# Trees spanning 2

## Description

Finding a spanning tree of a graph

Source: PROLOG programming for artificial intelligence, 3rd Edition, Harlow, 2001, ISBN 0-201-40375-7.

Program source code: trees_spanning_2.pl

## Listing

```% Figure 9.23   Finding a spanning tree of a graph: a `declarative'
% program. Relations node and adjacent are as in Figure 9.22.

:- op( 900, fy, not).

% not Goal): negation as failure;
%   Note: This is often available as a built-in predicate,
%   often written as prefix operator "\+", e.g. \+ likes(mary,snakes)

not Goal  :-
Goal, !, fail
;
true.

% Finding a spanning tree
% Graphs and trees are represented as lists of edges.

% stree( Graph, Tree): Tree is a spanning tree of Graph

stree( Graph, Tree)  :-
subset( Graph, Tree),
tree( Tree),
covers( Tree, Graph).

tree( Tree)  :-
connected( Tree),
not hasacycle( Tree).

% connected( Graph): there is a path between any two nodes in Graph

connected( Graph)  :-
not ( node( A, Graph), node( B, Graph), not path( A, B, Graph, _) ).

hasacycle( Graph)  :-
path( Node1, Node2, Graph, [Node1, X, Y | _] ). % Path of length > 1

% covers( Tree, Graph): every node of Graph is in Tree

covers( Tree, Graph)  :-
not ( node( Node, Graph), not node( Node, Tree) ).

% subset( List1, List2): List2 represents a subset of List1

subset( [], [] ).

subset( [X | Set], Subset)  :-            % X not in subset
subset( Set, Subset).

subset( [X | Set], [X | Subset])  :-      % X included in subset
subset( Set, Subset).```