The average case time complexity for sorting N items with a minimum binary heap is O(N log N), derived from the process of building the heap as O(N) and the subsequent N removal and heapification operations at O(log N) each.
Sorting N items with a minimum binary heap involves building the heap and then repeatedly removing the minimum element to achieve a sorted order. The average case time complexity for building the heap is O(N), whereas the removal of each element and heapifying each time involves O(log N) operations. However, since we have to perform this removal operation for N elements, the total average case time complexity for heap sort is O(N log N).