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24.9
And for that, I think I'm going to need a struct.
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And indeed let me propose that to solve this problem we give ourselves
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this building block as a new C data type called a node.
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You can call it anything you want, but the convention
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would be to call something like this in a data structure-- that's
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like a puzzle piece or a building block in a data structure
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would be called a node.
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Let me propose that we define it as follows.
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I'm using that same syntax from last time with which we declared a student
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data type, but here I'm saying inside of this data structure,
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this node shall be an int.
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And that's pretty straightforward.
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Just like a student might have a name and a dorm,
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this node will have an int called n arbitrarily.
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And then the only piece of detail that's a little bit new now is
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the second line, struct node star next.
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Now, what does that mean?
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It's pretty verbose, but struct node is just recursively, if you will,
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referring to this same type of data structure.
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Star means this is going to be a pointer, the address of one such thing,
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and next is just an arbitrary but pretty reasonable
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name to give to such a pointer.
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So this line here, struct node star next,
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is the incantation in C with which you declare
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one of those arrows that will point from one node, one rectangle
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to another node, another rectangle.
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And the fact that we have a little bit of additional verbiage
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up here, typedef struct node, is because again C
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is a language that is read top to bottom, left to right,
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so words have to exist before you actually use them.
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So, whereas last time when we declared a student,
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we didn't actually mention struct student or anything like that.
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We just said typedef open curly brace.
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Today, when declaring a node, we actually
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have to have some additional syntax here just called struct node.
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And technically this word could be anything,
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but I'll leave it as node for consistency.
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And that allows me inside of this definition
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or to specify that the second data member is
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going to be a pointer to exactly that kind of data structure.
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But typedef, just to be clear, allows me to type a smaller name for this data
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structure here, which I will simply called node at this point.
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So, what can we actually do with this kind of data structure now?
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And, indeed, let's give this data structure a name.
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Let's start calling a linked list.
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Previously, we had arrays, but now we have linked lists, both of which
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at the end of the day are types of lists, but linked lists,
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as the name suggests, are linked or threaded together using pointers.
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Now, when you have a linked list, what might be some operations,
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some algorithms that you might want to run on them?
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Well, if you've got a linked list of say numbers, for the sake of discussion,
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you might want to insert a new number into that list.
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You might want to delete a number from that list
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and you might want to search that list.
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And that allows us to then consider how we might implement
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each of these kinds of things.
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But it turns out while all simply-- while fairly simple intuitively,
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we're going to have to be a little careful now by way of our pointers.
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So, let's more formally declare a linked list to look something like this.
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It's a collection of nodes that are linked together
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with pointers as represented by these arrows here,
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but we're going to need some special pointer, at least
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at the beginning of the list.
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Let's just call it first.
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It doesn't necessarily store a actual integer.
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It itself first is just a pointer to the start of the list.
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And by way of that pointer can we access the first actual node in the list.
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From there can we get at the second, from there can we get at the third,
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and the fourth, and the fifth, and any number of others.
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And this syntax over here might just represent null.
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Because you don't want to have that pointer just
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pointing off into no man's land, that will have to be a null pointer so
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that if we check for that with a condition we know,
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OK, we're at the end of the list.
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So, let's pause for just a moment and consider these three algorithms--
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insert, delete, and search, and consider what's going to be involved.
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Well, how would you go about searching for an element of this list?
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Suppose I wanted to find the number 22?
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What do you do?
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Well, me, I, the human can just look at this and be like all right,
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22 is right there.
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But a computer can't do that.
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A computer every time we've had this discussion
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can only look at one thing at a time.
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But moreover the computer this time is even more constrained
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because it can't just use our old friend binary search
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or divide and conquer, because how do you get to the middle of a linked list?
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Well, you have to find your way there.
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The only thing you have in a linked list from the outset
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is one pointer called first or whatever it is, but one pointer that leads you
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to the beginning of the list, the first node in the list.
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So, if you want to get to the second node in the list,
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you can't just go to bracket one, or bracket two, or bracket three
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to get any number of other elements in the list.
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You have to follow these bread crumbs, if you will.
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You have to follow these arrows or these addresses to go from one node's address
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to the other to the other.
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And so, we've paid a price already.
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And we'll see that there is still an advantage here,
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but what's the running time?
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