1. Priority Queues

2. Use of Heaps As we mentioned, heaps can be used in Heapsort
Priority Queues

3. Priority Queues
A queue where we add objects, each with a value (“priority”).
Priority queues are very common for job scheduling
Two Types:
Max-Priority Queue  we use Max Heap
Min-Priority Queue  we use Min Heap

4. Operations on Priority Queues (Assume Max Queue)
Add a new object with priority K
Return the object with the highest priority
Remove the object with the highest priority
Increase the priority of object O
Heap data structure can implement all these operations efficiently

5. Remember If we need Max-Queue, we use Max Heap
If we need Min-Queue, we use Min Heap

6. 1- Add New Object With Priority 9
Add the object to the heap
Re-heapify if needed
O (Log n) 14 12 9 8 10 14 12 5 8 10 5 9

7. 2- Return the Highest-Priority Object
Return the root of the tree
Same as: Return the first element in the Heap array
In our example, return 14
O (1) 14 12 9 8 10 5

8. 3- Remove the Highest-Priority Object
Remove the root of the tree
Replace it with the lowest right-most object
Re-heapify
O (Log n) 14 12 9 8 10 5 5 12 9 8 10 12 5 9 8 10 12 10 9 8 5

9. 4- Increase the Priority of Object O
Change 12 to 20
Change the value and re-heapify upwards
O (Log n) 14 12 9 8 10 5 14 20 9 8 10 5 20 14 9 8 10 5

10. Summary of Heaps Very interesting data structure Common Usage
Balanced, left-justified binary trees
Arrays
Common Usage
Heapsort  always O(n log n)
Priority queues  most operations need O(log n)
Two main types (depend on your application)
MaxHeap: Parent value >= children values
MinHeap: Parent value <= children values