#-(and) "

P27 (**) Group the elements of a set into disjoint subsets.

a) In how many ways can a group of 9 people work in 3 disjoint
subgroups of 2, 3 and 4 persons? Write a function that generates
all the possibilities and returns them in a list.

Example: * (group3 '(aldo beat carla david evi flip gary hugo
ida)) ( ( (ALDO BEAT) (CARLA DAVID EVI) (FLIP GARY HUGO IDA) )
... )

b) Generalize the above predicate in a way that we can specify a
list of group sizes and the predicate will return a list of
groups.

Example: * (group '(aldo beat carla david evi flip gary hugo ida)
'(2 2 5)) ( ( (ALDO BEAT) (CARLA DAVID) (EVI FLIP GARY HUGO IDA) )
... )

Note that we do not want permutations of the group members;
i.e. ((ALDO BEAT) ...) is the same solution as ((BEAT ALDO)
...). However, we make a difference between ((ALDO BEAT) (CARLA
DAVID) ...) and ((CARLA DAVID) (ALDO BEAT) ...).

on discrete mathematics under the term \"multinomial
coefficients\".
"

(defun group3 (set)
(group set '(2 3 4)))

(defun group (set sizes)
(cond
((endp sizes)
(error "Not enough sizes given."))
((endp (rest sizes))
(if (= (first sizes) (length set))
(list (list set))
(error "Cardinal mismatch |set| = ~A ; required ~A" (length set) (first sizes))))
(t
(mapcan (lambda (combi)
(mapcar (lambda (group) (cons combi group))
(group (set-difference set combi) (rest sizes))))
(combinations (first sizes) set)))))

;; (map nil 'print (group3 '(aldo beat carla david evi flip gary hugo ida)))
;; (map nil 'print (group '(aldo beat carla david evi flip gary hugo ida) '(2 2 5)))

;;;; THE END ;;;;
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