The Quicksort process
نویسندگان
چکیده
منابع مشابه
The Quicksort process
Quicksort on the fly returns the input of n reals in increasing natural order during the sorting process. Correctly normalized the running time up to returning the l-th smallest out of n seen as a process in l converges weakly to a limiting process with path in the space of cadlag functions. AMS-classification: Primary 60 F 05, Secondary 68 P 10, 60 K 99
متن کاملQuicksort Revisited - Verifying Alternative Versions of Quicksort
We verify the correctness of a recursive version of Tony Hoare’s quicksort algorithm using the Hoare-logic based verification tool Dafny. We then develop a non-standard, iterative version which is based on a stack of pivot-locations rather than the standard stack of ranges. We outline an incomplete Dafny proof for the latter.
متن کاملQuicksort asymptotics
The number of comparisons Xn used by Quicksort to sort an array of n distinct numbers has mean μn of order n log n and standard deviation of order n. Using different methods, Régnier and Rösler each showed that the normalized variate Yn := (Xn−μn)/n converges in distribution, say to Y ; the distribution of Y can be characterized as the unique fixed point with zero mean of a certain distribution...
متن کاملApproximating the limiting Quicksort distribution
The limiting distribution of the normalized number of comparisons used by Quicksort to sort an array of n numbers is known to be the unique fixed point with zero mean of a certain distributional transformation S. We study the convergence to the limiting distribution of the sequence of distributions obtained by iterating the transformation S, beginning with a (nearly) arbitrary starting distribu...
متن کاملQuicksort Algorithm Again Revisited
We consider the standard Quicksort algorithm that sorts n distinct keys with all possible n! orderings of keys being equally likely. Equivalently, we analyze the total path length n in a randomly built binary search tree. Obtaining the limiting distribution of n is still an outstanding open problem. In this paper, we establish an integral equation for the probability density of the number of co...
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ژورنال
عنوان ژورنال: Stochastic Processes and their Applications
سال: 2014
ISSN: 0304-4149
DOI: 10.1016/j.spa.2013.09.014