# Insertion Sort

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In these next couple of videos, we’re going to introduce the concept of sorting algorithms. Sorting algorithms are used when we want to arrange sets of data in order either from smallest to largest or largest to smallest in our computer programs. As it turns out, there are many different ways that we can sort our data using different algorithms. And each of those algorithms have unique characteristics that make them suitable for certain types of data in certain situations. To really explore sorting algorithms, we’re going to perform these sorting algorithms using a deck of cards. So if you have access to a deck of cards, I encourage you to go find one and take out maybe 8 or 10 cards in a certain order. I have the cards Ace through 10 here, and you’ll be able to follow along with our examples on these next few videos. Before we get started, I’d like you to take the cards that you have selected, shuffled them up a little bit, and then lay them out in front of you and try and sort them in order from smallest to largest. And while you do that, I’d like you to think in your mind about the exact steps that you’re following. For example, are you looking for the smallest card and moving it to one side, or looking for the largest card and moving it to the other side? Or are you trying to arrange little bits of it at a time and slowly put those pieces together until they form the full sort of deck of cards, it might be really interesting to see how the method that you naturally follow matches up with one of these algorithms that we’re going to take a look at. In particular, we’re going to look at four different sorting algorithms, insertion Sort, bubble sort, merge, sort, and quicksort.

The first example is insertion sort. In insertion sort, there’s basically three steps. And you can see in this graphic up above how they work. First, we’ll choose an element from our array, and we’ll place it in the correct place in our destination. So we go through we take the card, we put it where we want, and we repeat until our array is empty and we have completely sorted the cards. So let’s take a look at it. An example of how to do that using a deck of cards. Let’s take a look at how to use a deck of cards to simulate insertion sorts. Here I’ve selected 10 cards out of a deck of cards, and I’ve arranged them in a random order. If you want to follow along at home, feel free to grab either a suit out of a deck of cards, or you can grab just 10 cards in numerical order. In this case, I’m using the ace is one at the low end of the scale. So to do insertion sort, all we have to do is take each value out of our initial array and place it where it would go in the final array. So the first value we’ll have is a nine and we know that that needs to go in the 9th position here. Then we have the 4 we know that the 4 has to go before the 9. Now we have the 8 and we know that the 8 goes between the 4 and the 9. We get a three. It needs to go before the 4. We get to it goes before the three now we get a 5 the 5, does not go here does not go here, but it goes after the four. So we’ll move all of these down and make room for the 5. The ace, of course goes here at the beginning, the 10, we look through, and we see that it goes all the way at the end. Then we have the seven, we see that goes here between the 5 and the 8. And then likewise, the sixth would go there as well.

So that’s what insertion sort looks like when we as a person does it. But what if a computer was trying to do insertion sort? Let’s take a look and see what that would look like. So now let’s do Insertion Sort like a computer would do it. Instead of knowing exactly where the cards might go. A computer has to only compare two cards at a time and see what should go. So the computer would start by grabbing the 5 and placing it in our destination. Then the computer would grab the ace and say, does the ace go below or before the 5? It does. So we’ll put the ace before the 5. That’s all the computer does. Next, the computer grabs the three and says, “Does the three go before the ace?” Nope. Does the three go before the 5? Yes. So it would place the 3 before the 5. Then it would do the same thing for the 10. It would see does the 10 go before the ace? No. Does it go before the 3? No. Does it go before the 5? No, it goes at the end. So go ahead and see if you can do insertion sort and keep track of how many times you ask yourself does this card go before this card? Does this card go before this card that will give you an idea of how many steps it would take a computer to do insertion sorts a little bit later, we will analyze what that looks like using some complexity. The analysis with our algorithms doesn’t go there doesn’t go there doesn’t go there doesn’t go there must go at the end. And we can repeat this process for all the rest of these cards by going from the front to the back, and figuring out where each card belongs. That’s an example of how to do Insertion Sort using a deck of cards. See if you can do it yourself and follow along and understand how this algorithm works.