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A limit theorem for “Quicksort”. (English) Zbl 0718.68026
Summary: Let $$X_ n$$ be the number of comparisons needed by the sorting algorithm Quicksort to sort a list of n numbers into their natural ordering. We show that $$(X_ n-E(X_ n))/n$$ converges weakly to some random variable Y. The distribution of Y is characterized as the fixed point of some contraction. It satisfies a recursive equation, which is used to provide recursive relations for the moments. The random variable Y has exponential tails. Therefore the probability that Quicksort performs badly, e.g. that $$X_ n$$ is larger than 2 E(X$${}_ n)$$ converges polynomially fast of every order to zero.

##### MSC:
 68P10 Searching and sorting
Quicksort
Quicksort
Full Text:
##### References:
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