void heapInsert(heap_type& heap, double key, Action::Type hat);
void heapRemove(heap_type& heap);
void heapUpdate(heap_type& heap, double key, Action::Type hat);
void heapInsert(heap_type& heap, double key, Action::Type hat);
void heapRemove(heap_type& heap);
void heapUpdate(heap_type& heap, double key, Action::Type hat);