[PRL] Stooge sort - Wikipedia, the free encyclopedia
John Clements
clements at brinckerhoff.org
Thu Jun 16 17:32:26 EDT 2011
On Jun 16, 2011, at 1:36 PM, Mitchell Wand wrote:
> Anybody want to give a proof that this works? --Mitch
>
> Link: http://en.wikipedia.org/wiki/Stooge_sort (sent via Shareaholic)
A real proof, or just a proof sketch?
1) It works for lists of size 1 & 2.
2) Assume it works for lists of size n. Then prove that it works for lists of size 1.5 * n, as follows:
Given an unsorted list of size 1.5n, consider the elements that belong in the upper third (there are 0.5n of these); they're scattered all over. After sorting the lower 2/3, though, the elements from this set that occurred in the lower 2/3 must now all be in the upper half of that set, and thus contained in the middle third of the range. Then, sorting the upper 2/3, they're all in the top half of the upper 2/3, and hence in their correct spots. By a similar logic, the elements that belong in the lower third are moved into the middle or lower third by the first two sorts, and the third sort moves them into their proper locations. By a counting argument, the elements belonging in the middle third will be in the lower 2/3 after the first two sorts, and in their correct locations after the third.
There's still some detail to fill in w.r.t. which way to round the division between thirds; everything could fall apart in there, I suppose.
John
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