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  2. Multiple subset sum - Wikipedia

    en.wikipedia.org/wiki/Multiple_subset_sum

    It is possible to enumerate all possible utility profiles in time () where n is the number of items and c is the maximum size of an item. For separate items: for each agent j , define a dynamic array Q j {\displaystyle Q_{j}} , such that Q j ( w ) = true {\displaystyle Q_{j}(w)={\text{true}}} iff there exists a solution giving a total weight of ...

  3. Euclidean algorithm - Wikipedia

    en.wikipedia.org/wiki/Euclidean_algorithm

    In the second step, any natural number c that divides both a and b (in other words, any common divisor of a and b) divides the remainders r k. By definition, a and b can be written as multiples of c: a = mc and b = nc, where m and n are natural numbers. Therefore, c divides the initial remainder r 0, since r 0 = a − q 0 b = mc − q 0 nc = (m ...

  4. Bubble sort - Wikipedia

    en.wikipedia.org/wiki/Bubble_sort

    Take an array of numbers "5 1 4 2 8", and sort the array from lowest number to greatest number using bubble sort. In each step, elements written in bold are being compared. Three passes will be required; First Pass ( 5 1 4 2 8 ) → ( 1 5 4 2 8 ), Here, algorithm compares the first two elements, and swaps since 5 > 1.

  5. List of data structures - Wikipedia

    en.wikipedia.org/wiki/List_of_data_structures

    "Ordered" means that the elements of the data type have some kind of explicit order to them, where an element can be considered "before" or "after" another element. This order is usually determined by the order in which the elements are added to the structure, but the elements can be rearranged in some contexts, such as sorting a list. For a ...

  6. Floor and ceiling functions - Wikipedia

    en.wikipedia.org/wiki/Floor_and_ceiling_functions

    In mathematics, the floor function is the function that takes as input a real number x, and gives as output the greatest integer less than or equal to x, denoted ⌊x⌋ or floor(x). Similarly, the ceiling function maps x to the least integer greater than or equal to x , denoted ⌈ x ⌉ or ceil( x ) .

  7. Extended Euclidean algorithm - Wikipedia

    en.wikipedia.org/wiki/Extended_Euclidean_algorithm

    In arithmetic and computer programming, the extended Euclidean algorithm is an extension to the Euclidean algorithm, and computes, in addition to the greatest common divisor (gcd) of integers a and b, also the coefficients of Bézout's identity, which are integers x and y such that + = (,).

  8. Partially ordered set - Wikipedia

    en.wikipedia.org/wiki/Partially_ordered_set

    In our running example, {,,} and {} are the maximal and minimal elements. Removing these, there are 3 maximal elements and 3 minimal elements (see Fig. 5). Upper and lower bounds: For a subset A of P, an element x in P is an upper bound of A if a ≤ x, for each element a in A.

  9. List of algorithms - Wikipedia

    en.wikipedia.org/wiki/List_of_algorithms

    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.