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Count source-to-sink paths in a DAG via Kahn's topological sort
plus accumulation:
paths[source] = 1
for u in topological order:
for v in adj[u]: paths[v] += paths[u]
Same 6-node DAG as topo_sort.ml:
0 -> {1, 2} 1 -> {3} 2 -> {3, 4} 3 -> {5} 4 -> {5}
The three witnesses 0 -> 5:
0 -> 1 -> 3 -> 5
0 -> 2 -> 3 -> 5
0 -> 2 -> 4 -> 5
Tests Queue-driven Kahn order + List.rev to recover topological
order, module-level mutable arrays (in_deg, paths), accumulation
in topological traversal.
191 baseline programs total.
43 lines
781 B
OCaml
43 lines
781 B
OCaml
let n = 6
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let adj = [|
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[1; 2];
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[3];
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[3; 4];
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[5];
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[5];
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[]
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|]
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let in_deg = Array.make n 0
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let paths = Array.make n 0
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let count_paths () =
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for u = 0 to n - 1 do
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List.iter (fun v -> in_deg.(v) <- in_deg.(v) + 1) adj.(u)
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done;
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let order = ref [] in
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let q = Queue.create () in
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for v = 0 to n - 1 do
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if in_deg.(v) = 0 then Queue.push v q
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done;
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while not (Queue.is_empty q) do
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let u = Queue.pop q in
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order := u :: !order;
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List.iter (fun v ->
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in_deg.(v) <- in_deg.(v) - 1;
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if in_deg.(v) = 0 then Queue.push v q
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) adj.(u)
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done;
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paths.(0) <- 1;
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let topo = List.rev !order in
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List.iter (fun u ->
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List.iter (fun v ->
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paths.(v) <- paths.(v) + paths.(u)
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) adj.(u)
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) topo;
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paths.(n - 1)
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;;
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count_paths ()
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