From mboxrd@z Thu Jan 1 00:00:00 1970 Path: news.gmane.io!.POSTED.blaine.gmane.org!not-for-mail From: Emanuel Berg Newsgroups: gmane.emacs.help Subject: Re: puzzle with string permutations [photo] Date: Wed, 08 Jun 2022 00:04:16 +0200 Message-ID: <87h74wm8pr.fsf@dataswamp.org> References: <87r141rn8n.fsf@dataswamp.org> <87wndtrlpg.fsf@mbork.pl> <87k09ssycf.fsf@dataswamp.org> <87fskgsy4c.fsf@dataswamp.org> <87bkv4sxnu.fsf@dataswamp.org> <87bkv4r35k.fsf@dataswamp.org> <8735ggr1z0.fsf@dataswamp.org> Mime-Version: 1.0 Content-Type: text/plain; charset=utf-8 Content-Transfer-Encoding: 8bit Injection-Info: ciao.gmane.io; posting-host="blaine.gmane.org:116.202.254.214"; logging-data="35481"; mail-complaints-to="usenet@ciao.gmane.io" User-Agent: Gnus/5.13 (Gnus v5.13) Emacs/29.0.50 (gnu/linux) To: help-gnu-emacs@gnu.org Cancel-Lock: sha1:mbHgR8UlpjO2zbpE7R2apy20XOA= Original-X-From: help-gnu-emacs-bounces+geh-help-gnu-emacs=m.gmane-mx.org@gnu.org Wed Jun 08 01:28:04 2022 Return-path: Envelope-to: geh-help-gnu-emacs@m.gmane-mx.org Original-Received: from lists.gnu.org ([209.51.188.17]) by ciao.gmane.io with esmtps (TLS1.2:ECDHE_RSA_AES_256_GCM_SHA384:256) (Exim 4.92) (envelope-from ) id 1nyicG-000908-31 for geh-help-gnu-emacs@m.gmane-mx.org; Wed, 08 Jun 2022 01:28:04 +0200 Original-Received: from localhost ([::1]:41244 helo=lists1p.gnu.org) by lists.gnu.org with esmtp (Exim 4.90_1) (envelope-from ) id 1nyicE-0005qu-Nz for geh-help-gnu-emacs@m.gmane-mx.org; Tue, 07 Jun 2022 19:28:02 -0400 Original-Received: from eggs.gnu.org ([2001:470:142:3::10]:54764) by lists.gnu.org with esmtps (TLS1.2:ECDHE_RSA_AES_256_GCM_SHA384:256) (Exim 4.90_1) (envelope-from ) id 1nyhJM-0007K7-Sf for help-gnu-emacs@gnu.org; Tue, 07 Jun 2022 18:04:29 -0400 Original-Received: from ciao.gmane.io ([116.202.254.214]:43148) by eggs.gnu.org with esmtps (TLS1.2:ECDHE_RSA_AES_256_GCM_SHA384:256) (Exim 4.90_1) (envelope-from ) id 1nyhJL-0004Zc-4r for help-gnu-emacs@gnu.org; Tue, 07 Jun 2022 18:04:28 -0400 Original-Received: from list by ciao.gmane.io with local (Exim 4.92) (envelope-from ) id 1nyhJJ-0007uT-FJ for help-gnu-emacs@gnu.org; Wed, 08 Jun 2022 00:04:25 +0200 X-Injected-Via-Gmane: http://gmane.org/ Mail-Followup-To: help-gnu-emacs@gnu.org Mail-Copies-To: never Received-SPF: pass client-ip=116.202.254.214; envelope-from=geh-help-gnu-emacs@m.gmane-mx.org; helo=ciao.gmane.io X-Spam_score_int: -16 X-Spam_score: -1.7 X-Spam_bar: - X-Spam_report: (-1.7 / 5.0 requ) BAYES_00=-1.9, HEADER_FROM_DIFFERENT_DOMAINS=0.249, SPF_HELO_NONE=0.001, SPF_PASS=-0.001, T_SCC_BODY_TEXT_LINE=-0.01 autolearn=no autolearn_force=no X-Spam_action: no action X-BeenThere: help-gnu-emacs@gnu.org X-Mailman-Version: 2.1.29 Precedence: list List-Id: Users list for the GNU Emacs text editor List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , Errors-To: help-gnu-emacs-bounces+geh-help-gnu-emacs=m.gmane-mx.org@gnu.org Original-Sender: "help-gnu-emacs" Xref: news.gmane.io gmane.emacs.help:137519 Archived-At: Yuri Khan wrote: > This extension of the concept of sets is called a multiset > or a bag. For each element, we also have a multiplicity. > Let’s write it as {o:2, g:1, d:1}. OK, cool! > n_perm = (n_1 + ... + n_k)! / (n_1)! ... (n_k)! Right, that's tedious to do programming of tho (but possible of course) because of the expanding summation and product ... > This problem was part of my exam in maths when I was > applying at Novosibirsk State University, Mechanics & Maths > Department, in 1997. :) > You might also notice the formula is similar to that of > a binomial coefficient: C_{n,k} = n! / k! (n-k)!. That's > no coincidence. That OTOH is easy to implement, but what is n and k exactly? Can you use that here? (defun binom (n k) (/ (cl-faculty n) (* (cl-faculty k) (cl-faculty (- n k)) ))) -- underground experts united https://dataswamp.org/~incal