These functions select the easiest-to-remove element in the heap, which
is either the most recently inserted aux list element or the root. If
no calls are made to first() or remove_first(), the behavior (and time
complexity) is the same as for a LIFO queue.
Refactor ph to support configurable comparison functions. Use a cpp
macro code generation form equivalent to the rb macros so that pairing
heaps can be used for both run heaps and chunk heaps.
Remove per node parent pointers, and instead use leftmost siblings' prev
pointers to track parents.
Fix multi-pass sibling merging to iterate over intermediate results
using a FIFO, rather than a LIFO. Use this fixed sibling merging
implementation for both merge phases of the auxiliary twopass algorithm
(first merging the aux list, then replacing the root with its merged
children). This fixes both degenerate merge behavior and the potential
for deep recursion.
This regression was introduced by
6bafa6678f (Pairing heap).
This resolves#371.
Initial implementation of a twopass pairing heap with aux list.
Research papers linked in comments.
Where search/nsearch/last aren't needed, this gives much faster first(),
delete(), and insert(). Insert is O(1), and first/delete don't have to
walk the whole tree.
Also tested rb_old with parent pointers - it was better than the current
rb.h for memory loads, but still much worse than a pairing heap.
An array-based heap would be much faster if everything fits in memory,
but on a cold cache it has many more memory loads for most operations.
