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Ingy döt Net 2023-07-01 11:58:00 -04:00
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Task/Bell-numbers/REXX/bell-numbers.rexx Normal file
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/*REXX program calculates and displays a range of Bell numbers (index starts at zero).*/
parse arg LO HI . /*obtain optional arguments from the CL*/
if LO=='' & HI=="" then do; LO=0; HI=14; end /*Not specified? Then use the default.*/
if LO=='' | LO=="," then LO= 0 /* " " " " " " */
if HI=='' | HI=="," then HI= 15 /* " " " " " " */
numeric digits max(9, HI*2) /*crudely calculate the # decimal digs.*/
!.=.; !.0= 1; !.1= 1; @.= 1 /*the FACT function uses memoization.*/
do j=0 for HI+1; $= j==0; jm= j-1 /*JM is used for a shortcut (below). */
do k=0 for j; _= jm - k /* [↓] calculate a Bell # the easy way*/
$= $ + comb(jm, k) * @._ /*COMB≡combination or binomial function*/
end /*k*/
@.j= $ /*assign the Jth Bell number to @ array*/
if j>=LO & j<=HI then say ' Bell('right(j, length(HI) )") = " commas($)
end /*j*/
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
commas: parse arg _; do c=length(_)-3 to 1 by -3; _=insert(',', _, c); end; return _
/*──────────────────────────────────────────────────────────────────────────────────────*/
comb: procedure expose !.; parse arg x,y; if x==y then return 1
if x-y<y then y= x - y; if !.x.y\==. then return !.x.y / fact(y)
_= 1; do j=x-y+1 to x; _= _*j; end; !.x.y= _; return _ / fact(y)
/*──────────────────────────────────────────────────────────────────────────────────────*/
fact: procedure expose !.; parse arg x; if !.x\==. then return !.x; != 1
do f=2 for x-1; != ! * f; end; !.x= !; return !