That sounds right -- it probably wants a Random Access Container that is also a Back Insertion Sequence. It would work with vector, deque, or the fixed_max_size_vector that is earlier in d_ary_heap.hpp.
Yes, you are right. In it comments, it says container means random access container. Maybe array and list are less used in development. I still consider it's necessary to make them available for d-ary in the new library. So I want to rebuild d_ary_heap.hpp by using iterator in the new library. Will that be redundancy for Boost? Besides, my understanding on "A second requirement is that heaps may be "mutable", meaning that a value already stored in the heap can be modified and the heap efficiently updated to accommodate the new change" is that we can modify all the nodes in the key, not just the root. If my understanding was right, there would be the other reason to include d-ary in the new library becuse the original one in the BGL dose not support this operation ( operation update in d_ary_heap.hpp is only for root). Thank you for your time. Yours sincerely, Tao Lin