# [racket] Looking for feedback on code style

http://programmingpraxis.com/2009/12/11/selection/
On Thu, Sep 9, 2010 at 10:26 AM, David Van Horn <dvanhorn at ccs.neu.edu>wrote:
>* On 9/9/10 10:04 AM, Prabhakar Ragde wrote:
*>*
*>>* I don't think vectors help very much in this case (median-finding). For
*>>* the given code, the O(n) access to the middle of the list is dominated
*>>* by the cost of the sorting, which is at least O(n log n) [*].
*>>*
*>>* It is theoretically possible to compute the median in O(n) time, but the
*>>* method is complicated and not very practical. But sorting definitely
*>>* does too much work. If only the median (or the kth largest, a problem
*>>* called "selection") is needed, a method which is both practical and of
*>>* pedagogical interest stems from adapting Quicksort, which is a good
*>>* exercise after section 25.2 of HtDP. This has expected cost O(n) on
*>>* random data, and vectors offer no asymptotic advantage over lists. --PR
*>>*
*>>* [*] Technically, "at least Omega(n log n)".
*>>*
*>*
*>* The original post got me interested in median algorithms and I started to
*>* read up on the selection problem. Wikipedia (I know, I know) says the same
*>* thing as you: medians can be computed in O(n) time and points to selection
*>* as the way to do it. But I don't see how to use selection to achieve a
*>* O(n)-time median algorithm -- selection (of the kth largest/smallest
*>* element) is O(n), but that's were k is some fixed constant. To compute the
*>* median, you let k=n/2 (right?), so it's no longer constant. Can you point
*>* me to (or sketch) a O(n) method? Or just correct me if my reasoning is
*>* going astray.
*>*
*>* Thanks!
*>*
*>* David
*>*
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