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Combinatorics in a functional way
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Date: -- (:)
From: Fernando Alegre <fernando@c...>
Subject: Re: [Caml-list] Combinatorics in a functional way

Hi,

This is what I would do:

let get i (i0,i1,i2,i3,i4,i5,i6,i7) = match i with
  | 0 -> i0 | 1 -> i1 | 2 -> i2 | 3 -> i3 | 4 -> i4 | 5 -> i5 | 6 -> i6
  | 7 -> i7 | _ -> invalid_arg "get"

let set i (i0,i1,i2,i3,i4,i5,i6,i7) x = match i with
  | 0 -> (x,i1,i2,i3,i4,i5,i6,i7) | 1 -> (i0,x,i2,i3,i4,i5,i6,i7)
  | 2 -> (i0,i1,x,i3,i4,i5,i6,i7) | 3 -> (i0,i1,i2,x,i4,i5,i6,i7)
  | 4 -> (i0,i1,i2,i3,x,i5,i6,i7) | 5 -> (i0,i1,i2,i3,i4,x,i6,i7)
  | 6 -> (i0,i1,i2,i3,i4,i5,x,i7) | 7 -> (i0,i1,i2,i3,i4,i5,i6,x)
  | _ -> invalid_arg "set"

let next bounds index =
  let rec loop i index =
    if i = 8 then index else
      let x = get i index in
        if x < get i bounds then set i index (x+1)
        else loop (i+1) (set i index 0)
  in
    loop 0 index

let fold f acc bounds =
  let rec next i index =
    if i = 7 then index
    else if index < get i bounds then set i (index+1)
    else next (i+1) (set i index 0)
  and loop a index =
    if i = 8 then acc else loop (f a index) (next bounds index)
  in
    loop 0 (0,0,0,0,0,0,0)

let find_combi ((p0,p1,p2,p3,p4,p5,p6,p7) as bounds) =
  fold (fun l x -> x :: l) [] bounds

Fernando

On Wed, Feb 21, 2007 at 08:36:03PM +1100, Erik de Castro Lopo wrote:
> Hi all,
> 
> I'm currently working on something where I need to to generate a
> set of permutations that fit a set of rules. Currently I am doing
> something like: