کامپیوتر-دانلود-سورس-توابع- اموزش-فیلم

Prolog exercises

1. print all elements of a list ?-print_list([a,b,c]). a b c

print_list([]):-nl. %nl = newline

print_list([H|T]):-write(H),write(’ ’),print_list(T).

2. reverse all elements of a list ?-reversex([a,b,c],X). X=[c,b,a]

addtoend(H,[],[H]).

addtoend(X,[H|T],[H|T1]):-addtoend(X,T,T1).

reversex([],[]).

reversex([H|T],Y):- reversex(T,T1), addtoend(H,T1,Y).

3. create list ?-create_list(5,12,S). S=[5,6,7,8,9,10,11,12]

create_list(X,X,[X]).

create_list(A,X,[A|T]):- AA is A+1, create_list(AA,X,T).

4. mean value [1,2,3,4,5] => 3

sum_list([],0,0).

sum_list([H|T],Length,Sum):-sum_list(T,L1,S1), Length is L1+1, Sum is S1+H.

mean(L,M):-sum_list(L,Length,Sum), M is Sum/Length.

5. detect whether list contains a number [a,b,c,d,e,1,f] => T

numberinlist([]):-fail.

numberinlist([X|T]):-number(X).

numberinlist([X|T]):-numberinlist(T).

6. increment elements of list [5,6,7,8] => [6,7,8,9]

increment([],[]).

increment([H|T],[X|Y]):-increment(T,Y),X is H+1.

7. factorial function

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factorial(0,1).

factorial(N,X):-N>0, N1 is N-1, factorial(N1,S), X is S*N.

8. implement append function [a,1,2,b,c], [b,c,d,e] => [a,1,2,b,c,b,c,d,e]

appendx([],A,A).

appendx([H|T],A,[H|U]):-appendx(T,A,U).

9. encapsulate list elements [a,b,1,d,e] => [[a],[b],[1],[d],[e]]

encapsulate([],[]).

encapsulate([H|T],[[H]|Y]):-encapsulate(T,Y).

10. insert zeros [1,2,3,4,5] => [1,0,2,0,3,0,4,0,5,0]

insert_zeros([],[]).

insert_zeros([H|T],[H,0|Y]):-insert_zeros(T,Y).

11. clone list [g,6,7] => [[g,6,7][g,6,7]]

clone_list(T,[T,T]).

12. modify list element ?-modify_list([m,o,d,i,f,y,e,t], 6, i,Y). Y=[m,o,d,i,f,y,i,t],

?-modify_list([m,o,d],6,i,Y). Y=[m,o,d]

modify_list([],N,X,[]).

modify_list([H|T],0,X,[X|T]).

modify_list([H|T],N,X,[H|Y]):-N>0, N1 is N-1, modify_list(T,N1,X,Y).

13. rotate list [1,2,3,4,5] => [2,3,4,5,1]

addtoend(H,[],[H]).

addtoend(X,[H|T],[H|T1]):-addtoend(X,T,T1).

rotate_list([H|T],L1):-addtoend(H,T,L1).

14. Fibonacci numbers: print nth Fibonacci number.

fib(1,1).

fib(2,1).

fib(N,F):- N>2,

N1 is N-1, fib(N1,F1),

N2 is N-2, fib(N2,F2),

F is F1+F2.

15. test whether a number is a prime number 333667 => T

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16. recursive square root function.

Compute square root (with given error) by using Newton’s algorithm

17. generate random (values 0-9) square matrix: [[2,4,5],[1,0,3],[9,3,2]].

Inner elements represent matrix rows.

random10(N):-frandom(X), Y is X*10, fix(Y,N).

rand_row(0,[]).

rand_row(N,[H|T]):-N>0,random10(H),N1 is N-1, rand_row(N1,T).

square_matrix_rand(N,S):-smr(N,N,S).

smr(N,0,[]).

smr(N,X,[R|T]):-N>0, rand_row(N,R),X1 is X-1,smr(N,X1,T).

18. sin function using Taylor series

19. member ?-memberx(2,[1,2,3]). yes,

?-memberx([1,2,a],[1,2,3,[1,2,a]]). yes,

?-memberx(4,[1,2,3,[1,2,a]]). no

memberx(N,[N|T]).

memberx(N,[X|T]):-memberx(N,T).

20. implement insertion into a sorted list (the result is sorted as well)

insertinto(N,[],[N]).

insertinto(N,[H|T],[N,H|T]):-H>=N,!.

insertinto(N,[H|T],[H|Y]):-insertinto(N,T,Y).

21. search duplicates. Result don’t contain duplicate elements. [a,b,1,c,3,d,2,2,f,3] => [3,2]

memberx(N,[N|T]).

memberx(N,[X|T]):-memberx(N,T).

deleteall(N,[],[]).

deleteall(N,[N|T],U):-!,deleteall(N,T,U).

deleteall(N,[H|T],[H|U]):-deleteall(N,T,U).

delete_dupl([],[]).

delete_dupl([H|T],Y):-memberx(H,T),!,deleteall(H,T,T1),delete_dupl(T1,Y).

delete_dupl([H|T],[H|Y]):-delete_dupl(T,Y).

22. remove unique elements [6,2,3,3,5,2,3,1,4] => [2,3,3,2,3]

memberx(N,[N|T]).

memberx(N,[X|T]):-memberx(N,T).

delete_unique([],[]).

delete_unique([H|T],[H|Y]):-memberx(H,T),!,delete_unique(T,Y).

delete_unique([H|T],Y):-delete_unique(T,Y).

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23. make a list unique [a,b,c,d,a,b,e,f] => [a,b,c,d,e,f]

memberx(N,[N|T]).

memberx(N,[X|T]):-memberx(N,T).

deleteall(N,[],[]).

deleteall(N,[N|T],U):-!,deleteall(N,T,U).

deleteall(N,[H|T],[H|U]):-deleteall(N,T,U).

make_unique([],[]).

make_unique([H|T],[H|Y]):-memberx(H,T),!,deleteall(H,T,T1),make_unique(T1,Y).

make_unique([H|T],[H|Y]):-make_unique(T,Y).

or [a,b,c,d,a,b,e,f] => [c,d,a,b,e,f]

memberx(N,[N|T]).

memberx(N,[X|T]):-memberx(N,T).

make_unique([],[]).

make_unique([H|T],Y):-memberx(H,T),!,make_unique(T,Y).

make_unique([H|T],[H|Y]):-make_unique(T,Y).

24. maximum function [1,-2,3] => 3

maximumx(P,D,V):- P>=D, V=P, !.

maximumx(P,D,V):-V=D.

max([H],H).

max([H|T],X):-max(T,S),maximumx(H,S,X).

25. return elements >k, [4,6,7,3] and k=5 => [6 7]

morethan(_,[],[]).

morethan(K,[H|T],[H|U]):- H>=K, morethan(K,T,U),!.

morethan(K,[H|T],U):- morethan(K,T,U).

26. remove value ?-deleteall(3,[1,3,2,3,0,1,2],X). X=[1,2,0,1,2]

deleteall(N,[],[]).

deleteall(N,[N|T],U):-!,deleteall(N,T,U).

deleteall(N,[H|T],[H|U]):-deleteall(N,T,U).

27. remove element at given position ?-deleteat(3,[a,b,c,d],X). X=[a,b,d]

deleteat(_,[],[]).

deleteat(0,[H|T],T):-!.

deleteat(N,[H|T],[H|Y]):-N1 is N-1, deleteat(N1,T,Y).

28. split a list into two parts. Length of the first is given.

?-split_list(4,[a,b,c,1,2,3,d,e,f],X). X=[[a b c 1],[2 3 d e f]]

split_list(_,[],[[],[]]).

split_list(0,T,[[],T]).

split_list(N,[H|T],[[H|Y],Z]):-N1 is N-1, split_list(N1,T,[Y,Z]).

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29. couple elements ?-couple_elem([1,a,b,4,5,6],X). X=[[1,a],[b,4],[5,6]]

?-couple_elem([1,a,b,4,5],X). no

couple_elem([],[]).

couple_elem([H1,H2|T],[[H1,H2]|Y]):-couple_elem(T,Y).

30. translator([[1,2],[3],[0]],[[5],[1],[7,2]],[[1,2],[0],[3],[3]],X). X =[[5],[7,2],[1],[1]]

translator(A,B,X,Y) defines transformation A=>B and applies it to X. X is always subset of A.

find_key([H|A],[R|B],H,R):-!.

find_key([H1|A],[R|B],H,Y):-find_key(A,B,H,Y).

translator(_,_,[],[]).

translator(A,B,[H|T],[R|Y]):-find_key(A,B,H,R), translator(A,B,T,Y).

31. full member ?-fullmember(8,[1,2,[2,3],[4,5,[6,8,7]]]). yes,

?-fullmember([6,8,7],[1,2,[2,3],[4,5,[6,8,7]]]). yes

fullmember(N,[N|T]):-!.

fullmember(N,[X|T]):-fullmember(N,X),!.

fullmember(N,[X|T]):-fullmember(N,T).

32. remove parenthesis [1,2,[3,4],5,6,[7,[8,9]]] => [1,2,3,4,5,6,7,8,9]

simple_list([],[]).

simple_list([H|T],Y):-is_list(H),!,simple_list(H,L1),simple_list(T,L2),append(L1,L2,Y).

simple_list([H|T],[H|Y]):-simple_list(T,Y).

33. implement list difference ?-difference_list([a,b,c,d,1,2,3],[d,2,3],X). X=[a,b,c,1]

difference_list([],_,[]).

difference_list([H|T],X,Y):-member(H,X),!,difference_list(T,X,Y).

difference_list([H|T],X,[H|Y]):-difference_list(T,X,Y).

34. find number of occurrences

?-occurrences([a,b,c,1,2,a,b,1,1,1],X). X=[[a,2],[b,2],[c,1],[1,4],[2,1]]

deleteall(N,[],[]).

deleteall(N,[N|T],U):-!,deleteall(N,T,U).

deleteall(N,[H|T],[H|U]):-deleteall(N,T,U).

count(N,[],0).

count(N,[N|T],U):-!,count(N,T,U1), U is U1+1.

count(N,[H|T],U):-count(N,T,U).

occurrences([],[]).

occurrences([H|T],[[H,X]|Y]):-count(H,[H|T],X), deleteall(H,T,T1), occurrences(T1,Y).

35. separation function ?-separation_list([1,2,a,b,3,d],X) X=[[1,2,3],[a,b,d]]

separation_list([],[[],[]]).

separation_list([H|T],[[H|T1],Y]):-number(H),separation_list(T,[T1,Y]),!.

separation_list([H|T],[N,[H|T1]]):-separation_list(T,[N,T1]).

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36. sort (use the sort function) according to second elements

( (1 2 3) (8 1 0) (2 3 10) ) => ( (8 1 0) (1 2 3) (2 3 10) )

37. algebrogram: SEND+MORE = MONEY

solve(S,E,N,D,M,O,R,Y):-c(S),c(E),c(N),c(D),c(M),c(O),c(R),c(Y),

1000*S+100*E+10*N+D + 1000*M+100*O+10*R+E =:= 10000*M+1000*O+100*N+10*E+Y,

S>0, M>0.

c(1). c(2). c(3). c(4). c(5). c(6). c(7). c(8). c(9). c(0).

38. quick sort

appendx([],A,A).

appendx([H|T],A,[H|U]):-appendx(T,A,U).

splittotwo(_,[],[],[]).

splittotwo(I,[H|T],[H|U],V):- H=

splittotwo(I,[H|T],U,[H|V]):- splittotwo(I,T,U,V).

quick([],[]).

quick([H|T],L):-splittotwo(H,T,U,V), quick(U,X),quick(V,Y), appendx(X,[H|Y],L).

39. matrix determinant

40. Tower of Hanoi

hanoi_tower(N):-move(N,a,b,c),!.

move(0,_,_,_):-!.

move(N,X,Y,Z):-M is N-1, move(M,X,Z,Y), info(X,Y), move(M,Z,Y,X).

info(X,Y):-write(’Move disk from ’), write(X), write(’ to ’), write(Y), nl.

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