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So, in this video, we're going to look at a specific algorithm for sorting data.

And throughout the examples, we're just going to use an array of integers, but

the same ideas and principles translate whenever we have information that's

all of the same type and we can compare pairs of information of that type.

So by the end of this video, you'll be able to explain the selection sort

algorithm and write code for it yourself.

So let's get started and let's think of a toy example and it's always useful

when developing algorithms to think of a specific concrete example

that we can work through the steps of the algorithm with respect to this example and

then afterwards think about generalizing it.

So let's think about this array of integers.

And there's only six elements in this array so

we can probably do it in our head but

let's think about it systematically how we would go about sorting these elements.

And what we might do is, first of all,

say at the end I want the smallest element to be in the first position of the array,

the second smallest to be in the second position of the array, the third smallest

to be in the third position of the array, and so on and so forth.

And so let's look for the smallest element.

So we're looking through our entire array,

and we're looking for the smallest element.

And lo and behold, we found it.

It's 7, it's already in the first position, so we really don't need to do

anything else to it, it's already where it's supposed to be.

And so we don't need to ever think about it again.

It's in place, it's done.

And so now what we want to do is move forward and

say, well what about the rest of the elements in the array?

What's smallest among those?

Because whatever's smallest in the rest of the array is going to be

the second smallest out of everything.

And so we should bring it into the second position in the array.

Okay and so, we have now five elements to consider, one less then before and

we're looking for the smallest element and oh my goodness we're lucky again,

16 is the smallest it's already at the beginning, we don't need to do anything,

leave it in place.

Okay, so our problem is reduced further yet.

Now we need to find the third smallest element overall, but that's just

the smallest element in the remaining unsorted elements that we haven't thought

about yet, and so we've got four elements to consider and we want the smallest one.

Now we see that it's 43,

it's not the first one like we had in the previous two examples.

And so what we need to do is to put it in it's correct location.

And it's correct location as it would be in the sorted version of the array.

And so we need to swap it with 66 in order to move 43 to it's correct location.

Okay, and so we go ahead and do that.

And now 43 is in it's correct location for the sorted array, we don't think about it

anymore and we move on to look at the three remaining elements.

Look for their smallest, oh, 51 and now we move 51

to it's correct location where it's going to be once the array is sorted.

And so we have to swap it with 66,

go ahead and do that and now 51 is done and it's in it's correct location,

we don't need to think about it ever again and we look at the remaining two elements.

Look for the smallest among those, that's 66.

Swap it, and now we're actually done, because for

the last item, while the only reason it's in the last position is because it wasn't

the first smallest, it wasn't the second smallest, it wasn't the third smallest.

It's already in it's correct position.

We can't compare it to anything else.

And so when we've got to our last position in the array, we're actually done.

We don't need to do anything.

Okay and so what that means is that we've got a algorithm, a series of steps that we

can take algorithmically to perform this task, so we've got Selection Sort.

Being described here as,

first by the smallest element, then put in location zero in the array.

Then find the next smallest, put it in location one, etc.