Recall the structure and properties of a binary heap, then generalize them to a d-ary heap (where each node has up to d children).

Derive the time complexity for the `insert` operation in a d-ary heap by analyzing the number of comparisons and swaps required to maintain the heap property.

Prove that the height of a d-ary heap with n elements is ⌊log_d(n)⌋, and explain how this affects the worst-case time complexity of `extract-min` and `decrease-key` operations.