Conditional Prolog Sorting approach

Question

I am new to prolog language. I came across an interesting problem in prolog.

Generally, quicksort works well for large lists. But for smaller lists, insertion sort works better than quicksort. How can i write a sorting algorithm in Prolog that uses quicksort initially, but switches to insertion sort for sublists of 15 or fewer elements.

The hint is that we can count the number of elements during the partition operation. But i don't know how to form an algorithm for this problem. Can anyone please guide/help.

Thanks a lot in advance.

For more efficient ways, see stackoverflow.com/questions/8429479/sorting-a-list-in-prolog/… — false
– false, Commented Nov 11, 2013 at 16:51

Will Ness · Accepted Answer · 2013-11-10 08:59:08Z

1

partition puts each element either to one or the other sublist. so just maintain two more arguments which are counts for the sublists, starting as 0, and increment the corresponding counter when adding another element to its sublist:

part([]    ,[],[],0 ,0).
part([P|LS],L , R,CL,CR):- part(P,LS,L,[],R,[],0,CL,0,CR).

part(_,[]    ,LZ,LZ,RZ,RZ,CL,CL,CR,CR).
part(P,[X|LS],L ,LZ,R ,RZ,IL,CL,JR,CR):-
   X < P -> L=[X|T],I2 is IL+1, part(P,LS,T,LZ,R,RZ,I2,CL,JR,CR)
 ; .....

answered Nov 10, 2013 at 8:59

Will Ness

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Sergey Kalinichenko · Accepted Answer · 2013-11-11 16:43:17Z

1

You can make several clauses for the mysort rule that choose the algorithm based on the length of the list, like this:

mySort(In, Out) :-
    count(In, Cnt),
    Cnt < 15,
    insertionSort(In, Out).
mySort(In, Out) :-
    count(In, Cnt),
    Cnt >= 15,
    quickSort(In, Out).

quickSort(In, Out) :-
    partition(In, Left, Right),
    mySort(Left, SortedLeft),
    mySort(Right, SortedRight),
    mergeSorted(SortedLeft, SortedRight, Out).

The trick is that the quickSort/2 rule references sort, not quickSort, after partitioning the input. This means that as soon as the count drops below 15, insertionSort is going to be used to sort the smaller partitions.

edited Nov 11, 2013 at 16:43

answered Nov 10, 2013 at 2:31

Sergey Kalinichenko

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6 Comments

lurker Over a year ago

Is count/2 defined somewhere, or do you mean length/2?

Sergey Kalinichenko Over a year ago

@mbratch This is intended as a skeletal implementation, so partition, mergeSorted, and count are up to the OP to define (or to use an existing one, such as length/2 for count/2).

Will Ness Over a year ago

the OP wanted partition also to count the length, to spare the unneeded extra traversal.

Sergey Kalinichenko Over a year ago

@WillNess This is only a skeleton of the algorithm - the OP is free to optimize this, passing around the counts. The key idea is in these three clauses.

false Over a year ago

sort/2 is a built-in predicate. You should not be able to redefine it. What Prolog did you use? It must be a very old version.

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