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could use or equations to express the running time of algorithms.
2,750.48
3.89
But many of the algorithms we'll look at in CS50 certainly
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2.47
fall into these categories.
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1.67
So let's take an example.
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2.89
What algorithm has the running time of big O of n squared?
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2.73
Well, bubble sort for one thing.
2,764.13
3.02
And it turns out selection sort.
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2.12
And it turns out insertion sort.
2,769.27
2.84
All three of those algorithms actually have the same running time,
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3.81
even though they're fundamentally different in execution.
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3.44
But they do share a commonality.
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2.01
All of them are comparison-based.
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2.72
In each case did we actually compare values,
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2.31
either adjacent or we would look at a number there, compare it to a number
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3.33
here, and then decide whether or not to do a switch.
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2.234
So they were all comparison-based.
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1.416
And all of them, frankly, involved quite a bit of movement or walking,
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3.24
either on my part or the humans-- volunteers part.
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2.48
For instance, in bubble sort's case, I had
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2.64
to walk through the whole list, sorting elements pairwise like this.
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3.425
But that wasn't enough.
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1.575
I then had to do it again and walk across the stage.
2,806.74
4.14
And then I had to do it again and walk across the stage.
2,810.88
2.78
And this is what n squared feels like.
2,813.66
1.627
And even though the problem was getting a little smaller
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2.333
as the big elements bubbled up, mathematically, even that algorithm,
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4.32
it's kind of essentially like doing n things, looking at n people,
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3.76
n times, iterating n total times, which is roughly n times n, or n squared.
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4.517
It's just going to add up a lot.
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1.333
So what about selection sort?
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1.61
What did I do in selection sort's case?
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1.65
Here, it's even more obvious, perhaps.
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1.8
To find the smallest element in a list, I
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2.2
have to look logically at every element before I can confidently conclude,
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5.105
yes, I have found the smallest element.
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1.625
Once you find it, you can plop it at the beginning.
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2.125
And that's easy.
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0.785
But then you have to find the second smallest element.
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1.95
And even though we humans could kind of eyeball things and realize,
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2.791
oh, 2 is the next smallest.
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1.249
You don't know that as the computer unless you look at every element.
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2.91
Ah, I found 2.
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1.49
And then you could put 2 where it belongs.
2,858.84
1.75
So again, there's this walking back and forth.
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2.18
And if you're going to walk as many as n steps and have to do this n times--
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3.9
one for every element-- that, too, is n times n.
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2.13
And insertion sort, same damn problem, even though it's
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2.9
sort of logically different, the algorithm.
2,871.7
1.91
Insertion sort, beautifully I only move one step at a time
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4.51
and I never turn back.
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1.14
Because I just deal with, as you did for the blue books, each problem one
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5.24
at a time, never again backtracking.
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2.36
But where was all the work happening?
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3.34
In the shifting of humans.
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1.44
Now, technically you guys helped out by doing the shifting yourselves.
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2.92
But if I'm the computer, it actually would
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1.749
have been like me tiptoeing back, shifting, shifting, shifting,
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3.391
inserting, shifting, shifting, shifting.
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2.18
So again, in the worst case, I might have
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1.71
had to shift everyone all the way over to make room for someone.
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3.94
Because in the worst case, what's the worst possible input
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2.55
you might get to a sorting algorithm?
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3.4
What input would create the most work for you?
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3.805
AUDIENCE: Backwards.
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0.86
SPEAKER 1: Backwards.
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0.875
If the list is perfectly backwards, every darn element
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2.69
is out of place, which means you have to traipse back and forth
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3.14
and back and forth to insert or to select or to swap all of those elements
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5.85
that many times.
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1.1
So in all of these cases, they are not numerically identical.
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3.53
Some of those algorithms might take fewer steps than others in totality,
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3.97
but they're all on the order of n squared for the reason
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2.86
that they're all involving comparisons as many as n times n times.
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4.79
All right.
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0.68
What about an algorithm that's big O of n?
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3.2
An algorithm that only takes n steps?
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3.65
We've seen one.
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0.878
Derek showed us one.
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1.26
What's an algorithm that takes n steps?
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1.68
Derek, hopefully.
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1.094
AUDIENCE: [INAUDIBLE].
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0.916
SPEAKER 1: A random search?
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1.49
Kind of, sort of.
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1.07
It's a little harder to put a number to because it
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3.244
depends what you mean by "random."
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1.416
Because if you have random with repetition such
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2.11
that you're checking foolishly the same elements again and again,
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2.877
it can actually add up to more than n steps.
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1.833
So not random, but-- yeah.
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2.805
AUDIENCE: Binary.
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0.8
SPEAKER 1: Binary is even better.
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1.375
Hold that answer.
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0.708
You're about to be correct.
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2.012
Linear search, right?
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1
If you just blindly go from left to right
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1.88
or right to left looking for some element,
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1.81
that is on the order of n steps.
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1.49
Because you are just doing foolishly unnecessary
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2.61
work if you go beyond the end of the list
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2.2
or beyond the beginning of the list.
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1.5