I wanted to ask about Fibonacci heaps. If I have this scenario:
A
|
B
Then, we add two more nodes C and D:
A
|\
B C
|
D
Now we delete B:
A
|
C
|
D
Now we add E and F.
I saw it creates a tree like that:
E
|\
F A
|
C
|
D
But I don't understand why E and F are connected with the tree. From what I read, we connect trees with the same rank (for example, a tree of one node with another tree of one node), am I wrong?
Thank you very much.
If you add the nodes C and D into the first Fibonacci heap, you would not end up with the tree you drew. Instead, you'd have this heap:
A C D
|
B
Remember that Fibonacci heaps lazily add each newly added value to the top-level list of trees and only coalesce things on a deletion. If you were to delete B, you'd promote it to the top level, like this:
A B C D
You'd then remove B:
A C D
Now, you'd scan the root list and coalesce the trees of the same order together. Let's suppose you scan the nodes in the order A, C, D. First, you'll coalesce A and C together, like this:
A D
|
C
At this point, no further coalesces will happen, since there's exactly one tree of each order.
If you then add in E and F, you'd put them at the top level, like this:
A D E F
|
C
So yes, you're right, those nodes shouldn't get added into the tree.