B-Crypt algorithm - traduction vers Anglais
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B-Crypt algorithm - traduction vers Anglais

ALGORITHM THAT COMPUTES THE GREATEST COMMON DIVISOR OF TWO INTEGERS USING ONLY ARITHMETIC SHIFTS, COMPARISONS, AND SUBTRACTION
Binary gcd algorithm; Binary gcd; Knuth's algorithm B; Stein's Algorithm; Binary Euclidean algorithm; Stein's algorithm

algorithm         
  • Alan Turing's statue at [[Bletchley Park]]
  • The example-diagram of Euclid's algorithm from T.L. Heath (1908), with more detail added. Euclid does not go beyond a third measuring and gives no numerical examples. Nicomachus gives the example of 49 and 21: "I subtract the less from the greater; 28 is left; then again I subtract from this the same 21 (for this is possible); 7 is left; I subtract this from 21, 14 is left; from which I again subtract 7 (for this is possible); 7 is left, but 7 cannot be subtracted from 7." Heath comments that "The last phrase is curious, but the meaning of it is obvious enough, as also the meaning of the phrase about ending 'at one and the same number'."(Heath 1908:300).
  • "Inelegant" is a translation of Knuth's version of the algorithm with a subtraction-based remainder-loop replacing his use of division (or a "modulus" instruction). Derived from Knuth 1973:2–4. Depending on the two numbers "Inelegant" may compute the g.c.d. in fewer steps than "Elegant".
  • 1=IF test THEN GOTO step xxx}}, shown as diamond), the unconditional GOTO (rectangle), various assignment operators (rectangle), and HALT (rectangle). Nesting of these structures inside assignment-blocks results in complex diagrams (cf. Tausworthe 1977:100, 114).
  • A graphical expression of Euclid's algorithm to find the greatest common divisor for 1599 and 650 <syntaxhighlight lang="text" highlight="1,5"> 1599 = 650×2 + 299 650 = 299×2 + 52 299 = 52×5 + 39 52 = 39×1 + 13 39 = 13×3 + 0</syntaxhighlight>
SEQUENCE OF INSTRUCTIONS TO PERFORM A TASK
Algorithmically; Computer algorithm; Properties of algorithms; Algorithim; Algoritmi de Numero Indorum; Algoritmi de numero indorum; Algoritmi De Numero Indorum; Алгоритм; Algorithem; Software logic; Computer algorithms; Encoding Algorithm; Naive algorithm; Naïve algorithm; Algorithm design; Algorithm segment; Algorithmic problem; Algorythm; Rule set; Continuous algorithm; Algorithms; Software-based; Algorithmic method; Algorhthym; Algorthym; Algorhythms; Formalization of algorithms; Mathematical algorithm; Draft:GE8151 Problem Solving and Python Programming; Computational algorithms; Optimization algorithms; Algorithm classification; History of algorithms; Patented algorithms; Algorithmus
algorithm noun math. алгоритм algorithm validation - проверка правильности алгоритма
algorithmic method         
  • Alan Turing's statue at [[Bletchley Park]]
  • The example-diagram of Euclid's algorithm from T.L. Heath (1908), with more detail added. Euclid does not go beyond a third measuring and gives no numerical examples. Nicomachus gives the example of 49 and 21: "I subtract the less from the greater; 28 is left; then again I subtract from this the same 21 (for this is possible); 7 is left; I subtract this from 21, 14 is left; from which I again subtract 7 (for this is possible); 7 is left, but 7 cannot be subtracted from 7." Heath comments that "The last phrase is curious, but the meaning of it is obvious enough, as also the meaning of the phrase about ending 'at one and the same number'."(Heath 1908:300).
  • "Inelegant" is a translation of Knuth's version of the algorithm with a subtraction-based remainder-loop replacing his use of division (or a "modulus" instruction). Derived from Knuth 1973:2–4. Depending on the two numbers "Inelegant" may compute the g.c.d. in fewer steps than "Elegant".
  • 1=IF test THEN GOTO step xxx}}, shown as diamond), the unconditional GOTO (rectangle), various assignment operators (rectangle), and HALT (rectangle). Nesting of these structures inside assignment-blocks results in complex diagrams (cf. Tausworthe 1977:100, 114).
  • A graphical expression of Euclid's algorithm to find the greatest common divisor for 1599 and 650 <syntaxhighlight lang="text" highlight="1,5"> 1599 = 650×2 + 299 650 = 299×2 + 52 299 = 52×5 + 39 52 = 39×1 + 13 39 = 13×3 + 0</syntaxhighlight>
SEQUENCE OF INSTRUCTIONS TO PERFORM A TASK
Algorithmically; Computer algorithm; Properties of algorithms; Algorithim; Algoritmi de Numero Indorum; Algoritmi de numero indorum; Algoritmi De Numero Indorum; Алгоритм; Algorithem; Software logic; Computer algorithms; Encoding Algorithm; Naive algorithm; Naïve algorithm; Algorithm design; Algorithm segment; Algorithmic problem; Algorythm; Rule set; Continuous algorithm; Algorithms; Software-based; Algorithmic method; Algorhthym; Algorthym; Algorhythms; Formalization of algorithms; Mathematical algorithm; Draft:GE8151 Problem Solving and Python Programming; Computational algorithms; Optimization algorithms; Algorithm classification; History of algorithms; Patented algorithms; Algorithmus

математика

алгоритмический метод

Euclidean algorithm         
  • A 24-by-60 rectangle is covered with ten 12-by-12 square tiles, where 12 is the GCD of 24 and 60. More generally, an ''a''-by-''b'' rectangle can be covered with square tiles of side-length ''c'' only if ''c'' is a common divisor of ''a'' and ''b''.
  • Plot of a linear [[Diophantine equation]], 9''x''&nbsp;+&nbsp;12''y''&nbsp;=&nbsp;483. The solutions are shown as blue circles.
  • cube root of 1]].
  • Subtraction-based animation of the Euclidean algorithm. The initial rectangle has dimensions ''a''&nbsp;=&nbsp;1071 and ''b''&nbsp;=&nbsp;462. Squares of size 462&times;462 are placed within it leaving a 462&times;147 rectangle. This rectangle is tiled with 147&times;147 squares until a 21&times;147 rectangle is left, which in turn is tiled with 21&times;21 squares, leaving no uncovered area. The smallest square size, 21, is the GCD of 1071 and 462.
  • compass]] in a painting of about 1474.
  • ''u''<sup>2</sup> + ''v''<sup>2</sup>}} less than 500
ALGORITHM FOR COMPUTING GREATEST COMMON DIVISORS
Euclids algorithm; Euclidean Algorithm; Euclid's algorithm; Euclid's algorithem; Euclid algorithm; The Euclidean Algorithm; Game of Euclid; Euclid’s Algorithm; Euclid's division algorithm; Generalizations of the Euclidean algorithm; Applications of the Euclidean algorithm
алгоритм Евклида (для нахождения общего наибольшего делителя)

Définition

витамин B4
см. Холин.
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Wikipédia

Binary GCD algorithm

The binary GCD algorithm, also known as Stein's algorithm or the binary Euclidean algorithm, is an algorithm that computes the greatest common divisor of two nonnegative integers. Stein's algorithm uses simpler arithmetic operations than the conventional Euclidean algorithm; it replaces division with arithmetic shifts, comparisons, and subtraction.

Although the algorithm in its contemporary form was first published by the Israeli physicist and programmer Josef Stein in 1967, it may have been known by the 2nd century BCE, in ancient China.

https://en.wikipedia.org/wiki/Binary GCD algorithm
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