A note on the height of binary search trees
Journal of the ACM (JACM)
Asymptotic behavior of the Lempel-Ziv parsing scheme and digital search trees
Theoretical Computer Science - Special volume on mathematical analysis of algorithms (dedicated to D. E. Knuth)
How many comparisons does Quicksort use?
Journal of Algorithms
Large deviations for quicksort
Journal of Algorithms
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
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We consider the standard Quicksort algorithm that sorts n distinct keys with all possible n! orderings of keys being equally likely. Equivalently, we analyze the total path length Ln in a randomly built binary search tree. Obtaining the limiting distribution of Ln is still an outstanding open problem. In this paper, we establish an integral equation for the probability density of the number of comparisons Ln. Then, we investigate the large deviations of Ln. We shall show that the left tail of the limiting distribution is much "thinner" (i.e., double exponential) than the right tail (which is only exponential). We use formal asymptotic methods of applied mathematics such as the WKB method and matched asymptotics.