By Attila Csenki
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Extra resources for Applications of Prolog
Append(SuccNodes,OtherNodes,NewOpenNodes), write(’Successor nodes: ’), write(SuccNodes), nl, write(’Open nodes: ’), write(NewOpenNodes), nl, dfs loop(NewOpenNodes,Goal). successors(Node,SuccNodes) :findall(Successor,link(Node,Successor),SuccNodes). pl • Inspection. We may inspect the agenda’s head to see whether it is the goal node. • Updating. If the head is not the goal node, we determine the head’s successor or successors. They are collected into a list, SuccList , say, (which may well be empty) and a new agenda will be formed by appending the tail of the old agenda to SuccList .
In the ascending chain of successors produced by the algorithm, every partition of n appears since ≺n is a total ordering on the partitions of n. 2: A Ferrers Diagram (ii) if λr = λr−1 = · · · = λr−s+1 = 1 but λr−s = x = 1, then the parts of the next partition are obtained by replacing λr−s , λr−s+1 , . . , λr by x−1, x−1, x−1, . . , x−1, y, where 1 y x−1 and the number of parts x − 1 is chosen so that the result is a partition of n. 2 some typical instances for generating partitions of n = 22.
Depth first(Start,Goal,PathFound) :dfs loop([[Start]],,Goal,PathFoundRev), reverse(PathFoundRev,PathFound). dfs loop([[Goal|PathTail]| ], ,Goal,[Goal|PathTail]). dfs loop([[CurrNode|T]|Others],ClosedList,Goal,PathFound) :successors(CurrNode,SuccNodes), findall(Node,(member(Node,SuccNodes), not(member(Node,ClosedList))),Nodes), extend path(Nodes,[CurrNode|T],Paths), append(Paths,Others,NewOpenPaths), dfs loop(NewOpenPaths,[CurrNode|ClosedList],Goal,PathFound). successors(Node,SuccNodes) :findall(Successor,link(Node,Successor),SuccNodes).
Applications of Prolog by Attila Csenki