And if you only need a monotone priority queue (i.e. priority queue where the popped elements are monotonically increasing/decreasing) you should consider using

And if you only need a monotone priority queue (i.e. priority queue where the popped elements are monotonically increasing/decreasing) you should consider using a radix heap. This monotone requirement can be satisfied more than you would expect when eg. using time as key or in pathfinding. I have a simple radix heap implementation here: https://github.com/mpdn/radix-heap https://github.com/mpdn/radix-heap