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(*
* This module implements the Dijkstra algorithm for computing
* the single source shortest paths.
*
* -- Allen
*)
functor Dijkstra(Num : ABELIAN_GROUP_WITH_INF)
: SINGLE_SOURCE_SHORTEST_PATHS =
struct
structure Num = Num
structure Q = NodePriorityQueue(Array)
structure G = Graph
structure A = Array
fun single_source_shortest_paths{ graph=G' as G.GRAPH G, weight, s } =
let val N = #capacity G ()
val dist = A.array(N, Num.inf)
val pred = A.array(N, ~1)
val Q = Q.fromGraph (fn (i,j) => Num.<(A.sub(dist,i),A.sub(dist,j))) G'
fun relax(e as (u,v,_)) =
let val d_v = A.sub(dist,v)
val d_x = Num.+(A.sub(dist,u),weight e)
in if Num.<(d_x,d_v) then
(A.update(dist,v,d_x); A.update(pred,v,u); Q.decreaseWeight(Q,v))
else ()
end
in A.update(dist,s,Num.zero);
Q.decreaseWeight(Q,s);
(while true do
app relax (#out_edges G (Q.deleteMin Q))
) handle Q.EmptyPriorityQueue => ();
{ dist = dist,
pred = pred
}
end
end
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