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  • PROFESSOR: OK, to work.

  • A word of warning: fasten your seat belts.

  • Or, another way of saying it is, I'm going to open up the

  • fire hose a little bit today.

  • Last lecture, you might have thought this was a SHASS class,

  • it's not like a philosophy class, and it was important to

  • set the stage for what we're going to talk about, but

  • we talked about very high level things.

  • The notion of recipes, the notion of computation, why

  • you want to do this, what you're going to learn.

  • Today we're going to dive into the nitty-gritty, the nuts and

  • bolts of the basics of computation, and in particular,

  • what I'm going to do today is, I'm going to talk about

  • operators and operands, which we did a little bit real last

  • time, in particular how to create expressions, I'm going

  • to talk about statements as the key building blocks for writing

  • code, and I'm going to introduce simple sets of

  • programs, in particular I'm going to talk about branching,

  • conditionals, and iteration.

  • So, a lot to do.

  • OK?

  • So, let me jump straight to it.

  • At the end of last lecture, we started introducing some of

  • the pieces you want to do.

  • And I want to remind you of our goal.

  • We're trying to describe processes.

  • We want to have things that deduce new kinds

  • of information.

  • So we want to write programs to do that.

  • If we're going to write programs, we need at least

  • two things: we need some representation for

  • fundamental data.

  • And we saw last time two examples of that.

  • And the second thing we're going to need, is we're going

  • to need a way to give instructions to the computer

  • to manipulate that data.

  • We need to give it a description of the recipe.

  • In terms of primitive data, what we saw were

  • two kinds: Right?

  • Numbers and strings.

  • A little later on in the lecture we're going to

  • introduce a third kind of value, but what we're going to

  • see throughout the term is, no matter how complex a data

  • structure we create, and we're going to create a variety of

  • data structures, fundamentally all of them have their basis,

  • their atomic level if you like, are going to be some

  • combinations of numbers, of strings, and the third type,

  • which are booleans, which I'm going to introduce a little

  • later on in this lecture.

  • And that kind of makes sense right?

  • Numbers are there to do numeric things, strings are our

  • fundamental way of representing textual information.

  • And so we're going to see how to combine those

  • things as we go along.

  • Second thing we saw was, we saw that associated with every

  • primitive value was a type.

  • And these are kind of obvious, right?

  • Strings are strings.

  • For numbers, we had some variations; we had

  • integers, we had floats.

  • We'll introduce a few more as we go along.

  • But those types are important, because they tell us something

  • about what we want to do when we want to put them together.

  • OK, but nonetheless, I want to stress we have both a

  • value, yeah, and a type.

  • All right.

  • Once we have them, we want to start making combinations

  • out of them.

  • We want to put pieces together.

  • And for that, we combine things in expressions.

  • And what we saw as expressions are formed of operands

  • and operators.

  • And the simple things we did were the sort of things you'd

  • expect from numerical things.

  • Now I want to stress one other nuance here.

  • Which is, and we're going to do some examples of this,

  • initially we just typed in expressions into the

  • interpreter; that is, directly into Python.

  • And as I suggested last time, the interpreter is actually a

  • program inside of the machine that is basically following the

  • rules we're describing here to deduce the value

  • and print it up.

  • And if we type directly into the interpreter, it essentially

  • does an eval and a print.

  • It evaluates, and it prints.

  • Most of the time, we're going to be doing expressions inside

  • of some piece of code, inside of a script, which is the

  • Python word for program.

  • In there, I want to make this distinction, this nuance: the

  • evaluator is still going to be taking those expressions and

  • using its rules to get a value, but it's not going to

  • print them back out.

  • Why?

  • Because typically, you're doing that to use it somewhere

  • else in the program.

  • It's going to be stored away in a variable.

  • It's going to be stuck in a data structure.

  • It's going to be used for a side effect.

  • So, inside of code, or inside of a script, there's no print,

  • unless we make it explicit.

  • And that's a little bit down in the weeds, it's a detail,

  • but one I want to stress.

  • You need to, if you want something to be printed out

  • inside your code, you need to tell the machine to do that.

  • OK.

  • So let's do some simple examples.

  • We've already seen somebody's.

  • I just want to remind you, if I wanted to, for example, type in

  • an expression like that, notice the syntactical form, it's an

  • expression, a number, followed by an operand, followed

  • by another expression.

  • And of course I get out the value I'd like there.

  • Yes sir.

  • Oh, you don't like leaning that far to the left?

  • OK, if you're a Republican I'll be happy to shift

  • this over a little bit.

  • Wow, John, I got a laugh for a political joke,

  • I'm in big trouble.

  • That better?

  • Oh damn, all right, I'll have to do it even more.

  • OK, here we go, here we go, you see, I'm doing it down here, I

  • can't see it, does that-- ah, I hear his sighs of

  • relief, OK, good.

  • There we go.

  • Better.

  • All right.

  • One of the other things we showed last time is that

  • operators are overloaded.

  • And this is where you heard John and I disagree.

  • I don't happen to like this, but he thinks it's an ok thing.

  • In a particular-- if we, whoa, we don't do that, we do this--

  • that is, give a combination of a number multiplication in a

  • string, this will in fact give us back a new string with that

  • many replicas, if you like, of the string concatenated

  • together.

  • All right?

  • And if you want to do other things, for example, we can

  • take two strings and add-- whoops, sorry-- and add them

  • together, we will get out, again, a concatenation

  • of that string.

  • And these will, we'll let you work through the variations,

  • but these are the simple expressions we can use.

  • Now, sometimes things get a little interesting.

  • All right?

  • What's the value of that expression?

  • What do you think should happen if I evaluate that expression?

  • Somebody with a hand up, so I can see it.

  • What's going to happen?

  • STUDENT: [UNINTELLIGIBLE]

  • PROFESSOR JIM ERICSON: An error?

  • Why?

  • STUDENT: [UNINTELLIGIBLE]

  • PROFESSOR JIM ERICSON: Great.

  • OK.

  • That means, let's check it.

  • It certainly is.

  • We bribe people.

  • So I, ah, by the way, John's a Yankees fan, he throws like

  • Johnny Damon, I'm a Red Sox fan, so we'll see if

  • I, how about that?

  • And I almost hit John along the way, great.

  • My third right, exactly, what can I say?

  • All right, so we're into bribing you as we go along

  • here, and all right?

  • You'll be badly overweight by the end of the term.

  • Right, it's a syntactic error, because it doesn't know

  • how to deal with this.

  • But there's an important thing going on here, if I in fact

  • wanted to combine those into a string, I should have told the

  • machine to do that, and I can do that, by explicitly saying,

  • take that, which is a number, and convert it into a string,

  • and then-- bleah, I keep doing that-- then add it

  • to that string.

  • OK, so there's an important point here.

  • We've got what's called type conversion.

  • That is, if I want to combine two things together in a

  • particular way, I need to make sure that I give it the

  • kind of operand it expects.

  • So STR, which I just typed up there, takes in parens, some

  • input, and it converts it into a string, so that now I can

  • use that where I was expecting a string.

  • John.

  • PROFESSOR JOHN GUTTAG: You've got a static semantic

  • error in your syntax.

  • PROFESSOR JIM ERICSON: Thank you.

  • And I was going to come to that in a second, but thank you,

  • John, for pointing it out.

  • All right.

  • Why is it a static semantic error?

  • The syntax is OK in the sense of, it is an operand, an

  • operator, an operand, so syntactically it's OK.

  • The semantics was what caused the problem, because the

  • operator was expecting a particular kind of

  • structure there.

  • There's a second thing going on here that I want to highlight,

  • because it's really important.

  • Yes indeed.

  • OK, there we go.

  • The second thing I want to highlight is, that what's

  • going on, is that Python is doing some type checking.

  • It caught the error, because it checked the types of the

  • operands before it applied things, and it says,

  • I'm going to stop.

  • Now, you might have said, gee, why didn't it just assume that

  • I wanted to in fact treat these as strings, and

  • combine them together?

  • Sounds like a reasonable thing to do.

  • But it's a dangerous thing.

  • Because in doing that, Python would then have a value that it

  • could pass on into some other part of a computation, and if

  • it wasn't what I wanted, I might be a long ways downstream

  • in the computation before I actually hit some result

  • that makes no sense.

  • And tracing back where it came from can be really hard.

  • So I actually want to have type checking as much

  • as I can early on.

  • And in fact, under type checking, different languages

  • sometimes fall on a spectrum from weak to strong typing.

  • Which basically says, how much type checking do they do?

  • Now, you're going to hear John and I go back and forth a lot,

  • as I said I'm an old time-- well I'm certainly old

  • time, but I'm also an old time Lisp programmer.

  • I love Lisp, but Lisp is certainly in the category of a

  • very weakly typed language.

  • It does not check the types of its arguments at all.

  • Python is, I wouldn't say completely strong, but it's

  • much closer to the strong end of the spectrum.

  • It's going to do a lot of type checking for you before it

  • actually passes things back.

  • Nonetheless, I'm also going to argue that it's probably not as

  • strongly typed as we might like.

  • So, for example, there's an expression.

  • Now, less than is just, if you haven't used it before, it's

  • just the operator you'd expect, it's comparing two things and

  • it's going to return either true or false depending on

  • whether the first argument is less than the second argument.

  • What's going to happen here?

  • Again, I need a hand so I can know where to throw candy.

  • I've also got on my reading glasses on, I can't

  • see anything.

  • Anybody.

  • TAs don't count, they get their own candy.

  • When it, yep.

  • STUDENT: [INAUDIBLE]

  • PROFESSOR JIM ERICSON: Good question.

  • Sounds like a reasonable guess, right?

  • How in the world am I going to compare a string to a number?

  • So, see how good my aim is, ah, not bad.

  • All right.

  • A good quest-- sorry, a good thought, but in

  • fact, son of a gun.

  • Or as my younger son would say, fudge knuckle.

  • Yeah.

  • All right?

  • So, what in the world's going on here?

  • This is a place-- I don't know about you, John, I think this

  • is actually really not good, because right, what this is

  • doing is, it's allowing-- sorry, let me back up and say

  • it-- it's got an overload on the less-than that allows you

  • to compare basically the lexicographic ordering, or this

  • sequence of ordering of symbols, including numbers

  • inside of the machine.

  • And this, in my mind, should have been an error.

  • Why in the world would you want to compare that?

  • Just to give you an example of that, for instance, I can do

  • the following: all right, the number four is less than the

  • string three, whereas the string four, oops, is not

  • less than the string three.

  • And this is a place where it's comparing strings and

  • numbers in a strange way.

  • So why am I showing you this?

  • Partly to show you that it's kind of weird, but also to tell

  • you that one of the things you want to do is exercise what I'm

  • going to call some type discipline.

  • Meaning, when you write code, you want to get into the habit

  • of A, checking out operators or procedures to see what they do

  • under different circumstances, either check them out or read

  • the specifications of it, and two, when you write your own

  • code, you want to be disciplined about what types of

  • arguments or operands you apply to operators.

  • Because this is something that could certainly have screwed

  • you up if you didn't realize it did it, and you need to have

  • that discipline to make sure it's doing the right thing.

  • OK.

  • One of the other things you're going to see is that some of

  • the operators have odd meanings.

  • And again, I think we looked-- Yup?

  • STUDENT: So, the string A is less than three, is false

  • because they're comparing like ASCII values?

  • PROFESSOR JIM ERICSON: Yes.

  • I mean, I'm sorry.

  • The answer is, I don't know if it's ASCII.

  • John, do you know, are they doing ASCII

  • encoding inside of here?

  • I'm assuming so.

  • Right.

  • So, in case you didn't understand what the the

  • question was, basically every symbol gets translated into a

  • particular encoding, a string of bit, if you like, inside the

  • machine, there's a particular one called ASCII, which is, if

  • you like, an ordering of that, and that's what the machine's

  • actually comparing inside of here, which is why in under

  • ASCII encoding the numbers are going to appear after the

  • characters, and you get the strange kind of thing going on.

  • All right.

  • I want a couple of other things, just to quickly remind

  • you, and one of them is, remember, the operators do look

  • at the types, so division, for example nine divided by five is

  • one, because this is integer division, that is, it's the

  • largest number of integer multiples of five to go into

  • nine, and there would be a remainder associated with

  • it, which is in fact four.

  • And again, you've got to be careful about how

  • you use the operators.

  • Right, having done that, we can certainly get to more

  • complicated things, so for example, suppose I look

  • at that expression.

  • Three plus four times five.

  • All right.

  • Now.

  • There are two possible values here, I think.

  • One is 23, the other's 35.

  • Because this could be three plus four, times five, or it

  • could be three, plus four times five.

  • And of course, you know, when you look at code it doesn't

  • pause in between them.

  • But what I do?

  • I just separated, do I do the addition first or do the

  • multiplication first?

  • Anybody know what happens In this case?

  • Yeah, way up, oh God I'm going to have a hell of time throwing

  • up there, way up at the back.

  • STUDENT: Standard order of operations, I guess take

  • the multiplication first, and add the three.

  • PROFESSOR JIM ERICSON: Right.

  • I'm going to try, if I don't make it, you know, just get

  • somebody to pass back, whoa!

  • I just hit somebody in the head.

  • Thank you.

  • Please pass it back to that guy.

  • If you want candy, sit much closer down, and that way we

  • can film you as well as we go along.

  • Right.

  • So the point is, there is something here called operator

  • precedence, which is what the gentleman said.

  • I'm not going to say much more about it, but basically what it

  • says is, with all other things being equal, things like

  • exponentiation are done before you do multiplication or

  • division, which are done before you do things like

  • addition and subtraction.

  • And so, in fact, if I wanted the other version of it, in

  • fact, if I do this right, it's going to give me 23 because it

  • does the multiplication first, if I wanted the other version

  • of it, I need to tell it that, by using, excuse

  • me, parentheses.

  • And in general, what I would say is, when in

  • doubt, use parens.

  • OK.

  • Now, that just gives us expressions.

  • We can start having complex expressions, you can imagine we

  • can have things are lots of parens, and all sorts

  • of things in it.

  • Yes, question.

  • STUDENT: What does it mean, the operator used, when you were

  • calculating the remainder between nine and five?

  • PROFESSOR JIM ERICSON: It's the percent sign.

  • If you can't read it, I guess I'm going to have to blow that

  • font up, aren't I, next time around.

  • Yeah, it's a percent, so this percent sign will

  • give you the remainder.

  • OK.

  • Second thing I need to do, though, is I need to, when

  • I get those values, I want to hang on to them.

  • I'd like to give them a name, so I can refer to

  • them in other places.

  • And so we saw that as well, the last piece we had here is the

  • ability to create variables, which have their own values,

  • and that's done using an assignment statement.

  • So in particular, that is an assignment statement.

  • It says, take the name x and create a binding for that

  • name to the value of the sub-expression and in fact

  • to do this, to stress a point, let's do that.

  • It's not just a number, it's any expression.

  • What Python will do, is it will evaluate that expression using

  • the kinds of rules we talked about, and then it creates a

  • binding for x to that value.

  • And I want to stress this, we're going to come back to it

  • later on in the term, so the way I'd like you to think about

  • it for now, is that somewhere in the machine, there's a

  • big space that contains all possible values.

  • Right.

  • It's a slight lie, it doesn't have all possible values,

  • but you get the idea.

  • It has, if you like, intellectually, all

  • possible values.

  • And when I create a binding, I'm taking a variable name, in

  • this case x, stored somewhere in a table, and I'm creating

  • a link or a pointer from that name to that value.

  • This is a nuance.

  • It's going to make a lot more sense later on when we

  • introduce mutation into our language, but I want you to

  • start thinking of it that way.

  • Don't think of it as a specific box into which we're putting

  • things; think of it as a link to a value.

  • I could have, for example, another assignment statement,

  • and that creates a binding from y into that same value, and one

  • of the things as a conservist I can do is, I could have a

  • statement like, let z be bound to the value of x.

  • And I said it deliberately that way.

  • That statement says, get the value of x, which is this

  • link, and give z a pointer to the same place.

  • To the value, not to x.

  • OK, and we'll just plant that idea, we're going to come back

  • to later on, as we carry on.

  • OK.

  • So if we have variables, one of the questions we can ask

  • is, what's the type of the variable.

  • And the answer is, it inherits it from its value.

  • OK.

  • Yes.

  • So if somewhere in my code, I have that statement, that

  • assignment statement, x now is a variable whose

  • value is an integer.

  • Unfortunately, at least in my mind, in Python, these variable

  • bindings are dynamic, or the type, rather, is dynamic.

  • Meaning, it changes depending on what the current value is.

  • Or said a different way, if somewhere later on in the

  • program I do this, x now has changed its type

  • from INT to string.

  • Now why should you care?

  • OK, my view is, I don't like it.

  • Especially in the presence of operator overload.

  • Because I might have written some code in which I'm

  • expecting that particular variable to have

  • an integer value.

  • If somewhere later on in the code it shifts to string, I

  • might not be manipulating that and getting actual values out,

  • but not what I wanted, and it's going to be really hard

  • for me to chase it back.

  • So one of the things I would like to suggest is that you

  • develop some good style here, and in particular, don't

  • change types arbitrarily.

  • I can't spell today.

  • Meaning, sometimes you need to do this, but in general

  • there's-- at least in my view and I don't, John, would you

  • agree?-- you just don't want to do this.

  • You don't want to make those changes.

  • It just leads to trouble down the road.

  • OK.

  • Now, last thing about variables, and then we're going

  • to start pushing on this, is where can you use them?

  • And the answer is, you can use a variable anywhere

  • you can use the value.

  • So, any place it's legal to use the value.

  • OK.

  • Now.

  • This is just sort of bringing us back up to speed and adding

  • a few more details in.

  • What we really want to do now though is start

  • using this stuff.

  • So, operands.

  • Let us take expressions, get values out, we can store them

  • away in places, but ultimately we want to do something with

  • them, so we need to now start talking about what are the

  • things we can do inside of Python, or any programming

  • language, to manipulate them.

  • And for that, we're going to have statements.

  • Statements are basically, if you want to think about it,

  • legal, and I was about to use the word expression except

  • I've misused that elsewhere, so legal commands that

  • Python can interpret.

  • You've already seen a couple of them.

  • Print, assignment, certainly two obvious statements, they're

  • commands to do something.

  • Assignment is binding a name to a value, print is saying put

  • it back out in the screen.

  • Obviously if you have print as a way of putting things out, we

  • expect to have ways of getting input in, we're going to see an

  • example that in the second.

  • And as we go through the next few lectures, we're going to

  • add in more and more of these statements.

  • But let's look at what we could do with this, OK?

  • And to do this, I'm going to use some code that

  • I've already typed in.

  • So I'm hoping you can read that, and it's

  • also in your handout.

  • This is a little file I created, all right, and I'm

  • going to start with a sequence of these things and walk them

  • along, again I invite you to put comments on that handout

  • so that you can follow what we're going to do.

  • All right?

  • So let's look at the first part of this.

  • Right now, this is just a text file.

  • OK.

  • And I've highlighted in blue up there one of the pieces

  • I'm going to start with.

  • And what do I have?

  • I have a sequence of commands; I've got an assignment

  • statement, I've got another assignment statement, I've got

  • a print statement, I've got an input statement, which we'll

  • come back to in a second.

  • And I want to basically try and use these things to

  • do something with them.

  • Second thing I want to note is, the little hash mark

  • or the pound sign, that's identifying a comment.

  • So what's a comment?

  • It's words to you, or to the reader of the code, that are

  • telling you what's going on inside of this code.

  • OK?

  • Now, these comments, frankly, are brain-damaged, or

  • computationally challenged if you prefer.

  • Meaning, why in the world do I have to tell the reader that

  • I'm binding x to the value three?

  • All right?

  • I'm putting them in there to make a point.

  • In general, good programming style says you put in comments

  • that are going to be valuable in helping you as a reader

  • understand what's going on inside of the code.

  • It could be, what's the intuition behind

  • this piece of code.

  • It could be, preconditions I want to have on input.

  • It could be, explanations of specific things you're doing.

  • But you need to have those comments there.

  • Now, this becomes a little bit of one of those motherhood and

  • apple pie kinds of lectures.

  • You know, your mother always told you to eat brussels

  • sprouts because it was good for you.

  • Well this is a brussels sprouts comment. everybody goes yeah,

  • yeah, yeah, comments, of course.

  • Of course we're going to do comments.

  • And they never do.

  • So my challenge to you, and I know Professor Guttag can do

  • this, my challenge to you is, a year from now, come back and

  • look at code you wrote here.

  • Can you still understand what it was you were trying to do?

  • I don't know, John, if you'd agree, right?

  • If you can read the code a year later, even code you wrote

  • yourself, it's a good sign that you put good

  • comments in, right?

  • Second good piece of style here is choice of variable names.

  • These are lousy.

  • Deliberately.

  • OK?

  • I'm just using simple things like x and y and z because I

  • want to make it, just get through the lecture

  • if you like.

  • But in general, the choice of variable name is a great way

  • of commenting your code.

  • Use variable names that make sense.

  • That little problem set zero that you did.

  • You read in a couple of values, you probably stored them away.

  • My bet is, you used simple names like x and y.

  • A much better name would have been firstname, lastname, as

  • the name of the variable to tell you what you were

  • trying to capture there.

  • OK.

  • The other piece I want to say about variable names is, once I

  • have that choice of variable name, I can use it, but in fact

  • there are a few things that I can't use in terms

  • of variable names.

  • So, these are an important way of documenting, but there're

  • some things excluded.

  • And in particular, there are some key words that Python

  • is going to use that have to be excluded.

  • Let me highlight that.

  • As I said, right now that's just text file.

  • I'm going to save this away-- yeah, not that way, I'm going

  • to save this away-- with the subscript, or the suffix

  • rather, py to make it a Python file.

  • Yeah, and I know it's already there but I'm going to do

  • it, and I get some wonderful colors.

  • But these are important, OK?

  • So notice what I have up there now.

  • Comments appear in red.

  • I can see those.

  • There's a keyword, which I'm going to highlight right up

  • here, print, which is in, I don't know what that

  • color is, orange?

  • There's a function in purple, there's a string in green,

  • and in black I have the assignment statements.

  • That print is a keyword.

  • It's a command to Python to do something.

  • As a consequence, I can't use it as a variable name.

  • All right, think about it for a second.

  • If I wanted to use print as a variable name, how do I get the

  • system to decide gee, do I want print as a value for something,

  • or do I want print as a command?

  • So there's a sequence of these that are blocked out, and I--

  • John, I think there are what, twenty-eight?

  • Something like that, TAs, is that right?

  • Twenty-eight keywords that are blocked?

  • We'll find them as we go along--

  • OK.

  • Having done this now, I can simply go ahead and run this,

  • and in fact if I go up here to run, you'll see I've got both

  • an option to check the module, though in this case I'm

  • just going to run it.

  • Oh, notice what happened.

  • It ran through that sequence of instructions, in particular it

  • bound x to the value three, and then it took x times x, got the

  • value of x multipied by x, which of course is nine, bound

  • that to the value of x, and then it printed out the value,

  • and now it's sitting here waiting for an input.

  • You notice what it did, it printed out that little, right

  • up here I'd said enter a number and that's what it's printed

  • out, so I can enter a number and it prints it out.

  • Great.

  • Let's run it again.

  • Actually for that, I can just use, if I'm lucky, function F5,

  • which didn't work, so let me try it again., here we go.

  • We're going to run that module.

  • OK.

  • Whoa.

  • What happened?

  • I said enter a number.

  • I didn't.

  • I gave it a string.

  • And it still took it.

  • And printed it up.

  • Well, this is one of the places where I want to come back to

  • that highlighting of what do things do?

  • Even though my statement said enter a number, in particular,

  • raw input here simply takes in a set of characters and

  • treats it as a string.

  • And then prints it back out.

  • So if in fact I wanted to make sure this was a number, I

  • should have done something like either try and convert it to a

  • number, which of course failed here, or put in a check

  • to say where it is.

  • So it's a way of reminding you, I've got to be careful about

  • the types of things that I put in.

  • OK.

  • This is still boring, so let's step on the accelerator.

  • What I have now is the following: I can write

  • expressions, do combinations of things to get out values, I can

  • store them away, I can print them up.

  • But literally all I can do at this stage is write what we

  • would call a straight-line program, that is, a program in

  • which we execute in which we execute the sequence of

  • instructions one by one.

  • Simply walk down that list.

  • That's what we just did there, right?

  • We just walked through that list.

  • This is boring.

  • In fact, you can do some nice things to prove what is the

  • class of functions you can compute with straight-line

  • programs, and what you'd see if you did that is, it's not

  • particularly interesting.

  • OK.

  • Let's go back and think about our recipes.

  • What we use as our motivation here.

  • Even in real recipes, you have things like, if

  • needed, add sugar.

  • That's a decision.

  • That's a conditional.

  • That's a branch.

  • That says, if something is true, do something.

  • Otherwise, do something different.

  • So to really add to this, we need to have

  • branching programs.

  • What I mean by that is, a branching program is something

  • that can change the order of instructions based

  • on some test.

  • And that test is usually a value of a variable.

  • OK.

  • And these get a whole lot more interesting.

  • So let's look at a little example, and this is going to,

  • excuse me, both allow us introduce the syntax as well as

  • what we want to have as the flow of control inside of here.

  • So let me go back up here, and I'm going to comment

  • out that region, and let's uncomment this region.

  • I want to write a little piece of code.

  • It's going to print out even or odd, depending on whether the

  • value I put in, which is x in this case, is even or odd.

  • Think about that.

  • That says, if this thing has some particular value, I want

  • to do one thing; otherwise, I want to do something different.

  • And let's look at the syntax of this.

  • This is the first of the conditionals that

  • we're going to see.

  • Notice the format.

  • I'm going to go up there.

  • The first statement right here, that's just an assignment

  • statement, I'm giving some value to x.

  • We could make it something different.

  • And then, notice the structure here.

  • The next three statements.

  • First of all, IF is a keyword. which makes sense.

  • It is followed, as you can see there, by some expression,

  • followed by a colon.

  • And in fact, that colon is important, so let me

  • stress this over here.

  • The colon is important It's defining the beginning of

  • a block of instructions.

  • Yes sir.

  • STUDENT: [UNINTELLIGIBLE]

  • PROFESSOR JIM ERICSON: Based on a test.

  • Usually the value of a variable.

  • OK, so let me go back to where I am.

  • I'm looking at that piece of code.

  • What that colon is saying is, I'm about to begin a sequence

  • of instructions that I want to treat as a block.

  • So it identifies a block of instructions.

  • It's, and in particular, the colon is the start, and the

  • carriage return is the end.

  • Now what in the world does that mean?

  • I'm doing a lot of words here, let me try and say this

  • a little bit better.

  • That code says the following: the IF says, I've got an

  • expression, I'm going to evaluate it.

  • If that value is true, I want to do a set of things.

  • And that set of things is identified by the sequence of

  • commands that are indented in, this one right here, following

  • the colon but before I get back to the same place in

  • terms of the indentation.

  • If that test is not true, I want to skip this instruction,

  • and there's a second keyword else, followed by a colon, and

  • that tells me the thing I want to do in the case

  • that it's false.

  • So in fact if I run this, ah, and save it, and

  • it prints out odd.

  • So, what happened here?

  • Well, let's look at the code.

  • Right? x is initially bound to fifteen.

  • I get to the IF.

  • The IF says, evaluate that next expression.

  • In that next expression, I'm actually taking advantage of

  • the fact that I'm doing integer multiplication

  • and division here.

  • Right, that divide is, if x is an integer and two is an

  • integer, what's it going to do?

  • If x was even, x divided by two is going to be actually

  • the half of x, right?

  • If x is odd, that integer division is going to give me

  • the number of multiples of two, that go into x, plus a

  • remainder, which I'm going to throw away.

  • In either case, I take that value and multiply back by two,

  • if it was even I get back the original number, if it was odd,

  • I'm not going to get back the original number, so I can

  • just check to see if they're the same.

  • OK, so a little nuance that I'm using there.

  • So, the first thing that IF does, bleah that IF says is,

  • evaluate that expression and if it's true, do the next thing,

  • the thing after the colon.

  • In this case it's not true, so it's going to skip down

  • and evaluate the thing printed up the odd.

  • OK.

  • What-- yes.

  • STUDENT: [INAUDIBLE]

  • PROFESSOR JIM ERICSON: Thank you.

  • I was hoping somebody would ask that question.

  • The question was, if you didn't hear, why do I

  • have two equal signs?

  • It's like I'm doing this, right?

  • Anybody have a se--%uFFFD why don't I just use an equal sign?

  • I want to know if something's equal to something.

  • Yeah.

  • STUDENT: [INAUDIBLE]

  • PROFESSOR JIM ERICSON: Absolutely.

  • The equal sign is going to bind-- Nice catch.

  • John, this is so much fun, throwing candy.

  • I've got to say, we've got to do this more often-- Right.

  • Let me, let me get to the point.

  • What does an equal sign do?

  • It is an assignment.

  • It says, take this thing on the left and use it as a name to

  • bind to the value on the right.

  • It's not what I want here.

  • Having already chosen to use equal as an assignment, I

  • need something else to do comparison.

  • And that's why I use double equals.

  • Those two equal signs are saying, is this thing equal

  • to, in value, the thing on the other side?

  • OK.

  • Now, having done that, again I want to stress this idea and

  • I'm going to write it out one more time, that there's a

  • particular format here.

  • So we have if, and that is followed by, I'm going to use

  • angle braces here just to indicates something goes

  • in here, some test followed by a colon.

  • That is followed by a block of instructions.

  • And we have an ELSE, followed by a colon in some other

  • block of instructions.

  • And I want you to get used to this, that colon is important,

  • it identifies the start, and then the set of indented things

  • identify all the things at the same level, and when we reset

  • back to the previous level, that's when we go back

  • to where we were.

  • OK.

  • Now, that's a nice simple little test, let's look at a

  • couple of other examples to get a sense of what this will do.

  • OK, let me comment this out, and let's look at this

  • next little piece of code.

  • All right.

  • I'm binding a z to be some value, and then

  • I'm going to run this.

  • Well, let's just run it and see what it does.

  • Nothing.

  • OK, so why?

  • Well, let's look at it.

  • I'm doing a test there to say, if the string x is less than

  • the value of b, and x does not appear before b as strings,

  • then I was going to do, oh, a couple of things,

  • because they're at the same block level.

  • Given that that wasn't true, it did nothing.

  • Now, wait a minute, you say, where's the ELSE clause?

  • And the answer is, I don't need one.

  • All right, if this is purely a test of, if this is true do

  • this otherwise I don't care, I don't need the ELSE clause

  • in there to identify it.

  • All right?

  • Second thing I want to look at is, suppose I compare

  • that the one below it.

  • Oops, that I don't want to do.

  • Comment that out, and let's uncomment this.

  • Yeah, I've still got a binding for z and I'm giving it the

  • same test, but notice now I've got the two same commands but

  • they have different indentation.

  • In this case, in fact I do get a different behavior.

  • Why?

  • Because that block identifies a set of things that I'm going

  • to do if the test is true.

  • If the test was not true, notice that that last command

  • for print Mon is now back at the same level as the IF, so

  • what this says is the IF does the test, having done the test,

  • it decides I'm not going to do anything in the block below it,

  • I'm going to skip down therefore to the next

  • instruction at the same level as the IF, which gets me to the

  • second print statement.

  • OK.

  • So now we're seeing some of these variations, let's see

  • what else can we do here.

  • So let me just to try something a little more interesting, and

  • then we'll get to writing some simple programs.

  • So I'm going to comment those out, and let's go down to

  • this piece of code, and uncomment it.

  • Ooh yes, that was brilliant.

  • Let's try this again.

  • And uncomment that, and uncomment it again.

  • Right, so here's a little piece of code that's going to print

  • out the smallest value of three.

  • And notice what this is showing is that the IFs can be nested.

  • All right, it's so if I looked at it, it's going to say that

  • IF x is y-- sorry, IF x is less than y, THEN check to see IF x

  • is less than z, and if that's true, print out x

  • is the smallest.

  • And notice the structure of it, if it's not true I'm going

  • to go to that next ELSE, and print out that z is smallest.

  • If the first test wasn't true, I'm going to skip that whole

  • block and just go down and print out that y was smallest.

  • So notice the nesting, I can flow my way through how

  • those tests are actually going to take place.

  • All right, so let's run this and see what happens.

  • Great. y is smallest.

  • OK.

  • Is that code correct?

  • Is that a tentative hand back there?

  • Yeah.

  • STUDENT: Let me compare y to [INAUDIBLE]

  • PROFESSOR JIM ERICSON: Yeah, it's not doing

  • all of the comparisons.

  • All right, and let's just check this out, because I want to

  • make a point of this, let's go back and do the following.

  • Let's take y, change it to thirteen, let's run it, hmm.

  • So what did I miss here?

  • Two important points.

  • First one, when I write a piece of code, especially code that

  • has branches in it, when I design test cases for that

  • piece of code, I should try and have a specific test case for

  • each possible path through the code.

  • And by just doing that, I just spotted, there's a bug here.

  • And the bug was in my thinking, I did not look

  • for all of the tests.

  • So the way I can fix that, is, let me comment that out, and

  • keep doing that, comment that out, let's uncomment this,

  • notice the structure here.

  • I now have multiple tests.

  • So actually, let's just run it and then we'll talk

  • about what it does.

  • I run this, yeah, I have a syntax error, yes indeed,

  • because I forgot to comment that one out, all right, and

  • cue, we'll try it again.

  • Ah-ha!

  • And let's quickly look at the structure of this.

  • This now has, gee, a funny thing, it says IF x is less

  • than y AND x is less than z, then do something.

  • And then it has a strange thing called ELIF, which is simply

  • short for else/if in a second test.

  • So the way to think about this in terms of flow is, it starts

  • with that if and it says, check both of those things.

  • And that fact that both of those things is the fact

  • that we're using Boolean combination here.

  • It is to say, we can take any logical expressions, combine

  • them together with AND, OR, or NOT to make a complex

  • expression, and use the value of that expression as my test.

  • And that's literally what I've done there, right, I've got x

  • less than y, that's a test, it returns a Boolean, which by the

  • way is the other type, at least I would include here, it has

  • only two values, which are true and false, and what that code

  • says, if x is less than y, AND, logically, whatever I put up

  • there, x is less than z, then the combination is true, and

  • therefore I'm going to do something.

  • So AND is if both arguments are true it's true, OR is if either

  • argument it's true it's true, NOT is if the argument is not

  • true it's true, and then the last piece, as I said is, I can

  • now have a sequence of things I want to do.

  • So if this is true do something else, otherwise test and see if

  • this is true, do something else, as many as I like

  • followed by the end.

  • And ELSE, it says, here's what I want to do.

  • OK.

  • Now.

  • Having added this in, I have branching instructions.

  • I have simple branching programs.

  • These are still awfully simple.

  • OK?

  • And they're awfully simple because, all I can do now, is

  • decide whether to execute some piece of code or another.

  • Said a different way, in the case of the straight-line

  • programs, how long would it take to run a program?

  • Well, basically, however many instructions I have, because

  • I've got to do each one in order.

  • With simple branching, how long is it going to take

  • to run a piece of code?

  • Well at most, I'm going to execute each instruction once.

  • All right?

  • Because the IFs are saying, if it's true do this,

  • otherwise skip on it.

  • Therefore, for simple branching programs, the length of time,

  • the complexity the code, is what we would call constant.

  • That is, it's at most the length of the actual

  • number of instructions.

  • It doesn't depend on the input.

  • Real simple programs.

  • Let's take another simple example.

  • Suppose I want to compute the average age of

  • all the MIT faculty.

  • There's about a thousand of us.

  • However I do that, I know that should inherently take more

  • time than it takes to compute the average age of all

  • the EECS faculty.

  • There's only 125 of us.

  • And that should take more time than what it takes to compute

  • the average of John's and my ages, instructors in 600,

  • because there's only two of us.

  • All right, those pieces of code inherently involved something

  • that does depend on the size of the input, or on the

  • particular input.

  • And that is a preface to an idea of computational

  • complexity we're going to come back to.

  • One of the things we want to help you do is identify the

  • different classes of algorithms, what their costs

  • are, and how you can map problems into the most

  • efficient class to do the computation.

  • OK.

  • Now.

  • Think for a second about computing the average

  • age of the faculty.

  • You can already kind of see what I want to do.

  • I, somehow if, I want to walk through some sequence of data

  • structures, gathering up or doing the same thing, adding

  • ages in until I get a total age and then divide by

  • the number faculty.

  • How do I write a piece of code for that?

  • Well, let's go back up to our original starting

  • point of recipes.

  • And I'm sure you don't remember, but one of the things

  • I had in my recipe, is beat egg whites until stiff.

  • OK.

  • That until is an important word.

  • It's actually defining a test.

  • Let me rephrase it into garbled English that'll lead more

  • naturally into what I want to do.

  • While the egg whites are not stiff, beat them.

  • That is a different kind of structure.

  • It has a test in it, which is that while, while something

  • is true, do something, but I want to keep doing it.

  • And so for that, we need to add one last thing.

  • Which is iteration.

  • Or loops.

  • We're going to see variations of this, we're going to see a

  • variation of it called recursion, a little later on,

  • but for now we're just going to talk about how do

  • we do iterations.

  • And I want to show you an example of this, to lead

  • to both the syntax, and to the semantics.

  • And let me comment that out, and let's go to this one.

  • All right.

  • What does this piece of code say?

  • Not, what does it do, but what does it say.

  • Well, the first three statements are just

  • assignment statements.

  • I'm binding x, y, and iters left to some values.

  • And then notice the structure, I got a keyword WHILE, there's

  • that color identifying it, and in parentheses I have a test.

  • I'm expecting the value that test to be a Boolean.

  • Followed by a colon.

  • The colon's identifying a block of code.

  • And what this is saying is, gee.

  • Check to see if the variable iters left has a value

  • greater than zero.

  • If it does, then execute each of the instructions

  • in that block.

  • So I'm going to have an assignment of y, I'm going to

  • have an assignment of iters left, I've got a comment that I

  • had borrowed in order to do some debugging, and then

  • what do I want it to do?

  • I want it to go back around to the test.

  • Once again, say, is that test true?

  • If it is true, execute the sequence of instructions.

  • So in fact we can block this out and see what it does.

  • If I make a little chart here, I've got x, y, and iters left.

  • x starts off as I think I set it up as, here I can't even

  • read it, is x is three, y is zero, iters left is three.

  • I can hand-simulate it.

  • It says, is the value of iters left greater than zero?

  • Yes it is.

  • So, execute those two instructions.

  • It says, take value of y and value of x, add them

  • together, and create that as the new value of y.

  • All right.

  • That's the assigned statement.

  • It says, take iters left, subtract one from it, and

  • bind that as the new value of iters left.

  • Having reached the end of the block, go back up

  • and check the test.

  • Is iters left greater than zero?

  • Yes it is.

  • So, evaluate the same sequence of instructions again. y plus x

  • is six, that's my new value of y, two minus one is one, that's

  • my new value of iters left, go back up.

  • Is iters left greater than zero?

  • Yes it is.

  • So once more, thank God I didn't take 47 as an example, x

  • plus y, subtract one from iters left, go back up to the test.

  • Is iters left's value greater than zero?

  • No, it is not.

  • Therefore, skip the rest of that block of code and go

  • to the next instruction, which is, ah, print out y.

  • In fact, if we test this, son of a gun.

  • Got a simple square procedure,.

  • Right, It's just squaring an integer, is what it's doing.

  • But notice the structure.

  • Now I have the ability to create a loop, that is, to

  • reuse the same pieces of code over and over

  • again as I go around.

  • And this adds, now, a lot of power to the kinds

  • of code I can write.

  • Notice some other things I want to highlight on this.

  • All right?

  • The first one is, that test has to involve-- shouldn't have to,

  • but almost always is going to involve-- the value

  • of some variable.

  • What if I don't change the value of that variable

  • inside of the code?

  • Or, another way of saying it is, what if I did this?

  • Comment it up.

  • What happens if I run this sucker?

  • STUDENT: [INAUDIBLE]

  • PROFESSOR JIM ERICSON: Yeah.

  • It'll go forever.

  • Absolutely, right?

  • It's going to loop into an infinite loop-- I think I can

  • hit this close, ah, no I can't, boy what a terrible aim--

  • All right, what has [UNINTELLIGIBLE PHRASE]

  • try again, the point I'm trying to make here-- thank God we're

  • at the end of this lecture, my tongue is falling apart-- the

  • point I'm trying to make is, that test needs to involve some

  • loop variable that is changing.

  • Otherwise the test is always going to be true, we're going

  • to go off here, but this would loop forever if I did that.

  • All right.

  • Second question: or maybe a better way of saying this, and

  • the general format you're likely to see here is, a test

  • involving a variable name, which must be initialized

  • outside of the loop, and which interior to the loop gets

  • changed, so that the test is going to change.

  • Here's the second question.

  • What value of inputs, what values of x will this

  • run correctly for?

  • Probably should be integers, right?

  • Otherwise, this is going to be doing something

  • strange, but all integers?

  • All right, suppose I do this.

  • It's my last example.

  • Yeah, how about that, right?

  • We knew this was trying to do squaring, so intellectually we

  • know we can square -4, it ought to be 16, but what

  • happens here?

  • Double fudge knuckle.

  • All right?

  • It's going to run through the loop, accumulating the answers,

  • but because I'm subtracting, it's just going to keep making

  • x more and more negative as it goes along, again it's off

  • into an infinite loop.

  • Which is a way of reminding you that I need to think as I write

  • the code about what are my expectations from the input,

  • and how might I enforce them.

  • In this case, I probably want to make sure I use absolute

  • value of x before I carry it on.

  • Yes ma'am.

  • STUDENT: [UNINTELLIGIBLE]

  • PROFESSOR JIM ERICSON: You're absolutely right, because I

  • bind iters left to, um, yeah.

  • Yes.

  • Thank you.

  • Boy, two candy for you.

  • You caught me making an error.

  • Yes.

  • The point is, it's not going to work, and she caught both of

  • them, impressive, it's not going to work because iters

  • left is already negative, it's just going to skip the whole

  • loop, and I'm in trouble, so thank you for catching that.

  • All right.

  • I was going to do one more example, but I've run you

  • up to the end of the time.

  • I'll leave the example on the handout, it shows you another

  • version that we'll come back to next time.

  • The key thing to notice is, I now have the ability to

  • create iterations, which extends well I can do.

  • And we'll see you next time.

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