Final answer:
The worst-case time complexity of sorting N items with a minimum binary heap is O(N log N). Option 'd' is the correct choice.
Step-by-step explanation:
When sorting N items using a minimum binary heap, each operation of inserting an item into the heap or deleting an item from the heap has a worst-case time complexity of O(log N). However, for sorting, which involves building the heap with N items and then performing delete operations to extract the minimum, the heap construction has a linear time complexity of O(N), and the repeated deletion has a complexity proportional to N log N. Therefore, the overall worst-case time complexity for heap sort is O(N log N), which makes option 'd' the correct answer in this case.
The confusion often comes from the fact that building a heap itself can be done in O(N), but each subsequent extract-min operation (removal of the minimum element or root for a min-heap) used in the sorting process is O(log N), which when performed for N elements results in a total complexity of O(N log N).