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Hi, I'm Gayle Laakmann McDowell, author of Cracking the Coding Interview. Today we'll talk about a topic that a lot of candidates forget about, heaps. Heaps come in one of two forms, a min heap or max heap. We'll just focus on min heaps today because a max heap is essentially the reverse. In a min heap the elements are all smaller than their children so the root node will be the very smallest element and then looking down the tree down the heap, the elements get bigger and bigger and bigger. So that's the basics of what a heap is but how do we actually create and maintain such a data structure? So let's start with just insertion. So when we insert an element it always goes in the next empty spot looking top to bottom left to right. So we go, first we insert an element here, and then here and then here and then here and so on through the tree, through the heap. So that's how insertion works. But then of course what happens if that's not really where the element should go? What we can do is we can insert the element there and then bubble it up until we get to the right spot. So we take the inserted element, we compare it with its parent, if it's out of order, swap them and then keep going up the tree in this process. Now what about removing the minimum element? So we know the minimum element will always be the root node and so that's easy to find but then if we want to remove it we might have an empty spot. So what we do here is we remove the min element there, so we take out the root and then we swap that value at the root with the last element added. And then of course that element might not be in the right spot, so we take the root element and bubble it down to the next spot so we compare the root with its children, its left child and its right child, and then swap it with the smaller of the two. And then we keep going down the tree until the heap property is restored. So that's how a tree operates, let's think about implement- that's how a heap operates, let's talk about implementation now. So implementation is kind of interesting. You might have assumed that we'd implement it a simple class node with a left node and a right node, and certainly we could do it that way. But there's an even better way of implementing it. Note that when we add elements to the heap they're always getting added in a very particular spot. There aren't gonna be any gaps in the heap so we have the zeroth element here and then the first second third fourth etc and so that means that we can actually use an array instead to store these values and that makes...