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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
Keywords:
Quicksort
Software:
Quicksort
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References:
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