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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.
The variant in which all inputs are positive, and the target sum is exactly half the sum of all inputs, i.e., = (+ +). This special case of SSP is known as the partition problem . SSP can also be regarded as an optimization problem : find a subset whose sum is at most T , and subject to that, as close as possible to T .
In addition to support for vectorized arithmetic and relational operations, these languages also vectorize common mathematical functions such as sine. For example, if x is an array, then y = sin (x) will result in an array y whose elements are sine of the corresponding elements of the array x. Vectorized index operations are also supported.
(pred array)/array or pred {⍵ /⍨ ⍺⍺ ⍵} array: The second example is an APL dop. C# 3.0 ienum.Where(pred) or The where clause: Where is an extension method ienum is an IEnumerable Similarly in all .NET languages CFML: obj.filter(func) Where obj is an array or a structure. The func receives as an argument each element's value. Clojure ...
The iteration form of the Eiffel loop can also be used as a boolean expression when the keyword loop is replaced by either all (effecting universal quantification) or some (effecting existential quantification). This iteration is a boolean expression which is true if all items in my_list have counts greater than three:
Prefix sums are trivial to compute in sequential models of computation, by using the formula y i = y i − 1 + x i to compute each output value in sequence order. However, despite their ease of computation, prefix sums are a useful primitive in certain algorithms such as counting sort, [1] [2] and they form the basis of the scan higher-order function in functional programming languages.
Thus a one-dimensional array is a list of data, a two-dimensional array is a rectangle of data, [12] a three-dimensional array a block of data, etc. This should not be confused with the dimension of the set of all matrices with a given domain, that is, the number of elements in the array.
INT sum sq := 0; FOR i WHILE print(("So far:", i, new line)); # Interposed for tracing purposes. # sum sq ≠ 70↑2 # This is the test for the WHILE # DO sum sq +:= i↑2 OD Subsequent extensions to the standard ALGOL 68 allowed the to syntactic element to be replaced with upto and downto to achieve a small optimization.