The unpac monorepo manager self-hosting as a monorepo using unpac
Merge pull request #151 from backtracking/kneser-graphs
Classic: new functions kneser and petersen
authored by
Jean-Christophe Filliatre
and committed by
GitHub
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CHANGES.md
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CHANGES.md
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src/classic.ml
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src/classic.ml
···
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val full : ?self:bool -> int -> graph
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val cycle : int -> graph * vertex array
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val grid : n:int -> m:int -> graph * vertex array array
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val kneser : n:int -> k:int -> graph
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val petersen : unit -> graph
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end
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module Generic(B : Builder.INT) = struct
···
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let g = if i < n-1 then B.add_edge g v.(i).(j) v.(i+1).(j) else g in
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loop g i (j+1) in
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loop g 0 0, v
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let kneser ~n ~k =
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if n < 0 || k > n then invalid_arg "kneser";
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let vert = Hashtbl.create (1 lsl n) in
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let add x = Hashtbl.add vert x (B.G.V.create x) in
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let rec visit mask n k =
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assert (0 <= k && k <= n);
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if k = 0 then add mask else
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if k = n then add (mask lor (1 lsl n - 1)) else (
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let n = n - 1 in
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visit mask n k ;
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visit (mask lor (1 lsl n)) n (k - 1);
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) in
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visit 0 n k;
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let g = Hashtbl.fold (fun _ v g -> B.add_vertex g v) vert (B.empty ()) in
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let g = Hashtbl.fold (fun i vi g ->
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Hashtbl.fold (fun j vj g ->
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if i land j = 0 then B.add_edge g vi vj else g) vert g) vert g in
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g
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let petersen () =
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kneser ~n:5 ~k:2
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end
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src/classic.mli
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src/classic.mli
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wrapping around). Vertex [(i,j)] is labelled with [i*m+j].
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Vertices are also returned in a [n*m] matrix for convenience. *)
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val kneser : n:int -> k:int -> graph
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(** [kneser n k] builds the Kneser graph K(n, k), where vertices
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correspond to the k-element subsets of a set of n elements, and
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where two vertices are adjacent if and only if the two
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corresponding sets are disjoint. *)
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val petersen : unit -> graph
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(** [petersen ()] builds the Petersen graph, that is isomorphic
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to the Kneser graph K(5,2). It has 10 vertices and 15 edges. *)
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end
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module P (G : Sig.P with type V.label = int) :
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src/sig_pack.mli
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src/sig_pack.mli
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from vertex [(i,j)] to vertices [(i+1,j)] and [(i,j+1)] (and no
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wrapping around). Vertex [(i,j)] is labelled with [i*m+j].
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Vertices are also returned in a [n*m] matrix for convenience. *)
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val kneser : n:int -> k:int -> t
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(** [kneser n k] builds the Kneser graph K(n, k), where vertices
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correspond to the k-element subsets of a set of n elements, and
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where two vertices are adjacent if and only if the two
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corresponding sets are disjoint. *)
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val petersen : unit -> t
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(** [petersen ()] builds the Petersen graph, that is isomorphic
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to the Kneser graph K(5,2). It has 10 vertices and 15 edges. *)
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end
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(** Random graphs *)
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tests/dune
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tests/dune
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tests/test_classic.ml
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tests/test_classic.ml
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(**************************************************************************)
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(* *)
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(* Ocamlgraph: a generic graph library for OCaml *)
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(* Copyright (C) 2004-2007 *)
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(* Sylvain Conchon, Jean-Christophe Filliatre and Julien Signoles *)
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(* *)
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(* This software is free software; you can redistribute it and/or *)
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(* modify it under the terms of the GNU Library General Public *)
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(* License version 2, with the special exception on linking *)
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(* described in file LICENSE. *)
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(* *)
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(* This software is distributed in the hope that it will be useful, *)
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(* but WITHOUT ANY WARRANTY; without even the implied warranty of *)
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(* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. *)
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(* *)
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(**************************************************************************)
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open Graph.Pack.Graph
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let g = Classic.petersen ()
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let () = assert (nb_vertex g = 10)
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let () = assert (nb_edges g = 15)
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let () = dot_output g "petersen.dot"
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let g = Classic.kneser ~n:7 ~k:3
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let () = dot_output g "k_7_3.dot"