问题
I want to show that a Fibonacci heap with n nodes could have height n.
I tried this with examples but I don't know how to show this in general.
回答1:
(I assume you mean height n - 1: height n is impossible since with n nodes the maximum height is a linked list of height n - 1)
Getting to height one is easy: add in three nodes, then do a dequeue-min. This removes one node and combines the other two nodes, which have height 0, into this structure of height 1:
A
|
B
If you repeat this process again and ensure one of the new nodes has the lowest priority, you get two of these trees, which are then merged together like this:
A
|\
B C
|
D
Now, do a delete operation on B. This leaves A with order 1 and a mark:
A*
|
C
|
D
Repeat this process again (insert three nodes, all of which have infinite negative priority, and call dequeue-min) to get this:
E
|\
F A*
|
C
|
D
Delete F to get
E*
|
A*
|
C
|
D
If you repeatedly execute this process of adding three nodes, deleting one, then deleting the singleton child of the single remaining tree, you can make the Fibonacci heap a single tree of height n - 1 for any n you'd like.
Hope this helps!
来源：https://stackoverflow.com/questions/14300256/how-to-show-fibonacci-heap-with-n-nodes-can-have-height-n