' Puzzlet #199
' A sequence is formed from integer n
' thus: if any of n's digits are zero,
' n = n + the sum of its digits; if n
' contains no zeroes, n = the product
' of its digits. All subsequent terms
' are formed in the same way. The
' sequence terminates when a term is
' reduced to a single digit.
' Example: 27, 41, 45, 65, 95, 140, 5.
' For initial values under 1,000, find
' all sequences greater than 30 terms.
' By Dave Ellis.

' Declarations
declare SumDigits(s: int)
declare ProductDigits(p: int)
declare NoZeroes(n: int)
declare GenerateSequence(n: int, p: int)
def count, nr, n: int

' Screen SetUp
color 11, 0: cls
openconsole
print "Searching ... "
print
color 15, 0

' Initialisations
nr = 1

' Main routine
do
	n = nr: 'save initial term
	'get sequence length	
	count = GenerateSequence(n, 0)
	if count > 30: 'length > 30?
		print "Count: ", count, chr$(8),".  ",
		color 14, 0
		GenerateSequence(n, -1): 'print it
		color 15, 0		
		print: print
	endif
	nr = nr + 1: 'get new initial term
until nr > 1000

' Finished
color 11, 0
print "That's all, Folks!"
print: print "Press any key ... ",
do: until inkey$ <> ""
closeconsole
end

' +++ Subroutines and Functions +++

sub ProductDigits(p)
' Returns the product of the 
' digits of integer p. Will
' give incorrect answer if p
' larger than defined limits
' for integers.
def tot: int
tot = 1
do
	' separate out LSD and totalise
	tot = tot * (p % 10)
	' chop off LSD
	p = p/10
until p = 0: ' all chopped off!
return tot

sub SumDigits(s)
' Returns the sum of the 
' digits of integer s. Will
' give incorrect answer if s
' larger than defined limits
' for integers.
def tot: int
tot = 0
do
	' separate out LSD and totalise
	tot = tot + (s % 10)
	' chop off LSD
	s = s/10
until s = 0: 'all chopped off!
return tot

sub NoZeroes(n)
' If argument n is zero or it
' contains at least one zero
' after a non-zero digit, 
' returns FALSE (0), otherwise
' returns TRUE (-1).
' Note: this method is 35%
' faster than string method.
def flag: int
flag = -1
do
	if n % 10 = 0: 'is LSD a zero?
		flag = 0
	else
		n = n/10: 'chop off LSD
	endif
until not flag | n < 1: 'done
return flag

sub GenerateSequence(n, p)
' Generates the Sequence term by
' term, and returns the lenght of
' the sequence as saved in cnt.
' If argument p is TRUE, will also
' print out sequence as each term
' is generated.
' By Dave Ellis.
def cnt: int
cnt = 1
if p: 'is it for printing?
	print n,: 'yes!
endif
do
	if NoZeroes(n): 'contain zeroes?
		n = n + ProductDigits(n): 'yes!
	else: 'no zeroes in it
		n = SumDigits(n)
	endif
	if p: 'print it?
		print n,	
	endif
	cnt = cnt + 1
	if p & (cnt % 8 = 0)
		print chr$(13)
	endif
until (n < 10)
return cnt