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A minimum spanning tree of a weighted planar graph.Finding a minimum spanning tree is a common problem involving combinatorial optimization. Combinatorial optimization is a subfield of mathematical optimization that consists of finding an optimal object from a finite set of objects, [1] where the set of feasible solutions is discrete or can be reduced to a discrete set.
In computer science, all-pairs testing or pairwise testing is a combinatorial method of software testing that, for each pair of input parameters to a system (typically, a software algorithm), tests all possible discrete combinations of those parameters.
For example, a digital door lock with a 4-digit code (each digit having 10 possibilities, from 0 to 9) would have B (10, 4) solutions, with length 10 000. Therefore, only at most 10 000 + 3 = 10 003 (as the solutions are cyclic) presses are needed to open the lock, whereas trying all codes separately would require 4 × 10 000 = 40 000 presses.
In mathematics, a combination is a selection of items from a set that has distinct members, such that the order of selection does not matter (unlike permutations).For example, given three fruits, say an apple, an orange and a pear, there are three combinations of two that can be drawn from this set: an apple and a pear; an apple and an orange; or a pear and an orange.
Flowchart of using successive subtractions to find the greatest common divisor of number r and s. In mathematics and computer science, an algorithm (/ ˈ æ l ɡ ə r ɪ ð əm / ⓘ) is a finite sequence of mathematically rigorous instructions, typically used to solve a class of specific problems or to perform a computation. [1]
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.
Timsort is a hybrid, stable sorting algorithm, derived from merge sort and insertion sort, designed to perform well on many kinds of real-world data.It was implemented by Tim Peters in 2002 for use in the Python programming language.
The algorithm has an asymptotically optimal cache complexity under the Ideal cache model. [11] Interestingly, the algorithm itself is cache-oblivious [11] meaning that it does not make any choices based on the cache parameters (e.g., cache size and cache line size) of the machine.