Prolog - Sorting List using MergeSort

In this example, we will demonstrating the sorting of a List using mergesort algorithm in Prolog.

If the list is [4,5,3,7,8,1,2], then the result will be [1,2,3,4,5,7,8]. The steps of performing merge sort are shown below −

• Take the list and split them into two sub-lists. This split will be performed recursively.

• Merge each split in sorted order.

• Thus the entire list will be sorted.

We will define a predicate called mergesort(L, SL), it will take L and return result into SL.

Program (list_misc.pl)

mergesort([],[]).
mergesort([A],[A]).
mergesort([A,B|R],S) :-   split([A,B|R],L1,L2),   mergesort(L1,S1),   mergesort(L2,S2),   merge(S1,S2,S).
split([],[],[]).
split([A],[A],[]).
split([A,B|R],[A|Ra],[B|Rb]) :-   split(R,Ra,Rb).
merge(A,[],A).
merge([],B,B).
merge([A|Ra],[B|Rb],[A|M]) :-   A =< B, merge(Ra,[B|Rb],M).
merge([A|Ra],[B|Rb],[B|M]) :-   A > B, merge([A|Ra],Rb,M).

Output

| ?- consult('D:/TP Prolog/Sample Codes/list_misc.pl').
compiling D:/TP Prolog/Sample Codes/list_misc.pl for byte code...
D:/TP Prolog/Sample Codes/list_misc.pl compiled, 8 lines read - 3045 bytes written, 5 ms

yes
| ?- mergesort([4,5,3,7,8,1,2],L).

L = [1,2,3,4,5,7,8] ? 

yes
| ?- mergesort([8,5,3,4,7,9,6,1],L).

L = [1,3,4,5,6,7,8,9] ? 

yes
| ?- 

Explanation

split predicate

• split([],[],[]) is the base case where an empty list is split into two empty lists.

• split([A],[A],[]) is the base case where a one element list is split into two lists having one list with one element and another one is empty.

• split([A,B|R],[A|Ra],[B|Rb]) :- split(R,Ra,Rb). is the recursive call where a lsit is split into two approximately equal lists.

merge predicate

• merge(A,[],A). is the base case where one element list is merged with an empty list.

• merge([],B,B) is the base case where an empty list is merged with one element list.

• merge([A|Ra],[B|Rb],[A|M]) :- A =< B, merge(Ra,[B|Rb],M)) checks Head element, A of first list with Head element, B of second list. If A is less than or same as B then merge the Rest of the first List with second List and return the merged list.

• merge([A|Ra],[B|Rb],[B|M]) :- A > B, merge([A|Ra],Rb,M)) checks Head element, A of first list with Head element, B of second list. If A is greater than B then merge the first list with the Rest of the second List and return the merged list.

mergesort predicate

• mergesort([],[]) is the base case where an empty list is sorted and returned as such.

• mergesort([A],[A]) is the base case where an list of one element is sorted and returned as such.

• mergesort([A,B|R],S) :- , , mergesort(L2,S2), merge(S1,S2,S) sorts the first List using merge sort and return the sorted list as second list.

  • mergesort([A,B|R],S) is to divide the list where Head, Y represents the first element of the list and Tail represents the rest of the list. Sum is the summation of elements of the list.

  • split([A,B|R],L1,L2) calculates the sum of rest of the elements and store than in SumTemp.

  • mergesort(L1,S1) evaluates and assign addition of Head and SumTemp and returns the sum of all elements in turn.

  • mergesort(L2,S2) evaluates and assign addition of Head and SumTemp and returns the sum of all elements in turn.

  • mergesort(S1,S2,S) evaluates and assign addition of Head and SumTemp and returns the sum of all elements in turn.