For that heap of dollars?

The whole thing is a heap. We made a heap. Woohoo!

Update the heap so the heap property is restored and all of this information is communicated back and forth.

We have the heap structure.

We can say to build a heap, rooted at this node, make this new heap, make this new heap and then down heapify.

Another way to build a heap out of a set of values is insert the items one at a time into the heap.

This is a heap. We'll check them off as we go. This is a heap.

Removing the minimum value of a heap is log n.

Pile the hoard into a heap!

Get this blasted heap turned 'round!

That's a heap operation there's n things in the heap, so this is a logn operation.

The unemployed always wind up at the bottom of the heap.

Put the plan on the scrap heap.

When I lift the heap, I peek.

Because we didn't actually touched this sub tree. It had the heap property? It still has the heap property.

A delicatessen caught fire and burned down, leaving a heap of ashes.

I dig up a heap of, pardon... I'd better not name it.

I've made a couple of helpful routines to help with the heap. given a position i in the heap, left (i) returns the position of the left child.

She fell in a heap to the floor.

So, good. That's great. Heap property is restored.

Fan letters lay in a heap on the desk.

Then they began to heap reproaches on each other.

She left the old newspapers lying in a heap.

At which point, the heap property is satisfied globally.

We kind of have broken our big nice heap into two small nice heaps, but really want them to be one nice heap, so what can we do.

If we have some value in the heap and we know that the heap property is satisfied and what does that mean?

We'll give you down heapify and the build heap algorithm so that you can take a list, create a heap out of it and then remove the min from it.

We can apply this if the heap property is satisfied.

Ohh. That broken down old heap and 150 in cash.

So every time I lift the heap, I peek, right.

it takes a heap of living to make a house a home. Want another beer?

That seems like the sort of things that a heap would be really good at.

Now, this lady, on the wall of the dung cake heap, has made a painting.

Marley Marl, Ultramagnetic MC's, Charlie Chase, Grandmaster Caz and there was a whole heap of people.

The heap property is satisfied everywhere and we can just return.

It could actually not satisfy the heap property but that's okay.

This is sometimes called heap sort. You give it a (L).

Or, if the heap was already full, then the far left.

And if they were to see a fragment of the heaven falling, they would say A heap of clouds.

Why don't you put a heap of stones there and pretend it is a rockery? he said.

Is it (logn) like the other heap operations we've been looking at?

Here's a lovely heap. In fact, well, I just covered this up.

And were they to see a portion of the sky falling, they will say, It is a heap of clouds.

Here's two natural ways of implementing the heap operations of inserting and finding and removing the minimum from the structure.

To make this into a heap, we have to swap it with the smaller of the children 13.