Heapsort exercises

Author: lee-naish

src/algorithms/extra-info/HSInfo.md

@@ -20,4 +20,21 @@ Geeks for Geeks Link: [**Heap Sort**][G4GLink]
 
 [G4GLink]: https://www.geeksforgeeks.org/heap-sort/
 
+Many teaching resources say the best case for Heap sort is O(n log n).
+However, there is a case where it is O(n) - can you figure out what it is?
+
+Here we have presented the "bottom up" way of creating a heap from an
+unsorted array.  There is also a "top down" method where we start with
+just the first element of the array (which can be considered a heap)
+and repeatedly include the next element in the array until all array
+elements are included in the heap. At each stage some elements may need
+to be rearranged to ensure the heap condition is met (using an operation
+normally called *UpHeap*).  Work out (or look up) the details of this
+algorithm. Try to work out (or look up) the worst case time complexity
+for these two ways of creating a heap.
+
+Heaps are an efficient way of implementing the *piority queue* abstract
+data type.  What operations does this ADT support and how can they
+be implemented using a heap?  What are priority queues useful for?
+Can you find some algorithms in AIA that use priority queues?