Average Case Analysis of Java 7's Dual Pivot Quicksort

Recently, a new Quicksort variant due to Yaroslavskiy was chosen as standard sorting method for Oracle's Java 7 runtime library. The decision for the change was based on empirical studies showing that on average, the new algorithm is faster than the formerly used classic Quicksort. Surprisingly, the improvement was achieved by using a dual pivot approach, an idea that was considered not promising by several theoretical studies in the past. In this paper, we identify the reason for this unexpected success. Moreover, we present the first precise average case analysis of the new algorithm showing e.g. that a random permutation of length $n$ is sorted using $1.9n\ln n-2.46n+\mathcal{O}(\ln n)$ key comparisons and $0.6n\ln n+0.08n+\mathcal{O}(\ln n)$ swaps.