I was having a conversation with blokhead
in the CB concerning the most efficient solution to this problem. Not having any idea how to determine the big O notation, I ran a few tests to see how well my solution scaled.
The first thing I noticed was the average number of guesses doubled every time I increased the search group by a factor of 10. Then I noticed something really cool - it also corresponded to a power of 2. This allowed me to calculate the average case scenario for any number
my $num = $ARGV || 47;
my $length = length $num;
my $base = 10 ** ($length - 1);
my $base_ave = 2 ** ($length - 1);
my $next = 10 ** $length;
my $next_ave = 2 ** $length;
my $ave_diff = $next_ave - $base_ave;
my $tot_diff = $next - $base;
my $distance = $num - $base;
my $guess = $base_ave + ($distance * $ave_diff) / $tot_diff;
So for 12_345 you can expect 16.42, and for 123_456_789 you can expect 262.67 As you can see this scales quite well. While this is the average case, the worst case scenario should still scale reasonably well.
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