Structure of A Binomial Heap
A binomial heap is implemented as a set of binomial trees that satisfy the binomial heap properties:
- Each binomial tree in a heap obeys the minimum-heap property: the key of a node is greater than or equal to the key of its parent.
- There can only be either one or zero binomial trees for each order, including zero order.
The first property ensures that the root of each binomial tree contains the smallest key in the tree, which applies to the entire heap.
The second property implies that a binomial heap with n nodes consists of at most log n + 1 binomial trees. In fact, the number and orders of these trees are uniquely determined by the number of nodes n: each binomial tree corresponds to one digit in the binary representation of number n. For example number 13 is 1101 in binary, and thus a binomial heap with 13 nodes will consist of three binomial trees of orders 3, 2, and 0 (see figure below).
Example of a binomial heap containing 13 nodes with distinct keys.
The heap consists of three binomial trees with orders 0, 2, and 3.
Read more about this topic: Binomial Heap
Famous quotes containing the words structure of, structure and/or heap:
“I’m a Sunday School teacher, and I’ve always known that the structure of law is founded on the Christian ethic that you shall love the Lord your God and your neighbor as yourself—a very high and perfect standard. We all know the fallibility of man, and the contentions in society, as described by Reinhold Niebuhr and many others, don’t permit us to achieve perfection.”
—Jimmy Carter (James Earl Carter, Jr.)
“The philosopher believes that the value of his philosophy lies in its totality, in its structure: posterity discovers it in the stones with which he built and with which other structures are subsequently built that are frequently better—and so, in the fact that that structure can be demolished and yet still possess value as material.”
—Friedrich Nietzsche (1844–1900)
“But generally speaking philistinism presupposes a certain advanced state of civilization where throughout the ages certain traditions have accumulated in a heap and have started to stink.”
—Vladimir Nabokov (1899–1977)