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okay let's finish our derivation of the
condom problem we started Oct

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leads a very simple brewed for solution

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then and the second step we took

4
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an the generation process and we made
sure that we

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never generates expressions that were
invalid

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and what we're going to do in this third
step is we're going to

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shrink the search space by and
leveraging

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a algebraic properties of expression in
particular

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the fact that multiplication is
committed F

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and the fact that Wong is the new char
element

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for multiplication game saw

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these are the property we're going to
use multiplication

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is commuted F and and

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Wong is the new char element for

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multiplication alright

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sure here's the I am previous definition
of whether an

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expression was valid and every member

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an expression was valid when the

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numbers %uh which it was composure your
boss in Excel

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when we added to an

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values well thats now let's because
adding to positive numbers is

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get a positive number when we subtract
two numbers

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the result is positive when the first
number is larger than the second

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multiplication of two numbers positive
numbers is always positive

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and here we had to make sure that

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we I'm remains within the integer domain

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well in this case instead of just
returning true

28
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well we do now is we say we want
actually be less than why so we're going

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to make this thing biased so

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adding X to Y is valid

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if axes less than why and we were doing
we're going to do the same

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for multiplication K and now

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am we also want to say that

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if the axe is Wong

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00:02:13,150 --> 00:02:16,610
and we don't considered distinct sell it

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case you were drawing up on the way so
what we're what we did

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is really biased the representation we
say we always want the wall on the left

38
00:02:24,780 --> 00:02:28,569
to be larger than the right and by that
we have lemon and

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eliminated ads y ax as a valid
expression

40
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shit is funny clever trick so if action
wired the same it's still that let

41
00:02:37,780 --> 00:02:41,690
but they've X is less than why that's
very cool then why

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we have eliminated an the

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00:02:45,250 --> 00:02:48,780
an committed if expression at YX

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good and then we also

45
00:02:52,920 --> 00:02:56,170
onto an used to gauge where

46
00:02:56,170 --> 00:03:00,769
X or why is wrong K so this takes into
account

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00:03:00,769 --> 00:03:05,360
the community devotee of multiplication
and addition

48
00:03:05,360 --> 00:03:09,800
and the fact that an Wong is the neutral
element

49
00:03:09,800 --> 00:03:13,450
of multiplication I'm and finally

50
00:03:13,450 --> 00:03:16,890
also when we and divide by Wong

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00:03:16,890 --> 00:03:21,220
that's the same as X lemme

52
00:03:21,220 --> 00:03:25,590
applied is very simple an extension dude
ass

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00:03:25,590 --> 00:03:29,959
it as quite dramatic result so when we
look at the solutions

54
00:03:29,959 --> 00:03:35,700
for this there's now only two hundred
fifty dollars and valid expressions

55
00:03:35,700 --> 00:03:39,610
K so that's about twenty times less than
before

56
00:03:39,610 --> 00:03:42,790
and and when we look at the solutions

57
00:03:42,790 --> 00:03:47,830
there are about sixteen time less
because all the solutions that we had

58
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were duplicates of each other all the
solution there were many duplicates

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and ocean oceans so when we run this now

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runs it finds the first solution

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00:03:59,489 --> 00:04:05,129
and to understand the second but even
more important

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it's fine all the solutions and under

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hot of a second so is she

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really all that

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and problems from this TV program

66
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are solved by then of a second

67
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and we started out with all solutions
being about

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44 seconds over this is quite a dramatic
improvement

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you see there was not that difficult we
made to small steps

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starting with obviously correction ocean
that was slow

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and MBB factor it to remain correct

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but become fast and this is the way

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and Haskell programmers like to work so

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start with something that's right and
then you make it better

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great thank you so much happy hacking

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make sure you do your homework and then
see you next week