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An algorithm is fundamentally a set of rules or defined procedures that is typically designed and used to solve a specific problem or a broad set of problems.. Broadly, algorithms define process(es), sets of rules, or methodologies that are to be followed in calculations, data processing, data mining, pattern recognition, automated reasoning or other problem-solving operations.
Devised by Niklaus Wirth in the late 1960s and early 1970s, Pascal is a programming language.Originally produced by Borland Software Corporation, Embarcadero Delphi is composed of an IDE, set of standard libraries, and a Pascal-based language commonly called either Object Pascal, Delphi Pascal, or simply 'Delphi' (Embarcadero's current documentation refers to it as 'the Delphi language (Object ...
The first five layers of Pascal's 3-simplex (Pascal's pyramid). Each face (orange grid) is Pascal's 2-simplex (Pascal's triangle). Arrows show derivation of two example terms. In mathematics, Pascal's simplex is a generalisation of Pascal's triangle into arbitrary number of dimensions, based on the multinomial theorem.
A common algorithm design tactic is to divide a problem into sub-problems of the same type as the original, solve those sub-problems, and combine the results. This is often referred to as the divide-and-conquer method; when combined with a lookup table that stores the results of previously solved sub-problems (to avoid solving them repeatedly and incurring extra computation time), it can be ...
Pascal ← {' ' @ (0 =⊢) ↑ 0, ⍨¨ a ⌽ ¨ ⌽∊ ¨ 0, ¨¨ a ∘! ¨ a ← ⌽⍳ ⍵} ⍝ Create a one-line user function called Pascal Pascal 7 ⍝ Run function Pascal for seven rows and show the results below: 1 1 2 1 3 3 1 4 6 4 1 5 10 10 5 1 6 15 20 15 6 1 7 21 35 35 21 7
The shrink-wrapped Turbo Pascal version 3 and later incarnations, including Borland's Object Pascal and Delphi and non-Borland near-compatibles became popular with programmers including shareware authors, and so the SWAG library of Pascal code features a large amount of code written with such versions as Delphi in mind.
In geometry, a tiling is a partition of the plane (or any other geometric setting) into closed sets (called tiles), without gaps or overlaps (other than the boundaries of the tiles). [1]
[4] An important application of divide and conquer is in optimization, [ example needed ] where if the search space is reduced ("pruned") by a constant factor at each step, the overall algorithm has the same asymptotic complexity as the pruning step, with the constant depending on the pruning factor (by summing the geometric series ); this is ...