✎ pp:l112021 [books]

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====== Prolog Programming ======

===== 1. Lists =====

1.1. Write a predicate ''endsWith(X,L)'', which checks if the list ''L'' **ends** with element ''X''.

1.2. Write a predicate ''sameFirstLast(L)'' which checks if the list ''L'' **begins** and **ends** with the same element.

1.3. Write a predicate ''inner(L1,L2)'' which checks if the elements from ''L1'' appear in ''L2'' in exactly the same order. Example ''?- inner([3,4],[1,2,3,4]).''

1.4. Write a predicate ''find(L,K,L1)'' which binds ''K'' to the number of occurrences of ''L'' in ''L1''. Example, for ''L=[1,2,1]'' and ''L1=[1,2,1,2,1,2,1]'' the result will be ''K=3''.

===== 2. Graphs =====

We encode **undirected graphs** as lists ''[V,E]'', where ''V'' is a list of nodes and ''E'' is a list of undirected edges of the form ''[X,Y]''.

2.1. Write a predicate ''isolated(X,G)'' which is satisfied if ''X'' is a node with no edges.

2.2. Write a predicate ''neighbors(X,L,G)'' which computes the list of direct neighbours ''L'' of a given node ''X'' in ''G''.

2.3. Write a predicate ''accessible(X,L,G)'' which computes all nodes ''L'' accessible from ''X'' in graph ''G''.

2.4. Write a predicate which checks if a graph is **complete**.

2.5. Write a predicate which computes the **complement** of a graph.

===== 3. NP problems =====

3.1. Write a solution in PROLOG for the Partition Problem (There exists a partition $math[P] of naturals $math[x_1, \ldots, x_n], such that $math[\sum_{x_i\in P}x_i = \sum_{x_i \not\in P}x_i]).