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  2. Lazy initialization - Wikipedia

    en.wikipedia.org/wiki/Lazy_initialization

    Using a factory method to create instances of a class (factory method pattern) Storing the instances in a map, and returning the same instance to each request for an instance with same parameters (multiton pattern) Using lazy initialization to instantiate the object the first time it is requested (lazy initialization pattern)

  3. Lazy evaluation - Wikipedia

    en.wikipedia.org/wiki/Lazy_evaluation

    In Python 3.x the range() function [28] returns a generator which computes elements of the list on demand. Elements are only generated when they are needed (e.g., when print(r[3]) is evaluated in the following example), so this is an example of lazy or deferred evaluation:

  4. Divisor summatory function - Wikipedia

    en.wikipedia.org/wiki/Divisor_summatory_function

    In number theory, the divisor summatory function is a function that is a sum over the divisor function. It frequently occurs in the study of the asymptotic behaviour of the Riemann zeta function . The various studies of the behaviour of the divisor function are sometimes called divisor problems .

  5. Kahan summation algorithm - Wikipedia

    en.wikipedia.org/wiki/Kahan_summation_algorithm

    Starting with Python 3.12, the built-in "sum()" function uses the Neumaier summation. [ 25 ] In the Julia language, the default implementation of the sum function does pairwise summation for high accuracy with good performance, [ 26 ] but an external library provides an implementation of Neumaier's variant named sum_kbn for the cases when ...

  6. Divisor function - Wikipedia

    en.wikipedia.org/wiki/Divisor_function

    When z is 1, the function is called the sigma function or sum-of-divisors function, [1] [3] and the subscript is often omitted, so σ(n) is the same as σ 1 (n) (OEIS: A000203). The aliquot sum s ( n ) of n is the sum of the proper divisors (that is, the divisors excluding n itself, OEIS : A001065 ), and equals σ 1 ( n ) − n ; the aliquot ...

  7. Totient summatory function - Wikipedia

    en.wikipedia.org/wiki/Totient_summatory_function

    The summatory of reciprocal totient function is defined as ():= = ()Edmund Landau showed in 1900 that this function has the asymptotic behavior (+ ⁡) + + (⁡)where γ is the Euler–Mascheroni constant,

  8. Subset sum problem - Wikipedia

    en.wikipedia.org/wiki/Subset_sum_problem

    The subset sum problem (SSP) is a decision problem in computer science.In its most general formulation, there is a multiset of integers and a target-sum , and the question is to decide whether any subset of the integers sum to precisely . [1]

  9. Fold (higher-order function) - Wikipedia

    en.wikipedia.org/wiki/Fold_(higher-order_function)

    The extraneous intermediate list structure can be eliminated with the continuation-passing style technique, foldr f z xs == foldl (\ k x-> k. f x) id xs z; similarly, foldl f z xs == foldr (\ x k-> k. flip f x) id xs z ( flip is only needed in languages like Haskell with its flipped order of arguments to the combining function of foldl unlike e ...