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(* *)
(* Copyright (C) Jean-Christophe Filliatre *)
(* *)
(* This software is free software; you can redistribute it and/or *)
(* modify it under the terms of the GNU Library General Public *)
(* License version 2.1, with the special exception on linking *)
(* described in file LICENSE. *)
(* *)
(* This software is distributed in the hope that it will be useful, *)
(* but WITHOUT ANY WARRANTY; without even the implied warranty of *)
(* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. *)
(* *)
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(* Garsia-Wachs algorithm for optimum binary tree.
See TAOCP vol. 3 page 451. *)
type 'a tree =
| Leaf of 'a
| Node of 'a tree * 'a tree
val garsia_wachs : ('a * int) list -> 'a tree
(** given a list of elements together with nonnegative weights,
say [[x1,w1; ...; xn,wn]], this algorithm builds an optimum
binary tree for [x1,...,xn], that is a tree whose leaves
are [x1,...,xn] in symmetric order and which minimizes
the sum [w1*d(x1) + ... + wn*d(xn)] where [d(xi)] is the depth of
leaf [xi]. *)