Binomial Heap

A binomial heap that supports O(1) am. insertion and O(log n) merging, matching binary heaps for the time complexities of all other operations.

Currently, decrease-key and delete still need to be implemented, but all other functionality is supported.

Operation	Binary Heaps	Binomial Heaps
Report Min	$$O(1)$$	$$O(1)$$
Extract Min	$$O(log n)$$	$$O(log n)$$
Insert	$$O(log n)$$	$${\color{green}O(1) am.}$$
Decrease Key	$$O(log n)$$	$$O(log n)$$
Delete	$$O(log n)$$	$$O(log n)$$
Merge	$$O(n)$$	$${\color{green}O(log n)}$$

As a side note, binary heaps can also achieve O(1) am. for n inserts. That is, if n elements are being inserted into the heap at once, they can be appended onto the end, and the heap can be rebuilt for a total of linear time.

Additionally, if an application uses merges more than other operations, merges can be optimized to O(1) time as a simple union of the two heaps, and the structure will naturally be restored with subsequent operations.