Priority Queues

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

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

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

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

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

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

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

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

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