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QuickXsort is a strategy to combine Quicksort with another sorting method X,so that the result has essentially the same comparison cost as X in isolation,but sorts in place even when X requires a linear-size buffer. We solve therecurrence for QuickXsort precisely up to the linear term including theoptimization to choose pivots from a sample of k elements. This allows toimmediately obtain overall average costs using only the average costs ofsorting method X (as if run in isolation). We thereby extend and greatlysimplify the analysis of QuickHeapsort and QuickMergesort with practicallyefficient pivot selection, and give the first tight upper bounds including thelinear term for such methods.

Average Cost of QuickXsort with Pivot Sampling