Optimal Sampling Strategies in Quicksort and Quickselect
نویسندگان
چکیده
منابع مشابه
Optimal Sampling Strategies in Quicksort and Quickselect
It is well known that the performance of quicksort can be improved by selecting the median of a sample of elements as the pivot of each partitioning stage. For large samples the partitions are better, but the amount of additional comparisons and exchanges to find the median of the sample also increases. We show in this paper that the optimal sample size to minimize the average total cost of qui...
متن کاملRandomized Algorithms: QuickSort and QuickSelect
Let Q(A) be number of comparisons done on input array A: (A) For 1 ≤ i < j < n let R ij be the event that rank i element is compared with rank j element. (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. Q(A) = ∑ 1≤i<j≤n X ij and hence by linearity of expectation,
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,
متن کاملRandomized Algorithms: QuickSort and QuickSelect
Let Q(A) be number of comparisons done on input array A: (A) For 1 ≤ i < j < n let R ij be the event that rank i element is compared with rank j element. (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. Q(A) = ∑ 1≤i<j≤n X ij and hence by linearity of expectation,
متن کاملPartitioning schemes for quicksort and quickselect
We introduce several modifications of the partitioning schemes used in Hoare’s quicksort and quickselect algorithms, including ternary schemes which identify keys less or greater than the pivot. We give estimates for the numbers of swaps made by each scheme. Our computational experiments indicate that ternary schemes allow quickselect to identify all keys equal to the selected key at little add...
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ژورنال
عنوان ژورنال: SIAM Journal on Computing
سال: 2001
ISSN: 0097-5397,1095-7111
DOI: 10.1137/s0097539700382108