[racket] Looking for feedback on code style

From: David Van Horn (dvanhorn at ccs.neu.edu)
Date: Thu Sep 9 11:26:17 EDT 2010

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.



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