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Khugaung, Mangifera campnospermoides, Amanita armeniaca & Beamter.

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# -*- 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 from https://download.racket-lang.org/
* schedule
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://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+

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#lang racket
(require "group-scheduling.rkt")
;; define your group
(define fmba-group '("Fidelia" "Marcus" "Donnette" "Garrett" "Lida" "Reagan" "Myrta" "Ginny" "Juliann" "Maxwell" "Serena" "Chante" "Wen" "Malcom" "Lizbeth" "Aleida"))
;; the 'print-rounds' function determines if a particular arrangement of meetings
;; will nable everyon ein th egrouo to have met once.
;; it's given a group (i.e. a list of names) and the number of rounds of 2, 3 or 4
;; first. number of rounds of pairs
;; second. number of rounds of 3 person groups
;; third. number of rounds of 4 person groups
;; show the scenario for week 1
(print-test-rounds fmba-group 2 1 1)
;; begin with seting up the meetings
(start-meetings fmba-group)
;; make a few rounds...
(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)
;; and again...
(reset-meetings fmba-group)
(print-rounds-of-2 fmba-group 2)
(print-all-meetings fmba-group)
;; ...and by end of week 2
(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)

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#lang racket
(provide (all-defined-out))
(require racklog
control
math)
;;logics
(define %has-met %empty-rel) ;; collection of meetings...
(define %t0 %empty-rel) ;; tentative collection...
(define (meeting p1 p2)
(%assert! %has-met () ((p1 p2)))
(%assert! %has-met () ((p2 p1))))
;; various meetings...
;; e.g. (combinations '(p1 p2 p3 p4 p5) 4)
(define (meeting-2 p1 p2)
(meeting p1 p2))
(define (meeting-3 p1 p2 p3)
(meeting p1 p2)
(meeting p1 p3)
(meeting p2 p3))
(define (meeting-4 p1 p2 p3 p4)
(meeting-3 p1 p2 p3)
(meeting-3 p1 p2 p4)
(meeting-3 p1 p3 p4)
(meeting-3 p2 p3 p4))
(define (meeting-5 p1 p2 p3 p4 p5)
(meeting-4 p1 p2 p3 p4)
(meeting-4 p1 p2 p3 p5)
(meeting-4 p1 p2 p4 p5)
(meeting-4 p1 p3 p4 p5)
(meeting-4 p2 p3 p4 p5))
;; assume everyone has "met" themselves
(define (start-meetings group)
(map (lambda (x) (meeting x x)) group)
(printf "starting with group: ~a~n~n" group))
(define (reset-meetings group)
(printf "resetting.~n")
(set! %has-met %empty-rel)
(start-meetings group))
(define (have-they-met? x y)
(if (%which () (%has-met x y)) #t #f))
(define (all-meetings x)
(%find-all (who) (%has-met x who)))
;; make some pairs from a group
(define (make-new-2 group)
(cond
((empty? group) '())
((> 4 (length group)) (list group))
(else
(let* ((p1 (car (shuffle group)))
(p2 (findf (lambda (x)
(not (have-they-met? p1 x))) (remove p1 group))))
(if (and p1 p2)
(begin (meeting-2 p1 p2)
(cons (list p1 p2)
(make-new-2 (shuffle (remove* (list p1 p2) group)))))
'())))))
;; make some triples from a group
(define (make-new-3 group)
(cond
((empty? group) '())
((> 4 (length group)) (list group))
(else
(let* ((p1 (car (shuffle group)))
(p2 (findf (lambda (x)
(not (have-they-met? p1 x))) (remove p1 group)))
(p3 (findf (lambda (x)
(and (not (have-they-met? p1 x))
(not (have-they-met? p2 x)))) (remove* (list p1 p2) group))))
(if (and p1 p2 p3)
(begin (meeting-3 p1 p2 p3)
(cons (list p1 p2 p3)
(make-new-3 (shuffle (remove* (list p1 p2 p3) group)))))
'())))))
;; make some quads from a group
(define (make-new-4 group)
(cond
((empty? group) '())
((> 4 (length group)) (list group))
(else
(let* ((p1 (car (shuffle group)))
(p2 (findf (lambda (x)
(not (have-they-met? p1 x))) (remove p1 group)))
(p3 (findf (lambda (x)
(and (not (have-they-met? p1 x))
(not (have-they-met? p2 x)))) (remove* (list p1 p2) group)))
(p4 (findf (lambda (x)
(and (not (have-they-met? p1 x))
(not (have-they-met? p2 x))
(not (have-they-met? p3 x)))) (remove* (list p1 p2 p3) group))))
(if (and p1 p2 p3 p4)
(begin (meeting-4 p1 p2 p3 p4)
(cons (list p1 p2 p3 p4)
(make-new-4 (shuffle (remove* (list p1 p2 p3 p4) group)))))
'())))))
;; make some fivefiold from a group
(define (make-new-5 group)
(cond
((empty? group) '())
((> 5 (length group)) (list group))
(else
(let* ((p1 (car (shuffle group)))
(p2 (findf (lambda (x)
(not (have-they-met? p1 x))) (remove p1 group)))
(p3 (findf (lambda (x)
(and (not (have-they-met? p1 x))
(not (have-they-met? p2 x)))) (remove* (list p1 p2) group)))
(p4 (findf (lambda (x)
(and (not (have-they-met? p1 x))
(not (have-they-met? p2 x))
(not (have-they-met? p3 x)))) (remove* (list p1 p2 p3) group)))
(p5 (findf (lambda (x)
(and (not (have-they-met? p1 x))
(not (have-they-met? p2 x))
(not (have-they-met? p3 x))
(not (have-they-met? p4 x)))) (remove* (list p1 p2 p3 p4) group))))
(if (and p1 p2 p3 p4 p5)
(begin (meeting-5 p1 p2 p3 p4 p5)
(cons (list p1 p2 p3 p4 p5)
(make-new-5 (shuffle (remove* (list p1 p2 p3 p4 p5) group)))))
'())))))
;; brute repetitor
;; keep trying until something "complete" is output
;; determined by matching length as condition (TBC)
(define escape-counter 100)
(define (decrement-escape)
(set! escape-counter (- escape-counter 1)))
(define (reset-escape)
(set! escape-counter 100))
(define (ensure-new-5 group)
(decrement-escape)
(if (eq? 0 escape-counter)
(begin
(reset-escape)
(printf "escaped from loopland...~n")
'())
(let ((t0 %has-met))
(let ((c (make-new-5 group)))
(if (eq? (length group) (length (flatten c)))
c
(begin
(set! %has-met t0)
(ensure-new-5 group)))))))
(define (ensure-new-4 group)
(decrement-escape)
(if (eq? 0 escape-counter)
(begin
(reset-escape)
(printf "escaped from loopland...~n")
'())
(let ((t0 %has-met))
(let ((c (make-new-4 group)))
(if (eq? (length group) (length (flatten c)))
c
(begin
(set! %has-met t0)
(ensure-new-4 group)))))))
(define (check-group group)
(printf "group is ~s long. repeats? ~a~n~s~n"
(length (flatten group))
(check-duplicates (flatten group))
(sort (flatten group) string<?)))
;; etc etc+
(define (group-pairs l0)
(let ((l (shuffle l0)))
(when (> (remainder (length l) 2) 0)
(printf "there will be ~a leftover.\n" (remainder (length l) 2)))
(if (empty? l) '()
(if (= 1 (length l)) (cons l '())
(cons (list (first l) (second l)) (group-pairs (list-tail l 2)))))))
(define (group-threes l0)
(let ((l (shuffle l0)))
(when (> (remainder (length l) 3) 0)
(printf "there will be ~a leftover.\n" (remainder (length l) 3)))
(case (length l)
((0) '())
((1) (cons l '()))
((2) (cons (list (first l) (second l)) '()))
(else (cons (list (first l) (second l) (third l))
(group-threes (list-tail l 3)))))))
(define (group-fours l0)
(let ((l (shuffle l0)))
(when (> (remainder (length l) 4) 0)
(printf "there will be ~a leftover.\n" (remainder (length l) 4)))
(case (length l)
((0) '())
((1) (cons l '()))
((2) (cons (list (first l) (second l)) '()))
((3) (cons (list (first l) (second l) (third l)) '()))
(else (cons (list (first l) (second l) (third l) (fourth l))
(group-fours (list-tail l 4)))))))
;;; pairs
(define (select-pairs-acc p1 p2 l)
(if (empty? l) '()
(if (have-they-met? (list p1 p2))
(select-pairs-acc p1 (car l) (remove p2 l))
(begin
;(printf "adding: ~a and ~a from ~a\n" p1 p2 l)
(meeting-2 p1 p2)
(cons (list p1 p2) (select-pairs (remove* (list p1 p2) l)))))))
(define (select-pairs l)
(if (< (length l) 1) '()
(let ((p1 (car l))
(p2 (car (shuffle l))))
;(printf "possibly: ~a and ~a from ~a\n" p1 p2 l)
(select-pairs-acc p1 p2 l))))
;;; triples
(define (select-3fold-acc p1 p2 p3 l)
(if (empty? l) '()
(cond
((have-they-met? (list p1 p2))
(select-3fold-acc p1 (car l) p3 (remove p2 l)))
((have-they-met? (list p1 p3))
(select-3fold-acc p1 p2 (car l) (remove p3 l)))
((have-they-met? (list p2 p3))
(select-3fold-acc p1 p2 (car l) (remove p3 l)))
(else (begin
;(printf "adding: ~a, ~a and ~a from ~a\n" p1 p2 p3 l)
(meeting-3 p1 p2 p3)
(cons (list p1 p2 p3) (select-3fold (remove* (list p1 p2 p3) l))))))))
(define (select-3fold l)
(if (< (length l) 1) '()
(let ((p1 (car l))
(p2 (car (shuffle l))) ;; maybe duplicate
(p3 (car (shuffle l)))) ;; maybe duplicate
;(printf "possibly: ~a and ~a from ~a\n" p1 p2 l)
(select-3fold-acc p1 p2 p3 l))))
;;; fours
(define (select-4fold-acc p1 p2 p3 p4 l)
(if (empty? l) '()
(cond
((have-they-met? (list p1 p2 p3 p4))
(select-4fold-acc p1 (car l) p2 p3 (remove p2 l)))
((have-they-met? (list p1 p3))
(select-4fold-acc p1 p2 (car l) (remove p3 l)))
((have-they-met? (list p2 p3))
(select-4fold-acc p1 p2 (car l) (remove p3 l)))
(else (begin
;(printf "adding: ~a, ~a and ~a from ~a\n" p1 p2 p3 l)
(meeting-4 p1 p2 p3 p4)
(cons (list p1 p2 p3 p4) (select-3fold (remove* (list p1 p2 p3) l))))))))
(define (select-4fold l)
(if (< (length l) 1) '()
(let ((p1 (car l))
(p2 (car (shuffle l))) ;; maybe duplicate
(p3 (car (shuffle l))) ;; maybe duplicate
(p4 (car (shuffle l)))) ;; maybe duplicate
;(printf "possibly: ~a and ~a from ~a\n" p1 p2 l)
(select-4fold-acc p1 p2 p3 p4 l))))
;; printing and/or output
(define (print-combinations g n)
(printf "There are ~a combinations of ~a. \n~a\n\n"
(binomial (length g) n)
n
(when (>= 120 (binomial (length g) n))
(combinations g n))))
(define (cross-chatter n r1 r2 r3) ;; n = group size, r = num of rounds (at n=2,3,4)
(let ((m0 (- n 1)))
(printf "Each person needs to meet ~a other people, " m0)
(if (<= m0 (+ r1 (* r2 2) (* r3 3)))
(printf "which is possible.~n~n")
(printf "which is impossilbe with this arrangement.~n~n"))))
(define (print-test-rounds l n1 n2 n3)
(printf "There are ~a people (binomial ~a)\n" (length l) (binomial (length l) 2))
(printf "in ~a rounds of 2, there can be ~s distinct groupings\n" n1 (* n1 (/ (length l) 2)))
(printf "in ~a rounds of 3, there can be ~s distinct groupings\n" n2 (* n2 (/ (length l) 3)))
(printf "in ~a rounds of 4, there can be ~s distinct groupings\n" n3 (* n3 (/ (length l) 4)))
(cross-chatter (length l) n1 n2 n3))
(define (print-pairs l)
(printf "\nnext round, in pairs.\n")
(for ((p0 (select-pairs l)))
(printf "meeting: ~a and ~a\n" (car p0) (second p0))))
(define (print-3fold l)
(printf "\nnext round, groups of 3.\n")
(for ((p0 (select-3fold l)))
(printf "meeting: ~a, ~a and ~a\n" (car p0) (second p0) (third p0))))
;; print and/or ceate subgroups
(define (print-rounds-of-2 group n)
(dotimes (x n)
(printf "next round [2:~a]~n" (+ x 1))
(map (lambda (pair)
(printf "pair: ~a & ~a~n" (first pair) (second pair)))
(make-new-2 group))
(printf "~n")))
(define (print-rounds-of-3 group n)
(dotimes (x n)
(printf "next round [3:~a]~n" (+ x 1))
(for-each (lambda (g0)
(printf "3fold: ~a, ~a & ~a~n"
(if g0 (first g0) "?")
(if (< 1 (length g0)) (second g0) "?")
(if (< 2 (length g0)) (third g0) "?")))
(make-new-3 group))
(printf "~n")))
(define (print-rounds-of-4 group n)
(dotimes (x n)
(printf "next round [4:~a]~n" (+ x 1))
(for-each (lambda (g0)
(printf "4fold: ~a, ~a, ~a & ~a~n"
(if g0 (first g0) "?")
(if (< 1 (length g0)) (second g0) "?")
(if (< 2 (length g0)) (third g0) "?")
(if (< 3 (length g0)) (fourth g0) "?")
))
(make-new-4 group))
(printf "~n")))
(define (print-all-meetings group)
(printf "Meetings so far:~n")
(for-each (lambda (p0)
(printf "~a has met ~a~n"
p0 (drop (map (lambda (p1) (cdar p1))
(all-meetings p0)) 2)))
group)
(printf "~n"))