Question

1. Consider the min-priority queue implemented by a binary heap. (The max-priority queue is treated in §6.5 Priority queues in the textbook.)
   1. Show the binary tree implemented by the array A = 〈5, 8, 9, 11, 10, 12, 10, 12, 15, 11, 14, 13, 16, 15〉.
   2. Show the binary tree resulting from Heap-Insert(A, 6) where A is the array in (a).
   3. Show the binary tree resulting from Extract-Min(A) where A is the array in (a).
   4. Show the binary tree resulting from Heap-Decrease-Key(A, 10, 6) where A is the array in (a).

Answer 1

a)

Step 1: Insert keys 5 & 8      

  

Step 2: Insert key 9                     

      

Step 3: Insert key 11

Step 4: Insert key 10                    

                                   

Step 5: Insert key 12    

                     

Step 6: Insert key 10                         

                                                        

Step 7: Insert keys 12                

Step 8: Insert key 15              

            

Step 9: Insert key 11

Step 10: Insert key 14        

        

Step 11: Insert key 13                 

         

Step 12: Insert key 16

Step 13: Insert key 15               

Which is Required Binary Serach Tree(BST)

b) Insert 6:

c) Extract Min: