Question

Here’s a brain teaser that’s been on my mind for a few days.

We have a sequence S of n elements. Each element is an integer in the range [0, n^2-1]. Describe a simple method for sorting S in O(n) time.

Probably something obvious that I am just missing, but I’d appreciate any insight.

Answer 1

Bucket Sort!

Bucket sort, or bin sort, is a sorting algorithm that works by partitioning an array into a number of buckets. Each bucket is then sorted individually, either using a different sorting algorithm, or by recursively applying the bucket sorting algorithm. It is a distribution sort, and is a cousin of radix sort in the most to least significant digit flavour. Bucket sort is a generalization of pigeonhole sort. Since bucket sort is not a comparison sort, the Ω(n log n) lower bound is inapplicable. The computational complexity estimates involve the number of buckets.