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Mergeable Heap Operations

Make-Heap, Insert, Minimum, Extract-Min, Union

These always yield unordered binomial trees; thus, they maintain the binomial tree properties.

2k nodes
k = height of tree
\(\left( \begin{array}{c} k \\ i \end{array} \right)\) nodes at depth i
Unordered binomial tree Uk has root with degree k greater than any other node. Children are trees U0, U1, .., Uk-1 in some order.

For n-node Fibonacci Heap, D(n) is largest if all nodes are in one tree.

The maximum degree is at depth=1, \(\left( \begin{array}{c} k \\ 1 \end{array} \right)\) = k for tree with 2k nodes.

If n = 2k, then k = lg n

D(n) $\leq$ k = lg n
D(n) = O(lg n)

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