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in reply to Re: Can this be explained in layman's terms?
in thread [Answered; thanks.] Can this be explained in layman's terms?

Sometimes the rule S(n,k) = 0 if k>n is given for completeness

VERY important if you dont realize n elements ... k non-empty subsets and you just start with

for $n (0..10) { for $k (0..10) { print "$n $k '.fs($n,$k)."\n"; } }

use strict; use warnings; my $l='k '; $l.=sprintf "%3d ",0; for my $k (0..10){ $l.=sprintf " %10s",$k; } print $l."\n"; $l=~s/./-/g; print $l."\n"; for my $n (0..10){ printf "n %3d ",$n; for my $k (0..10){ printf " %10s",fs($n,$k); } print "\n"; } sub fs { my $n=shift; my $k=shift; if ( $n ==0 && $k == 0 ) {return 1}; if ( $k > $n ) {return 0}; # important if ( $n > 0 && $k == 0 ) {return 0} if ( $k == 1 ) {return 1} if ($n == $k ) {return 1} my $p1=fs($n-1,$k-1); my $p2=fs($n-1,$k ); return $p1 + ($k*$p2); }
And i learned never to name my subroutines s
use strict; use warnings; my $l='k '; $l.=sprintf "%3d ",0; for my $k (0..10){ $l.=sprintf " %10s",$k; } print $l."\n"; $l=~s/./-/g; print $l."\n"; for my $n (0..10){ printf "n %3d ",$n; for my $k (0..10){ printf " %10s",s($n,$k); } print "\n"; } sub s { my $n=shift; my $k=shift; if ( $n ==0 && $k == 0 ) {return 1}; if ( $k > $n ) {return 0}; # important if ( $n > 0 && $k == 0 ) {return 0} if ( $k == 1 ) {return 1} if ($n == $k ) {return 1} my $p1=s($n-1,$k-1); my $p2=s($n-1,$k ); return $p1 + ($k*$p2); }
output
Global symbol "$p2" requires explicit package name at buk-2.pl line 30 +. syntax error at buk-2.pl line 31, near "return" (Might be a runaway multi-line ;; string starting on line 29) Global symbol "$p1" requires explicit package name at buk-2.pl line 31 +. Global symbol "$p2" requires explicit package name at buk-2.pl line 31 +. Missing right curly or square bracket at buk-2.pl line 32, at end of l +ine syntax error at buk-2.pl line 32, at EOF Execution of buk-2.pl aborted due to compilation errors.