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The Floyd–Warshall algorithm is an example of dynamic programming, and was published in its currently recognized form by Robert Floyd in 1962. [3] However, it is essentially the same as algorithms previously published by Bernard Roy in 1959 [4] and also by Stephen Warshall in 1962 [5] for finding the transitive closure of a graph, [6] and is closely related to Kleene's algorithm (published ...
Floyd's cycle-finding algorithm is a pointer algorithm that uses only two pointers, which move through the sequence at different speeds. It is also called the "tortoise and the hare algorithm", alluding to Aesop's fable of The Tortoise and the Hare. The algorithm is named after Robert W. Floyd, who was credited with its invention by Donald Knuth.
The description above uses Floyd's improved heap-construction algorithm, which operates in O(n) time and uses the same siftDown primitive as the heap-extraction phase. Although this algorithm, being both faster and simpler to program, is used by all practical heapsort implementations, Williams' original algorithm may be easier to understand ...
English: Demonstration of Floyd-Warshall algorithm for all-pairs shortest path on a directed graph with 4 vertices. At k=0, prior to the first iteration of the outer loop, the only known paths correspond to single edges in the original graph.
Robert W. Floyd [1] (born Robert Willoughby Floyd; June 8, 1936 – September 25, 2001) was an American computer scientist. His contributions include the design of the Floyd–Warshall algorithm (independently of Stephen Warshall ), which efficiently finds all shortest paths in a graph and his work on parsing ; Floyd's cycle-finding algorithm ...
Floyd–Steinberg dithering is an image dithering algorithm first published in 1976 by Robert W. Floyd and Louis Steinberg. It is commonly used by image manipulation software. For example when converting an image from a Truecolor 24-bit PNG format into a GIF format, which is restricted to a maximum of 256 colors.
Hoare logic (also known as Floyd–Hoare logic or Hoare rules) is a formal system with a set of logical rules for reasoning rigorously about the correctness of computer programs. It was proposed in 1969 by the British computer scientist and logician Tony Hoare , and subsequently refined by Hoare and other researchers. [ 1 ]
For example, Floyd–Warshall algorithm, the shortest path between a start and goal vertex in a weighted graph can be found using the shortest path to the goal from all adjacent vertices. Dynamic programming and memoization go together. Unlike divide and conquer, dynamic programming subproblems often overlap.