DAVID MALAN: --we'll generally
call a loop, some kind of cycle,
because it's making
me do something again.
DOUG LLOYD: So as we discussed
a little bit earlier,
we're making a conscious effort here
to introduce students to concepts
without introducing them too much
to the heavy theoretical math that
might be behind these.
And so this demonstration about
falling onto the phone book example
where we did the counting by
one page, counting by two pages,
then showing binary
search, gives us a way
to show the different powers
or speeds of these algorithms
without getting too heavy
into the math just yet.
DAVID MALAN: Yeah, and I think it's
a nice way too of throwing away
the distractions of what might be
this plot with an x-axis and a y-axis,
and really just allowing
students to intuitively grasp
that, OK, size of problem gets
bigger that way and time to solve
gets bigger that way, and I
think that's pretty intuitive.
And we certainly don't need
to slap a formal analysis
at this point in the semester, we'll
come back to this in a few weeks' time.
But I think it's
reasonable at this point
to introduce N as just a generic
term for the number of pages,
show the distinction
between N and N over 2.
And what I try to do generally,
especially if I'm doing this demo not
on a digital screen but
on like a chalkboard,
is draw a vertical line as I'm sort
of imaginatively doing with my finger
here to point out that every
line on the yellow line
is half as high as the red line.
But this is what's really important,
and indeed this is deliberate,
the sort of stop light approach of red
is bad, yellow is OK, green is great.
DOUG LLOYD: Yeah, it's
a simple reinforcement,
but it does really
hammer home that point.
DAVID MALAN: And what's powerful too
here, if you have enough of a classroom
to walk left and right
on here, especially
if you can exceed the screen, to point
out that that green line really, it
does grow, and it doesn't
flatten out, but it
grows so slowly that you can be way over
there and have a huge number of pages,
but the time to solve
is still pretty low.
DOUG LLOYD: Right, with 4 billion pages
in the phone book, the first example
you've got 4 billion, with the
yellow line there it's 2 billion,
but with the green line
it's only 32 steps to do it.
DAVID MALAN: And that's
what's pretty powerful.
And that's why I think
it's important in class
to actually fast forward to
pretty big numbers, the 4 billion
which at least has the
relevance of being 2 to the 32,
but to point out to students just,
my god, you go from that many pages
so quickly to just one, it's I think
more compelling than to only go up
to 1,000 pages where dividing it in 10
times is great but it's not as magical.
DOUG LLOYD: It doesn't have that impact.
I agree.
