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The worst-case is when the pivot is always the largest or smallest value in the list (so the list is never divided). In this case, the algorithm takes time O(). If we assume that all possible permutations of the input list are equally likely, the average time taken for sorting is (). The best case occurs when each pivoting divides the list ...
Development and choice of algorithms is rarely based on best-case performance: most academic and commercial enterprises are more interested in improving average-case complexity and worst-case performance. Algorithms may also be trivially modified to have good best-case running time by hard-coding solutions to a finite set of inputs, making the ...
Competitive analysis is a way of doing worst case analysis for on-line and randomized algorithms, which are typically data dependent. In competitive analysis, one imagines an "adversary" which deliberately chooses difficult data, to maximize the ratio of the cost of the algorithm being studied and some optimal algorithm.
To obtain the average-case complexity, given an input distribution, the expected time of an algorithm is evaluated, whereas for the almost-always complexity estimate, it is evaluated that the algorithm admits a given complexity estimate that almost surely holds.
Amortized analysis requires knowledge of which series of operations are possible. This is most commonly the case with data structures, which have state that persists between operations. The basic idea is that a worst-case operation can alter the state in such a way that the worst case cannot occur again for a long time, thus "amortizing" its cost.
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Finding an item in an unsorted list or a malformed tree (worst case) or in an unsorted array; Adding two n-bit integers by ripple carry. () linearithmic, loglinear, or quasilinear: Performing a Fast Fourier transform; heapsort, quicksort (best and average case), or merge sort quadratic
According to a complaint filed in a Texas state court near Houston, Allstate profited by using the data to raise premiums or deny coverage, and by selling the data to other insurers. The software ...