Re: Cookies in boxes - algorithmic challenge

From	Michael S <already5chosen@yahoo.com>
Newsgroups	comp.lang.c
Subject	Re: Cookies in boxes - algorithmic challenge
Date	2026-04-10 16:16 +0300
Organization	A noiseless patient Spider
Message-ID	<20260410161638.00007745@yahoo.com> (permalink)
References	<20260401163447.000052de@yahoo.com> <86tstlwjak.fsf@linuxsc.com> <20260408222330.00005cf8@yahoo.com> <865x5zbg10.fsf@linuxsc.com>

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On Thu, 09 Apr 2026 21:22:51 -0700
Tim Rentsch <tr.17687@z991.linuxsc.com> wrote:

> Michael S <already5chosen@yahoo.com> writes:
> 
> > On Wed, 08 Apr 2026 08:42:11 -0700
> > Tim Rentsch <tr.17687@z991.linuxsc.com> wrote:
> >  
> >> Michael S <already5chosen@yahoo.com> writes:
> >>

<snip, answered in the other post>

> As it turns out my code handles N_BOXES up to 52.  You may laugh
> when you see why.
> 

The number of small+capital letters in English alphabet? 
Probably, not.
Indeed, after reading the rest, it's not that.

> > Now few words about my own solutions.
> > 1. Original solution:
> > This solution is based on the proof that was given to me by somebody
> > with abstract math mind.  
> 
> Yes, I posted a comment about that
> 
> > 2. It is solution that I found independently, for which I hopefully
> > have a proof in the head, but I didn't write it out yet and didn't
> > show yet to said mathematician.  It would not surprise me if idea
> > of these solution is the same as yours.  
> 
> I don't really understand that code yet, but it looks like your
> code is a bit fancier than mine (the code that wasn't posted
> because it uses a different interface).
> 
> > Later today (tonight) I plan to post both solutions here.  
> 
> Here is an outline of the first (non-interface-compatible) code that
> I wrote.
> 
> Use a straightforward backtracking scheme.  Make a choice at the
> current level, and do a recursive call to try the next level.  If
> the next level returns, it failed, so go on to the next choice at
> this level and call again.
>
> The output value is an array (passed recursively via pointer) with
> either a cookie type for each box or a box number for each cookie
> type (I don't remember which).  This array is filled in as the
> recursive backtrack progresses.
> 
> The whole search is started by doing a setjmp() before the call to
> the top level.  If the search succeeds, a longjmp() is done to
> deliver an answer.  That means that if the call to the top level
> returns then the search was a failure.  The central recursive
> function has four parameters:
> 
>   an Answer *'out', to hold the solution
>   a  jmp_buf 'found', for a longjmp() when a full answer is found
>   a  counter/index to reflect search depth (starting 0, 20 means done)
>   a  "solution state" to direct the search (conceptually by value)
> 
> The "solution state" is at the heart of the algorithm.  It's a
> structure holding an array of 20 "cookie values", where a cookie
> value is represented by an unsigned 64-bit int.  The bits are
> used as follows:
> 
>   low six bits: the cookie type
>   next 52 bits: a "box mask", indicating at least one cookie of
>                 this type in the corresponding box (so up to 52
>                 boxes)
>   upper bits:   count of boxes (ie, number of ones in the box mask)
> 
> The cookie type is important when storing a partial result in the
> answer, not at any other time.
> 
> The box mask is important to know which boxes to try during the
> backtracking.
> 
> The count of boxes is important to help guide the backtracking, in a
> way that we hope will get an answer faster.
> 
> At each level of recursion, do the following:
> 
>    If the search depth is the number of boxes, longjmp()
> 
>    Next find the cookie of cookies in the solution state at or
>    above this level that has the smallest number of boxes.  Because
>    the box count is held in the uppermost bits the 64-bit values can
>    simply be directly compared, without any masking. 

Is it proven that this step helps?
To me it sounds unnecessary.

>    Move that
>    cookie to the array location corresponding to the current depth
>    (and put the cookie that was there in the hole left by doing the
>    move).
> 
>    For each box in the box mask of that cookie, try selecting that
>    box for this cookie, which means:
> 
>       copy the state of cookies above this level to a new solution
>       state, so the changed solution state described above can be
>       left alone
> 
>       for each of those cookies, if the cookie has the "selected box"
>       set in its box mask, clear the bit and reduce the box count
>       by one.  (again since the box count is held in high order bits
>       this count can be reduced by just subtracting a scaled one
>       value.)
> 
>       recurse to continue searching at the next level
> 
>    If we run out of boxes to check, just return;  continue trying
>    alternatives at the next level up, if there is one.
> 
> I think that's it.  I hope it makes sense.

It makes sense, but it looks to me as solution by exhausting, augmented
by "smallest number of boxes" heuristic.
It's not obvious [to me] without further thinking that the worst case is
not very slow.

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Cookies in boxes - algorithmic challenge Michael S <already5chosen@yahoo.com> - 2026-04-01 16:34 +0300
  Re: Cookies in boxes - algorithmic challenge DFS <nospam@dfs.com> - 2026-04-01 10:02 -0400
    Re: Cookies in boxes - algorithmic challenge Michael S <already5chosen@yahoo.com> - 2026-04-01 17:15 +0300
      Re: Cookies in boxes - algorithmic challenge DFS <nospam@dfs.com> - 2026-04-01 10:28 -0400
        Re: Cookies in boxes - algorithmic challenge Michael S <already5chosen@yahoo.com> - 2026-04-01 17:58 +0300
  Re: Cookies in boxes - algorithmic challenge Bart <bc@freeuk.com> - 2026-04-01 15:20 +0100
    Re: Cookies in boxes - algorithmic challenge Michael S <already5chosen@yahoo.com> - 2026-04-01 17:56 +0300
      Re: Cookies in boxes - algorithmic challenge Bart <bc@freeuk.com> - 2026-04-01 19:50 +0100
        Re: Cookies in boxes - algorithmic challenge DFS <nospam@dfs.com> - 2026-04-01 15:56 -0400
          Re: Cookies in boxes - algorithmic challenge Bart <bc@freeuk.com> - 2026-04-01 23:33 +0100
        Re: Cookies in boxes - algorithmic challenge Richard Harnden <richard.nospam@gmail.invalid> - 2026-04-04 07:43 +0100
          Re: Cookies in boxes - algorithmic challenge Bart <bc@freeuk.com> - 2026-04-04 11:54 +0100
  Re: Cookies in boxes - algorithmic challenge DFS <nospam@dfs.com> - 2026-04-01 15:24 -0400
  Re: Cookies in boxes - algorithmic challenge DFS <nospam@dfs.com> - 2026-04-01 17:24 -0400
    Re: Cookies in boxes - algorithmic challenge Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2026-04-02 16:25 +0100
      Re: Cookies in boxes - algorithmic challenge Bart <bc@freeuk.com> - 2026-04-02 17:10 +0100
        Re: Cookies in boxes - algorithmic challenge Michael S <already5chosen@yahoo.com> - 2026-04-02 22:19 +0300
      Re: Cookies in boxes - algorithmic challenge DFS <nospam@dfs.com> - 2026-04-02 13:03 -0400
        Re: Cookies in boxes - algorithmic challenge Richard Harnden <richard.nospam@gmail.invalid> - 2026-04-02 18:52 +0100
        Re: Cookies in boxes - algorithmic challenge Bart <bc@freeuk.com> - 2026-04-02 19:50 +0100
          Re: Cookies in boxes - algorithmic challenge Michael S <already5chosen@yahoo.com> - 2026-04-02 22:24 +0300
        Re: Cookies in boxes - algorithmic challenge Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2026-04-02 20:13 +0100
          Re: Cookies in boxes - algorithmic challenge Michael S <already5chosen@yahoo.com> - 2026-04-02 22:36 +0300
      Re: Cookies in boxes - algorithmic challenge Michael S <already5chosen@yahoo.com> - 2026-04-02 22:14 +0300
    Re: Cookies in boxes - algorithmic challenge Michael S <already5chosen@yahoo.com> - 2026-04-02 22:10 +0300
      Re: Cookies in boxes - algorithmic challenge Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-04-06 22:36 +0100
        Re: Cookies in boxes - algorithmic challenge Tim Rentsch <tr.17687@z991.linuxsc.com> - 2026-04-06 15:42 -0700
        Re: Cookies in boxes - algorithmic challenge Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2026-04-06 15:44 -0700
  Re: Cookies in boxes - algorithmic challenge DFS <nospam@dfs.com> - 2026-04-04 13:33 -0400
    Re: Cookies in boxes - algorithmic challenge Michael S <already5chosen@yahoo.com> - 2026-04-04 21:03 +0300
      Re: Cookies in boxes - algorithmic challenge DFS <nospam@dfs.com> - 2026-04-04 14:19 -0400
      Re: Cookies in boxes - algorithmic challenge Bart <bc@freeuk.com> - 2026-04-04 20:22 +0100
        Re: Cookies in boxes - algorithmic challenge Michael S <already5chosen@yahoo.com> - 2026-04-04 22:40 +0300
  Re: Cookies in boxes - algorithmic challenge Tim Rentsch <tr.17687@z991.linuxsc.com> - 2026-04-04 17:08 -0700
  Re: Cookies in boxes - algorithmic challenge Tim Rentsch <tr.17687@z991.linuxsc.com> - 2026-04-08 08:42 -0700
    Re: Cookies in boxes - algorithmic challenge Michael S <already5chosen@yahoo.com> - 2026-04-08 22:23 +0300
      Re: Cookies in boxes - algorithmic challenge Tim Rentsch <tr.17687@z991.linuxsc.com> - 2026-04-09 21:22 -0700
        Re: Cookies in boxes - algorithmic challenge Michael S <already5chosen@yahoo.com> - 2026-04-10 12:23 +0300
          Re: Cookies in boxes - algorithmic challenge Tim Rentsch <tr.17687@z991.linuxsc.com> - 2026-04-10 22:41 -0700
        Re: Cookies in boxes - algorithmic challenge Michael S <already5chosen@yahoo.com> - 2026-04-10 16:16 +0300
          Re: Cookies in boxes - algorithmic challenge Tim Rentsch <tr.17687@z991.linuxsc.com> - 2026-04-11 04:27 -0700
        Re: Cookies in boxes - algorithmic challenge Michael S <already5chosen@yahoo.com> - 2026-04-11 22:56 +0300
          Re: Cookies in boxes - algorithmic challenge Tim Rentsch <tr.17687@z991.linuxsc.com> - 2026-04-11 15:57 -0700
            Re: Cookies in boxes - algorithmic challenge Michael S <already5chosen@yahoo.com> - 2026-04-12 02:15 +0300
            Re: Cookies in boxes - algorithmic challenge Michael S <already5chosen@yahoo.com> - 2026-04-13 02:03 +0300
            Re: Cookies in boxes - algorithmic challenge Michael S <already5chosen@yahoo.com> - 2026-04-13 17:11 +0300
              Re: Cookies in boxes - algorithmic challenge Tim Rentsch <tr.17687@z991.linuxsc.com> - 2026-04-16 23:52 -0700
                Re: Cookies in boxes - algorithmic challenge Michael S <already5chosen@yahoo.com> - 2026-04-17 14:44 +0300
                Re: Cookies in boxes - algorithmic challenge Tim Rentsch <tr.17687@z991.linuxsc.com> - 2026-04-17 07:40 -0700
                Re: Cookies in boxes - algorithmic challenge Michael S <already5chosen@yahoo.com> - 2026-04-17 18:30 +0300
                Re: Cookies in boxes - algorithmic challenge Michael S <already5chosen@yahoo.com> - 2026-04-20 00:43 +0300
                Re: Cookies in boxes - algorithmic challenge Michael S <already5chosen@yahoo.com> - 2026-04-21 20:37 +0300
                Re: Cookies in boxes - algorithmic challenge Tim Rentsch <tr.17687@z991.linuxsc.com> - 2026-04-21 18:22 -0700
                Re: Cookies in boxes - algorithmic challenge Michael S <already5chosen@yahoo.com> - 2026-04-22 12:05 +0300
    Re: Cookies in boxes - algorithmic challenge Michael S <already5chosen@yahoo.com> - 2026-04-15 02:15 +0300
      Re: Cookies in boxes - algorithmic challenge Tim Rentsch <tr.17687@z991.linuxsc.com> - 2026-04-16 02:57 -0700
        Re: Cookies in boxes - algorithmic challenge Michael S <already5chosen@yahoo.com> - 2026-04-17 17:04 +0300
  Re: Cookies in boxes - algorithmic challenge Michael S <already5chosen@yahoo.com> - 2026-04-08 23:45 +0300
    Re: Cookies in boxes - algorithmic challenge Tim Rentsch <tr.17687@z991.linuxsc.com> - 2026-04-09 16:37 -0700
      Re: Cookies in boxes - algorithmic challenge Michael S <already5chosen@yahoo.com> - 2026-04-10 17:02 +0300
        Re: Cookies in boxes - algorithmic challenge Tim Rentsch <tr.17687@z991.linuxsc.com> - 2026-04-11 03:45 -0700
  Re: Cookies in boxes - algorithmic challenge Michael S <already5chosen@yahoo.com> - 2026-04-09 00:01 +0300
    Re: Cookies in boxes - algorithmic challenge Tim Rentsch <tr.17687@z991.linuxsc.com> - 2026-04-09 17:07 -0700
      Re: Cookies in boxes - algorithmic challenge Michael S <already5chosen@yahoo.com> - 2026-04-10 18:06 +0300
        Re: Cookies in boxes - algorithmic challenge Tim Rentsch <tr.17687@z991.linuxsc.com> - 2026-04-11 04:31 -0700
        Re: Cookies in boxes - algorithmic challenge Tim Rentsch <tr.17687@z991.linuxsc.com> - 2026-04-16 03:22 -0700
  Re: Cookies in boxes - algorithmic challenge Bonita Montero <Bonita.Montero@gmail.com> - 2026-04-17 17:58 +0200
    Re: Cookies in boxes - algorithmic challenge Bonita Montero <Bonita.Montero@gmail.com> - 2026-04-17 18:08 +0200
    Re: Cookies in boxes - algorithmic challenge Bart <bc@freeuk.com> - 2026-04-17 17:47 +0100
      Re: Cookies in boxes - algorithmic challenge Bonita Montero <Bonita.Montero@gmail.com> - 2026-04-17 19:24 +0200
    Re: Cookies in boxes - algorithmic challenge scott@slp53.sl.home (Scott Lurndal) - 2026-04-17 19:58 +0000
      Re: Cookies in boxes - algorithmic challenge Bonita Montero <Bonita.Montero@gmail.com> - 2026-04-18 05:52 +0200
        Re: Cookies in boxes - algorithmic challenge Bart <bc@freeuk.com> - 2026-04-18 11:53 +0100
          Re: Cookies in boxes - algorithmic challenge Bart <bc@freeuk.com> - 2026-04-18 12:04 +0100
        Re: Cookies in boxes - algorithmic challenge Michael S <already5chosen@yahoo.com> - 2026-04-18 20:35 +0300
  Re: Cookies in boxes - algorithmic challenge Bonita Montero <Bonita.Montero@gmail.com> - 2026-04-17 19:52 +0200
    Re: Cookies in boxes - algorithmic challenge Bonita Montero <Bonita.Montero@gmail.com> - 2026-04-17 20:17 +0200

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