A Fibonacci heap is an interesting variant of heaps, which in some ways is similar to a binomial heap. First of all, it also consists of many trees, but there are no constraints regarding the shape of each tree, so it is much more flexible than the binomial heap. Moreover, it is allowed to have more than one tree with exactly the same shape in the heap.
An example of a Fibonacci heap is as follows:
One of the important assumptions is that each tree is a min-heap. Thus, the minimum value in the whole Fibonacci heap is certainly a root node in one of the trees. Moreover, the presented data structure supports performing various operations in the lazy way. That means that it does not perform additional complex operations unless it is really necessary. For example, it can add a new node just as a new tree with only one node.
You can find more information about Fibonacci heaps at https://en.wikipedia.org/wiki/Fibonacci_heap.
Similarly to the binomial heap, the implementation of...