It has a better amortized running time than a binomial heap.

This operation is basic to the complete merging of two binomial heaps.

Compared with binomial heaps, the structure of a Fibonacci heap is more flexible.

Binomial heaps add several more operations, but require O(log n) time for requests.

Then transform this list of subtrees into a separate binomial heap by reordering them from smallest to largest order.

They also find use in bootstrapped skew binomial heaps, which have excellent asymptotic guarantees.

This feature is central to the merge operation of a binomial heap, which is its major advantage over other conventional heaps.

Additionally, it helps explain the time analysis of some operations in the binomial heap and Fibonacci heap data structures.

All of the following operations work in O(log n) time on a binomial heap with n elements:

A Fibonacci heap is thus better than a binomial heap when b is asymptotically smaller than a.

When merging is a common task, a different heap implementation is recommended, such as binomial heaps, which can be merged in O(log n).

Two C implementations of binomial heap (a generic one and one optimized for integer keys)

In computer science, a binomial heap is a heap similar to a binary heap but also supports quick merging of two heaps.

The second property implies that a binomial heap with n nodes consists of at most log n + 1 binomial trees.

As mentioned above, the simplest and most important operation is the merging of two binomial trees of the same order within two binomial heaps.

A binomial heap is implemented as a collection of binomial trees (compare with a binary heap, which has a shape of a single binary tree).

For insertions, this is slower than binomial heaps which support insertion in amortized constant time, O(1) and O(log n) worst-case.

A binomial heap is implemented as a set of binomial trees that satisfy the binomial heap properties:

Just as binomial heaps are based on the binary number system, skew binary heaps are based on the skew binary number system.

Skew binary numbers find applications in skew binomial heaps, a variant of binomial heaps that support worst-case O(1) insertion, and in skew binary random access lists, a purely functional data structure.

Because each binomial tree in a binomial heap corresponds to a bit in the binary representation of its size, there is an analogy between the merging of two heaps and the binary addition of the sizes of the two heaps, from right-to-left.