# binomial - 22 Binomial Heaps Big Picture(Figure 19.1 Pg 456...

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22 Binomial Heaps Big Picture (Figure 19.1, Pg 456) New Operations: UNION( , ) creates and returns a new heap that contains all the nodes of heaps and (which are destroyed by this operation). DECREASE-KEY( ) assigns to a node in heap a new key value , which is its current value. DELETE( ) 22.1 Binomial Trees An ordered tree that is defined recursively (See Fig 19.2, Pg 458). 1. consists of a single node. 2. consists of two trees that are linked by making the root of one the leftmost child of the root of the other. 84

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Properties of 1. nodes. 2. height is 3. There are exactly nodes at depth for . 4. the root has degree . 5. Corollary: The maximum degree of any node in an -node binomial tree is . I’m skipping proofs because they are simple, but you should try them yourselves. Definition of a binomial heap A binomial heap is a set of binomial trees such that 1. each binomial tree has the min property. 2. for any integer , there is at most one binomial tree in whose root has degree .
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