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What's an upper bound on the running time of search for a linked list,
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5.71
even if it is sorted?
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1.195
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2.754
Any thoughts?
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0.541
1,075.55
3.07
Is it constant time like big O of 1?
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2.38
Is it log of n?
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1.4
Is it n, n squared?
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3.79
What's the running time going to be?
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1.79
Well, they're sorted, and that was this magical ingredient, this assumption
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3.27
we've been allowed to make in the past which was helpful,
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but that assumed that we had random access.
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2.4
In C, we had square bracket notation, so that using some simple arithmetic
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we could jump roughly to the middle, and then the next middle,
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2.14
and the next middle looking for Mike Smith or whatever element it is we're
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looking for.
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0.697
Unfortunately here, one price we have already
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3.15
paid already by taking this step toward linked lists is linear time.
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5.77
Big O of n would seem to be the running time of searching a linked list,
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3.71
because the only way you can start is at the beginning,
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2.58
and the only way you can get through the list is by following these arrows.
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3.9
And if there's n nodes in the list, you're
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2.7
going to need as many as n steps to find, something like 22, or 26, or 34,
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4.26
or any elements all together.
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2.277
Well, that's not all that great.
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1.333
What about insert?
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2.62
What's an upper bound on the running time of insert?
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4.51
Well, here too it depends.
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1.74
Suppose that we don't care about keeping the list sorted.
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4.06
That's kind of a nice advantage, so I can be a little lazy here.
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2.98
So, what's the running time going to be if I
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2.22
want to insert a new number like the number 50 into this list,
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3.54
but I don't care about keeping it sorted?
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2.39
Well, instinctively, where would you put this element?
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3.44
Where would you put it?
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2.01
You might be inclined-- you kind of want to put it over here,
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because it's the biggest element.
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1.54
But again, if you don't care about keeping it sorted,
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where is the fastest, the quickest and dirtiest place to put it?
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I would propose let's just put it at the front of the list.
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Let's take this first pointer, point it at the new number
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4.11
50 that we've have somehow added to the picture
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as by calling malloc, asking malloc for a new node.
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2.63
And then have 50, in turn, point to the number 9, and then 9 can point to 17,
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4.99
and 22, and so forth.
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1.17
What if we want to insert another number, 42,
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1.876
and we don't care about where it goes?
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1.582
Well, why don't we just put it at the beginning of the list?
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2.562
Then we have the first pointers pointing at 42,
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which in turn should point at 50, which in turn can point at 9, then 17, then
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3.77
22, and so forth.
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1.267
So, if we're just lazy about this, we can actually
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2.083
achieve a great running time for insert constant time.
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3.54
Unfortunately, if we want to keep things sorted then
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we're going to have to incur a linear time cost again, right?
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3.55
Because if we have to insert 42 or 50, worst case
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they might belong all the way at the end of the list and that's
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Big O of n steps.
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2.02
And delete, too, unfortunately, whether it's sorted or unsorted
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3.75
is also like search going to be Big O of n
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2.175
because you don't necessarily know when you're searching for a number
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2.875
to delete if it's going to be at the beginning, the middle, and the end.
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2.999
So, in the worst case, it might indeed be at the end.
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2.551
You know what?
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0.94
Why don't we instead of walking through this verbally,
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let's see if we can't get some volunteers?
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Can we get seven volunteers to play-- wow, to play the role of numbers here.
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1, 2, 3, 4, 5, 6, and yes, 7, come on up.
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All right, so I have here some printouts for all seven of you
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that represent exactly the nodes that we have here on the screen.
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Let's meet one of our first contestants.
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1.67
What is your name?
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0.5
AUDIENCE: Scully.
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0.59
SPEAKER 1: Scully, nice to see you.
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So, you shall be literally first and represent our first pointer.
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2.89
So, if you want to come and stand roughly over here.
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And then what is your name?
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AUDIENCE: Maria.
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SPEAKER 1: Maria, nice to see you.
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And you can be the number 9 right next to our first contestant.
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4.694
And your name?
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0.59
AUDIENCE: Sarah.
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0.36
SPEAKER 1: Sarah, nice to see you.
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1.416
You shall be the number 17.
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1.341
And your name?
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0.583
[? AUDIENCE: Satoshi. ?]
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0.42
[? SPEAKER 1: Satoshi, ?] nice to see you.
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1.75
You shall be 20.
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1.367
And your name?
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0.583
[? AUDIENCE: Mosof. ?]
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0.63
[? SPEAKER 1: Mosof, ?] nice to see you.
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1.666
And you shall be 22.
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1.361
AUDIENCE: Jed.
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0.583
SPEAKER 1: Jed, nice to see you-- 29, formerly 26.
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4.85
And your name?
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0.695
AUDIENCE: Erin.
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0.625
SPEAKER 1: Erin, nice to see you.
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1.375
You shall be 34.
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0.915
All right, so what we have here is seven elements, six of which
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are very similar to themselves, one of which is fundamentally different.
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