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(*
* Enumerate all simple cycles in a graph with no duplicates.
*
* This module enumerates all simple cycles in a graph.
* Each cycle is reprensented as a list of edges. Adjacent edges
* are adjacent in the list. The function works like fold: all cycles
* are ``folded'' together with a user supplied function.
*
* -- Allen
*)
structure GraphCycles : GRAPH_SIMPLE_CYCLES =
struct
structure G = Graph
structure A = Array
fun cycles (graph as G.GRAPH G) f x =
let val N = #capacity G ()
val inSCC = A.array(N,(~1,0))
val inCycle = A.array(N,false)
fun processSCC(scc,x) =
let val witness = hd scc
(* order each node in the scc *)
fun init([],_) = ()
| init(u::us,i) = (A.update(inSCC,u,(witness,i)); init(us,i+1))
fun dfs(n,root,u,cycle,x) = dfsSucc(n,root,#in_edges G u,cycle,x)
and dfsSucc(_,_,[],_,x) = x
| dfsSucc(n,root,(e as (v,u,_))::es,cycle,x) =
if root = v then dfsSucc(n,root,es,cycle,f(e::cycle,x))
else let val (w,m) = A.sub(inSCC,v)
in if w <> witness orelse m <= n orelse A.sub(inCycle,v)
then dfsSucc(n,root,es,cycle,x)
else let val _ = A.update(inCycle,v,true)
val x = dfs(n,root,v,e::cycle,x)
val _ = A.update(inCycle,v,false)
in dfsSucc(n,root,es,cycle,x)
end
end
fun hasBackEdge([],n) = false
| hasBackEdge((v,_,_)::es,n) =
let val (w,m) = A.sub(inSCC,v)
in w = witness andalso m >= n orelse hasBackEdge(es,n) end
fun enumerateAll(_,[],x) = x
| enumerateAll(n,u::us,x) =
let val x = if hasBackEdge(#in_edges G u,n)
then dfs(n,u,u,[],x) else x
in enumerateAll(n+1,us,x)
end
in init(scc,0);
enumerateAll(0,scc,x)
end
in GraphSCC.scc graph processSCC x
end
end
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