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(*
* This module implements the Bellman Ford algorithm for single source
* shortest paths.
*
* -- Allen
*)
functor BellmanFord(Num : ABELIAN_GROUP_WITH_INF) :
sig include SINGLE_SOURCE_SHORTEST_PATHS
exception NegativeCycle
end =
struct
structure Num = Num
structure G = Graph
structure A = Array
exception NegativeCycle
fun single_source_shortest_paths {graph=G.GRAPH G,s,weight} =
let val N = #capacity G ()
val dist = A.array(N, Num.inf)
val pred = A.array(N, ~1)
val count = A.array(N, 0)
fun driver([],[]) = ()
| driver([],B) = driver(rev B,[])
| driver(u::A,B) = driver(iterate(u,A,B))
and iterate(u,A,B) =
let val n = Int.+(A.sub(count,u), 1)
val _ = A.update(count,u,n)
val _ = if n >= N then raise NegativeCycle else ()
val du = A.sub(dist,u)
fun relax([],A,B) = (A,B)
| relax((e as (_,v,_))::es,A,B) =
let val c = Num.+(du,weight e)
in if Num.<(c,A.sub(dist,v)) then
(A.update(dist,v,c); A.update(pred,v,u);
relax(es,A,v::B))
else relax(es,A,B)
end
in relax(#out_edges G u,A,B)
end
in A.update(dist,s,Num.zero);
driver([s],[]);
{ dist = dist,
pred = pred
}
end
end
|
