Why are the runtime heap used for dynamic memory allocation in C-style languages and the data structure both called "the heap"? Is there some relation?
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Actually, reading about the way memory is allocated (see Buddy Blocks) reminds me of a heap in data structures.
The name collision is unfortunate, but not all that mysterious. Heap is a small, common word used to mean a pile, collection, group, etc. The use of the word for the data structure pre-dates (I'm pretty sure) the name of the pool of memory. In fact, pool would have been a much better choice for the latter, in my opinion. Heap connotes a vertical structure (like a pile), which fits with the data structure, but not the memory pool. We don't think of a memory-pool heap as hierarchical, whereas the fundamental idea behind the data structure is keeping the largest element at the top of the heap (and sub-heaps).
Heap the data structure dates back to the mid-60s; heap the memory pool, the early-70s. The term heap (meaning memory pool) was used at least as early as 1971 by Wijngaarden in discussions of Algol.
Possibly the earliest use of heap as a data structure is found seven years earlier in
Williams, J. W. J. 1964. "Algorithm 232 - Heapsort", Communications of the ACM 7(6): 347-348