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Ingy döt Net 2023-07-01 11:58:00 -04:00
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Task/Hailstone-sequence/REXX/hailstone-sequence-1.rexx Normal file
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/*REXX program tests a number and also a range for hailstone (Collatz) sequences. */
numeric digits 20 /*be able to handle gihugeic numbers. */
parse arg x y . /*get optional arguments from the C.L. */
if x=='' | x=="," then x= 27 /*No 1st argument? Then use default.*/
if y=='' | y=="," then y= 100000 - 1 /* " 2nd " " " " */
$= hailstone(x) /*▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒task 1▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒*/
say x ' has a hailstone sequence of ' words($)
say ' and starts with: ' subword($, 1, 4) " ∙∙∙"
say ' and ends with: ∙∙∙' subword($, max(5, words($)-3))
if y==0 then exit /*▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒task 2▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒*/
say
w= 0; do j=1 for y; call hailstone j /*traipse through the range of numbers.*/
if #hs<=w then iterate /*Not big 'nuff? Then keep traipsing.*/
bigJ= j; w= #hs /*remember what # has biggest hailstone*/
end /*j*/
say '(between 1 ──►' y") " bigJ ' has the longest hailstone sequence: ' w
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
hailstone: procedure expose #hs; parse arg n 1 s /*N and S: are set to the 1st argument.*/
do #hs=1 while n\==1 /*keep loop while N isn't unity. */
if n//2 then n= n * 3 + 1 /*N is odd ? Then calculate 3*n + 1 */
else n= n % 2 /*" " even? Then calculate fast ÷ */
s= s n /* [↑] % is REXX integer division. */
end /*#hs*/ /* [↑] append N to the sequence list*/
return s /*return the S string to the invoker.*/

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Task/Hailstone-sequence/REXX/hailstone-sequence-2.rexx Normal file
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/*REXX program tests a number and also a range for hailstone (Collatz) sequences. */
!.=0; !.0=1; !.2=1; !.4=1; !.6=1; !.8=1 /*assign even numerals to be "true". */
numeric digits 20; @.= 0 /*handle big numbers; initialize array.*/
parse arg x y z .; !.h= y /*get optional arguments from the C.L. */
if x=='' | x=="," then x= 27 /*No 1st argument? Then use default.*/
if y=='' | y=="," then y= 100000 - 1 /* " 2nd " " " " */
if z=='' | z=="," then z= 12 /*head/tail number? " " " */
hm= max(y, 500000) /*use memoization (maximum num for @.)*/
$= hailstone(x) /*▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒task 1▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒*/
say x ' has a hailstone sequence of ' words($)
say ' and starts with: ' subword($, 1, z) " ∙∙∙"
say ' and ends with: ∙∙∙' subword($, max(z+1, words($)-z+1))
if y==0 then exit /*▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒task 2▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒*/
say
w= 0; do j=1 for y; $= hailstone(j) /*traipse through the range of numbers.*/
#hs= words($) /*find the length of the hailstone seq.*/
if #hs<=w then iterate /*Not big enough? Then keep traipsing.*/
bigJ= j; w= #hs /*remember what # has biggest hailstone*/
end /*j*/
say '(between 1 ──►' y") " bigJ ' has the longest hailstone sequence: ' w
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
hailstone: procedure expose @. !. hm; parse arg n 1 s 1 o,@.1 /*N,S,O: are the 1st arg*/
do while @.n==0 /*loop while the residual is unknown. */
parse var n '' -1 L /*extract the last decimal digit of N.*/
if !.L then n= n % 2 /*N is even? Then calculate fast ÷ */
else n= n * 3 + 1 /*" " odd ? " " 3*n + 1 */
s= s n /* [↑] %: is the REXX integer division*/
end /*while*/ /* [↑] append N to the sequence list*/
s= s @.n /*append the number to a sequence list.*/
@.o= subword(s, 2); parse var s _ r /*use memoization for this hailstone #.*/
do while r\==''; parse var r _ r /*obtain the next hailstone sequence. */
if @._\==0 then leave /*Was number already found? Return S.*/
if _>hm then iterate /*Is number out of range? Ignore it.*/
@._= r /*assign subsequence number to array. */
end /*while*/; return s