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Kruskal's minimum spanning tree using path-compressing union-find:
edges (w, u, v):
(1, 0, 1) (2, 1, 2) (3, 0, 3) (4, 2, 3) (5, 3, 4) (6, 0, 4)
After sorting by weight and greedily unioning:
pick (1,0,1) -> components: {0,1} {2} {3} {4}
pick (2,1,2) -> {0,1,2} {3} {4}
pick (3,0,3) -> {0,1,2,3} {4}
skip (4,2,3) -- already connected
pick (5,3,4) -> {0,1,2,3,4}
skip (6,0,4) -- already connected
MST weight = 1 + 2 + 3 + 5 = 11
Tests List.sort with 3-tuple destructuring lambda, compare on int,
Array.init with closure, in-place array mutation in find, boolean
union returning true iff merge happened.
147 baseline programs total.
33 lines
627 B
OCaml
33 lines
627 B
OCaml
let edges = [
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(1, 0, 1); (2, 1, 2); (3, 0, 3); (4, 2, 3); (5, 3, 4); (6, 0, 4)
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]
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let make_uf n = Array.init n (fun i -> i)
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let rec find p x =
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if p.(x) = x then x
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else begin
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let r = find p p.(x) in
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p.(x) <- r;
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r
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end
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let union p x y =
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let rx = find p x in
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let ry = find p y in
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if rx <> ry then begin p.(rx) <- ry; true end
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else false
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let mst_weight n es =
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let sorted = List.sort (fun (w1, _, _) (w2, _, _) -> compare w1 w2) es in
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let p = make_uf n in
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let total = ref 0 in
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List.iter (fun (w, u, v) ->
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if union p u v then total := !total + w
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) sorted;
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!total
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;;
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mst_weight 5 edges
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