but then why does length(@a) report 5 when there is a value in $a[37865]? )
Because the string "37866" has five characters in it. You want 0+@a, scalar(@a) or similar to get the number of entries in the array.
Did you think you were proving Perl arrays are sparse? That's not the case. Quite the opposite, Perl usually allocates more memory than needed to allow future growth.
$ perl -MDevel::Peek -e'$a[37865]=1; Dump \@a,1; push @a,2; Dump \@a,1
+'
SV = RV(0x8176690) at 0x814ed9c
SV = PVAV(0x8153c64) at 0x814f6a8
FILL = 37865 <-- Index of last used ele
MAX = 37865 <-- Index of last allocated ele
SV = RV(0x8176690) at 0x814f684
SV = PVAV(0x8153c64) at 0x814f6a8
FILL = 37866 <-- Index of last used ele
MAX = 65531 <-- Index of last allocated ele
(Output trimmed to the relevant.)
So we can't compare arrays and hashes without looking at the costs to do operations or their built-in access methods.
Indeed. They each have their strengths.