Binomial Queues - Department of Computer Science and ...
Binomial Queues
Section 6.8
1
Heap Operations: Merge
Given two binary heaps H1 and H2, produce a new heap H' combining H1 and H2 Binary heaps take !(n1 + n2) time to merge i.e. they can never merge in better than linear time
We can do better, however Merge in O(log N) time this comes at the expensive of a slight performance hit on our other operations
2
Binomial Trees
B0
B1
B2
Binomial trees are recursive defined
Start with one node
B3
This is a binomial tree of height 0
To form a tree of height k, attach two trees of height k - 1 together
Attach one as a child of the root of the other
3
B4
B4
4
Binomial Tree Size
A binomial tree of height k has 2k nodes
B3
Conversely, a binomial tree with n nodes has log2(n) height
The number of nodes at level d of a tree with height k is the binomial
coefficient:
! #
k
$ &
=
k!
" d % d!(k - d)!
5
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