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Tarjan's strongly-connected components in a single DFS using
index/lowlink:
graph (8 nodes, directed):
0 -> 1 -> 2 -> 0 (3-cycle)
2 -> 3
3 -> 4
4 -> 5 -> 6 -> 4 (3-cycle)
4 -> 7
SCCs: {0,1,2}, {3}, {4,5,6}, {7} = 4 components
Module-level ref + array state (index_arr, lowlink, on_stack,
stack, scc_count). When lowlink(v) = index(v), pop from stack
until v is removed; that's a complete SCC.
Tests: recursive function with module-level mutable state,
nested begin/end branches inside List.iter closure, inner
`let rec pop ()` traversing a ref-of-list, pattern match on
[] / h :: rest cons-list shape.
154 baseline programs total.
54 lines
1.0 KiB
OCaml
54 lines
1.0 KiB
OCaml
let n = 8
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let adj = [|
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[1];
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[2];
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[0; 3];
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[4];
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[5; 7];
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[6];
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[4];
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[]
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|]
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let index_counter = ref 0
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let stack = ref []
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let on_stack = Array.make n false
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let index_arr = Array.make n (-1)
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let lowlink = Array.make n 0
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let scc_count = ref 0
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let rec strongconnect v =
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index_arr.(v) <- !index_counter;
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lowlink.(v) <- !index_counter;
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index_counter := !index_counter + 1;
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stack := v :: !stack;
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on_stack.(v) <- true;
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List.iter (fun w ->
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if index_arr.(w) = -1 then begin
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strongconnect w;
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if lowlink.(w) < lowlink.(v) then lowlink.(v) <- lowlink.(w)
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end else if on_stack.(w) then begin
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if index_arr.(w) < lowlink.(v) then lowlink.(v) <- index_arr.(w)
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end
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) adj.(v);
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if lowlink.(v) = index_arr.(v) then begin
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let rec pop () =
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match !stack with
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| [] -> ()
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| w :: rest ->
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stack := rest;
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on_stack.(w) <- false;
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if w <> v then pop ()
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in
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pop ();
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scc_count := !scc_count + 1
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end
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;;
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for v = 0 to n - 1 do
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if index_arr.(v) = -1 then strongconnect v
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done;
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!scc_count
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