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Lucky Cars and the Quicksort Algorithm.
- Source :
-
American Mathematical Monthly . May2024, Vol. 131 Issue 5, p417-423. 7p. - Publication Year :
- 2024
-
Abstract
- Quicksort is a classical divide-and-conquer sorting algorithm. It is a comparison sort that makes an average of 2 (n + 1) H n − 4 n comparisons on an array of size n ordered uniformly at random, where H n : = ∑ i = 1 n 1 i is the nth harmonic number. Therefore it makes n ! [ 2 (n + 1) H n − 4 n ] comparisons to sort all possible orderings of the array. In this article, we prove that this count also enumerates the parking preference lists of n cars parking on a one-way street with n parking spots resulting in exactly n − 1 lucky cars (i.e., cars that park in their preferred spot). For n ≥ 2 , both counts satisfy the second order recurrence relation f n = 2 n f n − 1 − n (n − 1) f n − 2 + 2 (n − 1) ! with f 0 = f 1 = 0 . [ABSTRACT FROM AUTHOR]
- Subjects :
- *ALGORITHMS
*AUTOMOBILES
*AUTOMOBILE parking
Subjects
Details
- Language :
- English
- ISSN :
- 00029890
- Volume :
- 131
- Issue :
- 5
- Database :
- Academic Search Index
- Journal :
- American Mathematical Monthly
- Publication Type :
- Academic Journal
- Accession number :
- 176862138
- Full Text :
- https://doi.org/10.1080/00029890.2024.2309103