June 2018 Update

Task/Permutations-Derangements/Perl/permutations-derangements-2.pl

@@ -0,0 +1,25 @@
+use ntheory ":all";
+
+# Count derangements using derangement iterator
+sub countderange {
+  my($n,$s) = (shift,0);
+  forderange { $s++ } $n;
+  $s;
+}
+# Count derangements using inclusion-exclusion
+sub subfactorial1 {
+  my $n = shift;
+  vecsum(map{ vecprod((-1)**($n-$_),binomial($n,$_),factorial($_)) }0..$n);
+}
+# Count derangements using simple recursion without special functions
+sub subfactorial2 {
+  my $n = shift;
+  use bigint;  no warnings 'recursion';
+  ($n < 1)  ?  1  :  $n * subfactorial2($n-1) + (-1)**$n;
+}
+
+print "Derangements of 4 items:\n";
+forderange { print "@_\n" } 4;
+printf "\n%3s %15s %15s\n","N","List count","!N";
+printf "%3d %15d %15d %15d\n",$_,countderange($_),subfactorial1($_),subfactorial2($_) for 0..9;
+printf "%3d %15s %s\n",$_,"",subfactorial2($_) for 20,200;