Using nonlinear difference equations to study Quicksort algorithms
نویسندگان
چکیده
منابع مشابه
Using Linear Difference Equations to Model Nonlinear Cryptographic Sequences
A new class of linear sequence generators based on cellular automata is here introduced in order to model several nonlinear keystream generators with practical applications in symmetric cryptography. The output sequences are written as solutions of linear difference equations, and three basic properties (period, linear complexity and number of different output sequences) are analyzed.
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متن کاملIntroduction to Randomized Algorithms: QuickSort and QuickSelect
QuickSort Hoare [1962] (A) Pick a pivot element from array (B) Split array into 3 subarrays: those smaller than pivot, those larger than pivot, and the pivot itself. (C) Recursively sort the subarrays, and concatenate them. Randomized QuickSort (A) Pick a pivot element uniformly at random from the array (B) Split array into 3 subarrays: those smaller than pivot, those larger than pivot, and the...
متن کاملIntroduction to Randomized Algorithms: QuickSort and QuickSelect
QuickSort Hoare [1962] (A) Pick a pivot element from array (B) Split array into 3 subarrays: those smaller than pivot, those larger than pivot, and the pivot itself. (C) Recursively sort the subarrays, and concatenate them. Randomized QuickSort (A) Pick a pivot element uniformly at random from the array (B) Split array into 3 subarrays: those smaller than pivot, those larger than pivot, and the...
متن کاملRandomized Algorithms: QuickSort and QuickSelect
(A) Let Q(A) be number of comparisons done on input array A: (A) R ij : event that rank i element is compared with rank j element, for 1 ≤ i < j ≤ n. (B) X ij is the indicator random variable for R ij. That is, X ij = 1 if rank i is compared with rank j element, otherwise 0. (B) Q(A) = ∑ 1≤i<j≤n X ij. (C) By linearity of expectation,
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ژورنال
عنوان ژورنال: Journal of Difference Equations and Applications
سال: 2020
ISSN: 1023-6198,1563-5120
DOI: 10.1080/10236198.2020.1720665