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###########################################################################
#
# File: partit.icn
#
# Subject: Procedures to partition integer
#
# Author: Ralph E. Griswold
#
# Date: December 5, 1995
#
############################################################################
#
# This file is in the public domain.
#
############################################################################
#
# partit(i, min, max) generates, as lists, the partitions of i; that is the
# ways that i can be represented as a sum of positive integers with
# minimum and maximum values.
#
# partcount(i, min, max) returns just the number of partitions.
#
# fibpart(i) returns a list of Fibonacci numbers that is a partition of i.
#
############################################################################
#
# Links: fastfncs, numbers
#
############################################################################
link fastfncs
link numbers
procedure partit(i, min, max, k)
local j
if not(integer(i)) | (i < 0) | (\min > \max) then
stop("*** illegal argument to partit(i)")
/min := 1
/max := i
max >:= i
/k := i
k >:= max
k >:= i
if i = 0 then return []
every j := k to min by -1 do {
suspend push(partit(i - j, min, max, j), j)
}
end
procedure partcount(i, min, max)
local count
count := 0
every partitret(i, min, max) do
count +:= 1
return count
end
# This is a version of partit() that doesn't do all the work
# of producing the partitions and is used only by partcount().
procedure partitret(i, min, max, k)
local j
/min := 1
/max := i
max >:= i
/k := i
k >:= max
k >:= i
if i = 0 then return
every j := k to min by -1 do {
suspend partitret(i - j, min, max, j)
}
end
# Partition of an integer into Fibonacci numbers.
procedure fibpart(i)
local partl, n
static m
initial m := 1 / log(( 1 + sqrt(5)) / 2)
partl := []
while i > 2 do {
push(partl, n := fib(ceil(log(i) * m)))
i -:= n
}
if i > 0 then push(partl, i)
return partl
end
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