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load 'stats'
NB. rank, combine, f, factorsof1, factorsof and helper are all helper functions used by factors
NB. to find all factorizations of a number. Works but is not so nice :)
rank=:{.@$@$
combine=: (*./`])@.(1: = rank)
f=: dyad define
factors=.x
length=.$factors
keep=.y{factors
rest=.(combine y~:"0 _ i.length)#factors
(*/rest),keep
)
factorsof1=: monad define
len=.$y
((y&f)"1)@comb&len len-2
)
factorsof=: monad define
cols=.<:{:$y
vals=.;factorsof1"1 y
rows=.($vals) % cols
~. (rows,cols)$vals
)
helper=: dyad : '<"1 factorsof^:x (1,$y)$y'
factors=: monad define
pfacts=.q:y
;(helper&pfacts) each i.$pfacts
)
NB. runme creates a large list of every possible factorization of numbers from 2 to 2*k
NB. Then it goes over that list and updates the numbers array with the smallest
NB. product-sum number. product-sum numbers from a set of factors such as 3 2 2 by adding
NB. enough ones, since that makes the sum large enough. the k for which a set of factors
NB. can be used can be calculated by (prod-sum)+$factors
NB. and can be read as "number of ones needed" + "number of factors"
NB. The slowest part of the program is finding all factorizations of numbers.
runme=: monad define
maxk=.y
maxn=.2*maxk
facts=. ; factors each 2+i.(maxn-1)
numbers=. maxn$_
factorcount=.$facts
index=.0
while. index < factorcount do.
nums=.>index{facts
index=. >:index
sum=.+/nums
prod=.*/nums
n=.(prod-sum)+$nums NB. any factors can be used when padded with enough ones :)
oldprod=.n{numbers
if. prod < oldprod do.
numbers=.prod n} numbers
end.
end.
numbers=. (-maxk-1)}. 2}. numbers NB. drop for k=0,1, and take (maxk-1) elements
+/~.numbers
)
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