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############################################################################
#
# File: memrfncs.icn
#
# Subject: Procedures for recursive functions using memory
#
# Author: Ralph E. Griswold
#
# Date: February 4, 1995
#
############################################################################
#
# This file is in the public domain.
#
############################################################################
#
# These procedures implement commonly referenced ``text-book''
# recursively defined functions using memory to avoid redundant calls.
#
# acker(i, j) Ackermann's function
# fib(i) Fibonacci sequence
# q(i) "Chaotic" sequence
#
############################################################################
#
# See also: fastfncs, iterfncs.icn, and recrfncs.icn
#
############################################################################
procedure acker(i, j)
static memory
initial {
memory := table()
every memory[0 to 100] := table()
}
if i = 0 then return j + 1
if j = 0 then /memory[i][j] := acker(i - 1, 1)
else /memory[i][j] := acker(i - 1, acker(i, j - 1))
return memory[i][j]
end
procedure fib(i)
static memory
initial {
memory := table()
memory[1] := memory[2] := 1
}
/memory[i] := fib(i - 1) + fib(i - 2)
return memory[i]
end
procedure q(i)
static memory
initial {
memory := table()
memory[1] := memory[2] := 1
}
/memory[i] := q(i - q(i - 1)) + q(i - q(i - 2))
return memory[i]
end
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