# -*- mode: org;  coding: utf-8; -*-
#+title: scheduling and grouping

A way to find various subgroups of a group… 

* install 

To run this programme you’ll need a working version of [[https://racket-lang.org/][Racket]] installed (an installer can be downloaded [[https://download.racket-lang.org/][here]])

on macOS
#+BEGIN_SRC shell
brew cask install racket
#+END_SRC

on debian/ubuntu
#+BEGIN_SRC shell
sudo apt intall racket
#+END_SRC

you might also need to install the ~control~ library
#+BEGIN_SRC shell
raco pkg install control 
#+END_SRC

* schedule

[[https://the-public-domain-review.imgix.net/collections/amundsen-s-south-pole-expedition/6504423149_f4ffeb13b8_o.jpg]]

setup…
#+BEGIN_SRC racket
(require "group-scheduling.rkt")
#+END_SRC

define your group as a list of names (or similar)…

#+BEGIN_SRC racket
(define fmba-group '("Fidelia" "Marcus" "Donnette" "Garrett" "Lida" "Reagan" "Myrta" "Ginny" "Juliann" "Maxwell" "Serena" "Chante" "Wen" "Malcom" "Lizbeth" "Aleida"))
#+END_SRC

the =print-test-rounds= function determines if a particular arrangement of meetings  will enable everyone in the group to  meet once….

it's given a group (i.e. a list of names) and the number of rounds of 2, 3 or 4 people
 - first. number of rounds of pairs
 - second. number of rounds of 3 person groups
 - third.  number of rounds of 4 person groups

So 2 rounds of pairs, one round of groups of 3 and one round of groups of 4 would look like this…
#+BEGIN_SRC racket
(print-test-rounds fmba-group 2 1 1)
#+END_SRC

begin with setting up the meetings
#+BEGIN_SRC racket
(start-meetings fmba-group)
#+END_SRC

make a few rounds…
#+BEGIN_SRC racket
(print-rounds-of-2 fmba-group 2)
(print-rounds-of-3 fmba-group 2)
(print-rounds-of-4 fmba-group 1)
(print-all-meetings fmba-group)
#+END_SRC

reset the meetings (i.e. forget who has net who) and go again…
#+BEGIN_SRC racket
(reset-meetings fmba-group)
#+END_SRC

#+BEGIN_SRC racket
(print-rounds-of-2 fmba-group 2)
#+END_SRC

show who has met in the meetings that have happened…
#+BEGIN_SRC racket
(print-all-meetings fmba-group)
#+END_SRC

try a few scenarios…

Week 1: 3x rounds of 2, 1x round of 3
Week 2: 2x rounds of 2, 1x round of 3, 1x round of 4
Week 3: 2x rounds of 2, 1x round of 3, 1x round of 4
Week 4: 2x rounds of 2, 2x rounds of 4

which looks like…
#+BEGIN_SRC racket
(print-test-rounds fmba-group 3 1 0)
(print-test-rounds fmba-group 2 1 1)
(print-test-rounds fmba-group 2 1 1)
(print-test-rounds fmba-group 2 0 2)
#+END_SRC

and test some other scenarios…

#+BEGIN_SRC racket
(printf "\nweek 1 & week 2 (scenario 1)\n\n")
(print-test-rounds fmba-group 5 2 1)

(printf "\nweek 1 & week 2 (scenario 2)\n\n")
(print-test-rounds fmba-group 4 3 1)

(printf "\nweek 1 & week 2 (scenario 3)\n\n")
(print-test-rounds fmba-group 4 2 2)

(printf "\nweek 1 & week 2  (scenario 4)\n\n")
(print-test-rounds fmba-group 4 1 3)
#+END_SRC

* further

- [[https://arxiv.org/abs/cs/0011047][Dancing Links]], [[https://www.geeksforgeeks.org/exact-cover-problem-algorithm-x-set-1/][Exact Cover Problem and Algorithm X]]
- [[https://en.wikipedia.org/wiki/Size_of_groups,_organizations,_and_communities][Size of groups, organizations, and communities]]
- etc+