Programming in Prolog - List of Exercises #3

1. Write a program that can print all elements of a list

   ?- print_list([a,b,c]). 
   a b c
   

2. Write a program that creates a list with first and last elements given.

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

3. Write a program that calculates the mean value of a list of numbers.

4. Write a program that detects if a list contains a number, and returns the number (or numbers) in an argument.

5. Write a program that increments each integer element found in a list. For example:

   ?- increment_elements([5,6,a,8,b],S). 
   S=[6,7,a,9,b]
   

6. Write a program that can encapsulate each element of a list as a list. For example:

   ?- encaps([a,b,1,d,e],S).
   S = [[a],[b],[1],[d],[e]]
   

7. Write a program that insert zeros between elements of a list. For example:

   ?- insert_zeros([1,2,3,4,5],S).
   S = [1,0,2,0,3,0,4,0,5,0]
   

8. Write a program that can clone a list:

   ?- clone([g,6,7],S).
   S = [[g,6,7][g,6,7]]
   

9. Write a program that, given a list of elements, modify its Nth element with a given element. For example:

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

10. Write a program that generates random integers between I and J, for a square matrix with N rows. For example:

    % random_matrix(I,J,N,Mat).
    ?- random_matrix(0,9,3,M).
    M = [[2,4,5],[1,0,3],[9,3,2]]
    

11. Consider a representation of sets as lists. Define the following predicates:

    (a)

    subset(L,K), which holds iff L is a subset of K.

    (b)

    disjoint(L,K), which holds iff L and K are disjoint (i.e. they have no elements in common).

    (c)

    union(L,K,M), which holds iff M is the union of L and K.

    (d)

    intersection(L,K,M), which holds iff M is the intersection of L and K.

    (e)

    difference(L,K,M), which holds iff M is the difference of L and K.

    Consider two different implementations: (1) the input list can have repeated elements, (2) the input list does not have repeated elements (it is, in fact, a set).

12. Define a predicate length(L,N) which holds iff N is the length of the list L.

13. Define a predicate sumlist(L,N) which, given a list of integers L, returns the sum N of all the elements of L. (the input list must contain only numbers.)

14. Define a predicate add_up_list(L,K) which, given a list of integers L, returns a list of integers in which each element is the sum of all the elements in L up to the same position. For example:

       ?- add_up_list([1,2,3,4],K).
          K = [1,3,6,10];
          no
    

15. Define a predicate merge(L,K,M) which, given two ordered lists of integers L and K, returns an ordered list M containing all the elements of L and K.

16. Consider a representation of binary trees as terms, as follows:

       emptybt           the empty binary tree
       consbt(N,T1,T2)   the binary tree with root N 
                         and left and right subtrees T1 and T2
    

    (a)

    Define a predicate preorder(T,L) which holds iff L is the list of nodes produced by the preorder traversal of the binary tree T.

    (b)

    Define a predicate search_tree(L,T) which, given a list of integers L, returns a balanced search-tree T containing the elements of L.