A DAG is a directed a cyclic graph.

edge list representation of the format edge$($v$1,$ v$2,$ cost$)$ for the graph:

edge$($a$,$ b$,2).$

edge$($a$,$ d$,1).$

edge$($a$,$ e$,1).$

edge$($a$,$ a$,0).$

edge$($b$,$ c$,6).$

edge$($b$,$ e$,2).$

edge$($b$,$ b$,0).$

edge$($c$,$ e$,9).$

edge$($c$,$ c$,0).$

edge$($d$,$ c$,10).$

edge$($d$,$ f$,7).$

edge$($d$,$ d$,0).$

edge$($e$,$ f$,8).$

edge$($e$,$ e$,0).$

edge$($f$,$ f$,0).$

In prolog, write a predicate dagPaths$($S$,$ F$,$ Path, Cost$)$ that lists all Paths from vertex S $($start$)$ to vertex F $($finish$)$

along with the total cost of the Path.

examples:

$?-$ dagPaths$($b$,$ b$,$ Path, Cost$).$

Path $=[$b$],$

Cost $=0$;

false.

$?-$ dagPaths$($b$,$ f$,$ Path, Cost$).$

Path $=[$b$,$ c$,$ e$,$ f$],$

Cost $=23$;

Path $=[$b$,$ e$,$ f$],$

Cost $=10$;

false.