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Welcome back. This video

is about regular expressions.

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We want to use regular

expressions in our lexer.

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And the purpose of the

lexer is to find

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out where the words in

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our programs are. However

regular expressions

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are fundamental tool

in computer science.

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And I'm sure you've used them

already on several occasions.

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And one would expect that about

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regular expressions since they are

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so well-known and well studied,

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that everything under the

sun is known about them.

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But actually there's

still some surprising

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and interesting

problems with them.

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And I want to show you

them in this video.

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I'm sure you've seen

regular expressions

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many, many times before.

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But just to be on the same page,

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let me just recap them.

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So here in this line,

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there is a regular expression

which is supposed to

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recognize some form

of email addresses.

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So an e-mail address

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has part which is

before the @ symbol,

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which is the name of the person.

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And that can be

any number between

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0 and 9, and letters between a and z.

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Let's say we avoiding

here capital letters.

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There can be underscores.

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There can be a dot and

there can be hyphens.

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And after the @ symbol

comes the domain name.

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So as you can see here,

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we use things like star to

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match letters

zero or more times.

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Or we have a plus,

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which means you have to match

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at least once or more

times. Then we have.

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question mark, which says you

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match either it is there

or it ss not there.

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You are also regular

expressions which

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match exactly n-times.

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Or this is a regular expression

for between n and m times.

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You can see in

this email address,

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the top-level domain

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name can be any letter 

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between a to z,

and contain dots,

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but can only be two

characters long

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up till six characters

and not more.

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Then you also have

something like ranges.

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So you can see, letters between a

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and z and 0 to 9 and so on.

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Here you also have regular

expression which can

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match something which

isn't in this range.

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So for example, if

you want for example match,

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letters but not numbers,

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you would say, well, if

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this is a number that

should not match.

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Typically you also

have these ranges.

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Lowercase letters,

capital letters.

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Then you have some

special regular expressions

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like this one is only

supposed to match digits.

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A dot is supposed to

match any character.

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And then they have also something

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called groups which

is supposed to be

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used when you are

trying to extract

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a string you've matched.

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Okay, so these are the

typical regular expressions.

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And here's a particular one.

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Trying to match something

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which resembles

an email address.

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Clearly that should be all easy.

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And our technology should

be on top of that.

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That we can take a

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regular expressions and

we can take a string,

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and we should have programs to

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decide whether this

string is matched

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by a regular expression or

not and should be easy-peasy, no?

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Well, let's have a

look at two examples.

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The first regular expression

is a star star b.

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And it is supposed

to match strings of

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the form 0 or more a's,

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followed by a b. The parentheses

you can ignore.

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And a star star

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also doesn't

make any difference

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to what kind of strings

that can be matched.

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It can only make 0 more

a's followed by a b.

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And the other regular expression

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is possibly a character a,

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n times, followed by character

a axactly n-times.

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And we will try out

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these two regular expressions

with strings of the form a,

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aa, and so on,

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and up to the length of n. And

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this regular expression should

actually not match any of

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the strings because the

final b is missing.

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But that is

okay. For example

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if you have a regular expression

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that is supposed to

check whether a string is

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an email address and the user

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gives some random

strings in there,

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then this regular expression

should not match that string.

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And for this regular expression

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you have to scratch a

little bit of your head,

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what it can actually match.

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But after a little bit

of head scratching,

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you find out can match

any string which is of

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the length n a's up

to 2n of a's.

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So anything in this range,

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this regular expression

can actually match.

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Okay, let's

take a random tool,

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maybe for example Python.

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So here's a little

Python program.

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It uses the library

function of Python to

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match the regular expressions of

a star star b.

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And we measure time with longer

and longer strings of a.

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And so conveniently we can give