mountain Time every weekday. I tweet out shortly before I begin each stream, and definitely if I am going to miss a stream. Currently I am learning
From playlist Rust Book
Priority Queue Inserting Elements
Related Videos: Priority queue intro: https://www.youtube.com/watch?v=wptevk0bshY Priority queue min/max heaps: https://www.youtube.com/watch?v=HCEr35qpawQ Priority queue insertion: https://www.youtube.com/watch?v=QOJ-CmQiXko Priority queue removals: https://www.youtube.com/watch?v=eVq8Cmo
From playlist Data structures playlist
RubyConf 2021 - Picoruby and PRK Firmware by Hitoshi Hasumi
PicoRuby is an alternative implementation of the mruby interpreter which runs on one-chip microcontrollers. PRK Firmware is the world's first keyboard firmware framework in Ruby. You can write not only your own "keymap" in PicoRuby but also configure additional behavior with Ruby's featur
From playlist RubyConf 2021
What do Fibonacci numbers have to do with combinatorics?
Part II: https://youtu.be/_RHXmGWXUvw Note: You ABSOLUTELY DON'T NEED TO HAVE KNOWN ANY COMBINATORICS because the combinatorics required in this video would be explained thoroughly. Source of the beautiful thumbnail: https://www.videoblocks.com/video/winter-stargate-deep-space-fibonacci-
From playlist Fibonacci