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In mathematics, Pascal's triangle is an infinite triangular array of the binomial coefficients which play a crucial role in probability theory, combinatorics, and algebra.In much of the Western world, it is named after the French mathematician Blaise Pascal, although other mathematicians studied it centuries before him in Persia, [1] India, [2] China, Germany, and Italy.
The earliest extant Chinese illustration of 'Pascal's triangle' is from Yang's book Xiángjiě Jiǔzhāng Suànfǎ (詳解九章算法) [1] of 1261 AD, in which Yang acknowledged that his method of finding square roots and cubic roots using "Yang Hui's Triangle" was invented by mathematician Jia Xian [2] who expounded it around 1100 AD, about 500 years before Pascal.
Flowchart of using successive subtractions to find the greatest common divisor of number r and s. In mathematics and computer science, an algorithm (/ ˈ æ l ɡ ə r ɪ ð əm / ⓘ) is a finite sequence of mathematically rigorous instructions, typically used to solve a class of specific problems or to perform a computation. [1]
Hasse diagram of the search graph of the algorithm for 3 variables. Given e.g. the subset = {, ¯, ¯, ¯ ¯, ¯ ¯} of the bottom-level nodes (light green), the algorithm computes a minimal set of nodes (here: {¯,}, dark green) that covers exactly .
Roberto Rossellini directed a filmed biopic, Blaise Pascal, which originally aired on Italian television in 1971. [61] Pascal was a subject of the first edition of the 1984 BBC Two documentary, Sea of Faith, presented by Don Cupitt. The chameleon in the animated film Tangled is named for Pascal. A programming language is named for Pascal.
For a grid map from a video game, using the Taxicab distance or the Chebyshev distance becomes better depending on the set of movements available (4-way or 8-way). If the heuristic h satisfies the additional condition h ( x ) ≤ d ( x , y ) + h ( y ) for every edge ( x , y ) of the graph (where d denotes the length of that edge), then h is ...
The starting point is on the line (,) =only because the line is defined to start and end on integer coordinates (though it is entirely reasonable to want to draw a line with non-integer end points).
The Bellman–Ford algorithm is an algorithm that computes shortest paths from a single source vertex to all of the other vertices in a weighted digraph. [1] It is slower than Dijkstra's algorithm for the same problem, but more versatile, as it is capable of handling graphs in which some of the edge weights are negative numbers. [2]