simultaneous multiple key sorting algorithm

[Andrew Krieger]

A k-d tree isn't directly applicable here - the problem is that 
the input data isn't normalized, so you can't just drop people 
into a 2d grid consisting of one axis being height, and the other 
axis being hair length. You need to 'normalize' the heights and 
lengths into ranks first, *then* insert them, and normalizing the 
lengths -> ranks is an NlogN process to begin with. Constructing 
a k-d tree isn't free either - you either have to pre-sort your 
inputs, or sort-as-you-go, which works out to NlogN as well.

On Friday, 27 January 2012 at 20:07:44 UTC, sclytrack wrote:
> On 01/27/2012 08:36 PM, Andrei Alexandrescu wrote:
>> Here's a multikey sorting problem that's bothering me; I think 
>> it's well
>> researched but I can't find the right keywords.
>>
>> Say we have a collection of people with height and hair length
>> information. We want to get people who are "tall and 
>> long-haired". More
>> precisely, we want to order people by rank(p.height) +
>> rank(p.hairlength), where rank(p.k) is the function that 
>> returns the
>> rank of person p if ordered by key k.
>>
>> The brute force approach would essentially compute the two 
>> ranks and
>> then sort by their sum. That's three sorts and at least one 
>> temporary
>> array. But I think things can be done considerably better. Any 
>> ideas?
>>
>>
>> Thanks,
>>
>> Andrei
>
>
> http://en.wikipedia.org/wiki/K-d_tree
>
>
> Sclytrack