We analyse a generalisation of the Quicksort algorithm, where k uniformly at random chosen pivots are used for partitioning an array of n distinct keys. Specifically, the expected cost of this scheme is obtained, under the assumption of linearity of the cost needed for the partition process. The integration constants of the expected cost are computed using Vandermonde matrices.

The complexity of the Quicksort algorithm is usually measured by the number of key comparisons used during its execution. When operating on a list of n data, permuted uniformly at random, the appropriately normalized complexity Yn is known to converge almost surely to a non-degenerate random limit Y. This assumes a natural embedding of all Yn on one probability space, e.g., via random binary se...

The complexity of the Quicksort algorithm is usually measured by the number of key comparisons used during its execution. When operating on a list of n data, permuted uniformly at random, the appropriately normalized complexity Yn is known to converge almost surely to a non-degenerate random limit Y. This assumes a natural embedding of all Yn on one probability space, e.g., via random binary se...

This is Section 5.4 in Mehlhorn/Sanders [DMS14, MS08] Quicksort is a divide-and-conquer algorithm. Let S be the set to be sorted. We select a uniformly random element p from S and split S into three parts. The set S< of elements smaller than p, the set S= of elements equal to p and the set S> of elements larger than p. The element p is usually called the pivot. Then we apply the algorithm recur...

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.

In this paper we study the Kolmogorov Complexity of a Binary Insertion Tree. We obtain a simple incompressibility argument that yields an asymptotic analysis of average tree height. This argument further implies that the QuickSort algorithm sorts a permutation of n elements in Θ(n log n) comparisons on average.