Several months ago, someone introduced a sorting algorithm called "Marriage Sort". The inspiration for it came from an article analyzing how to (mathematically) select the best wife/husband.

The "conclusion" drawn from the article is that, given `N`

candidates, the strategy with the best expected value is to skip past the first `sqrt(N) - 1`

candidates and then choose the next "best so far".

Translated loosely into a sorting algorithm, it goes something like this:

- Given
`N`

candidates, calculate the number to skip. - Find the "best" candidate within the skip distance.
- Move all the better candidates beyond the skip distance to the end.
- Reduce
`N`

by the number of candidates moved. - Repeat from Step 1 until we run out of candidates.
- Perform insertion sort.

The marriage sort algorithm is not particularly fast, with a runtime of O(n^{1.5}), but sorting algorithms are fundamental to computing, so I thought it would be fun to implement in Factor.

*Note: Factor comes with some sorting algorithms. The*

`sorting`

vocabulary implements merge sort and the `sorting.insertion`

vocabulary implements an in-place insertion sort.First, some vocabularies and a namespace (we will be using locals to implement a couple of the words):

USING: kernel locals math math.functions sequences sorting.insertion ; IN: sorting.marriage

We can take the loose algorithm and structure the `marriage-sort`

word, leaving the bulk of the work for the `(marriage-sort)`

inner loop:

: marriage-sort ( seq -- ) dup length [ dup sqrt 1 - >fixnum dup 0 > ] [ (marriage-sort) ] while 2drop [ ] insertion-sort ;

We'll need to find the index of the maximum element in a range:

:: find-max ( from to seq -- i ) from to >= [ f ] [ from from 1 + [ dup to < ] [ 2dup [ seq nth ] bi@ < [ nip dup ] when 1 + ] while drop ] if ;

That leaves the `(marriage-sort)`

word (probably more complex than necessary, but it works):

:: (marriage-sort) ( seq end skip -- seq end' ) 0 skip seq find-max skip end [ 2dup < ] [ 2over [ seq nth ] bi@ <= [ 1 - [ seq exchange ] 2keep ] [ [ 1 + ] dip ] if ] while nip 1 - [ seq exchange seq ] keep ;

Some performance numbers (given a 10,000 element random array):

( scratchpad ) 10000 [ random-32 ] replicate ( scratchpad ) dup clone [ natural-sort drop ] time Running time: 0.004123694 seconds ( scratchpad ) dup clone [ marriage-sort ] time Running time: 0.063077446 seconds ( scratchpad ) dup clone [ [ ] insertion-sort ] time Running time: 10.972027614 seconds

As you can see, slower than `natural-sort`

(which uses merge sort), but much faster than `insertion-sort`

, with similar in-place semantics. It's worth noting that the code for `insertion-sort`

seems a little slow and could probably be sped up quite a bit.

The code and some tests for this is on my Github.

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