68 lines
1.8 KiB
Standard ML
68 lines
1.8 KiB
Standard ML
structure BroTree =
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struct
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(* implementation of 1-2 brother tree ported from:
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* https://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/library/HOL/HOL-Data_Structures/document.pdf
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* *)
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datatype bro =
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N0
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| N1 of bro
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| N2 of bro * string * bro
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| L2 of string
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| N3 of bro * string * bro * string * bro
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val empty = N0
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fun n1 bro =
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case bro of
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L2 str => N2 (N0, str, N0)
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| N3 (t1, a1, t2, a2, t3) => N2 (N2 (t1, a1, t2), a2, N1 t3)
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| t => N1 t
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fun n2Left (t1, str, t2) =
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case (t1, str, t2) of
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(L2 a1, a2, t) => N3 (N0, a2, N0, a2, t)
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| (N3 (t1, a1, t2, a2, t3), a3, N1 t4) =>
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N2 (N2 (t1, a1, t2), a2, N2 (t2, a3, t4))
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| (N3 (t1, a1, t2, a2, t3), a3, t4) =>
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N3 (N2 (t1, a1, t2), a2, N1 t3, a3, t4)
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| (t1, a1, t2) => N2 (t1, a1, t2)
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fun n2Right (t1, str, t2) =
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case (t1, str, t2) of
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(t1, a1, L2 a2) => N3 (t1, a2, N0, a2, N0)
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| (N1 t1, a1, N3 (t2, a2, t3, a3, t4)) =>
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N2 (N2 (t1, a1, t2), a2, N2 (t3, a3, t4))
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| (t1, a1, N3 (t2, a2, t3, a3, t4)) =>
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N3 (t1, a2, N1 t2, a2, N2 (t3, a3, t4))
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| (t1, a1, t2) => N2 (t1, a1, t2)
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fun ins (str, tree) =
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case tree of
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N0 => L2 str
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| N1 t => n1 (ins (str, t))
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| N2 (l, a, r) =>
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if str < a then n2Left (ins (str, l), a, r)
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else if str > a then n2Right (l, a, ins (str, r))
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else N2 (l, a, r)
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| _ => raise Match (*impossible case*)
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fun insRoot tree =
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case tree of
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L2 str => N2 (N0, str, N0)
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| N3 (t1, a1, t2, a2, t3) => N2 (N2 (t1, a2, t2), a2, N1 t3)
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| tree => tree
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fun insert (str, tree) =
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insRoot (ins (str, tree))
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fun exists (str, tree) =
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case tree of
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N0 => false
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| N1 t => exists (str, t)
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| N2 (l, k, r) =>
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if str < k then exists (str, l)
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else if str > k then exists (str, r)
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else true
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| _ => raise Match
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end
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