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[smlnj] View of /MLRISC/releases/release-110.60/graphs/bellman-ford.sml
 [smlnj] / MLRISC / releases / release-110.60 / graphs / bellman-ford.sml

# View of /MLRISC/releases/release-110.60/graphs/bellman-ford.sml

Thu Nov 9 21:29:12 2006 UTC (12 years, 10 months ago) by blume
File size: 1470 byte(s)
`Release 110.60`
```(*
* 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

```