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Priority Queues

Priority Queues. What is a Priority Queue?. Container of elements where each element has an associated key A key is an attribute that can identify rank or weight of an element Examples – passenger, todo list. Priority Queue ADT Operations. size() isEmpty()

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Priority Queues

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  1. Priority Queues

  2. What is a Priority Queue? • Container of elements where each element has an associated key • A key is an attribute that can identify rank or weight of an element • Examples – passenger, todo list

  3. Priority Queue ADT Operations • size() • isEmpty() • insertItem(k, e) – insert element e with key k • minElement() – return ref to min element • minKey() – return const ref to smallest key • removeMin() – remove and return element with smallest key

  4. insertItem(5, A) insertItem(9, C) insertItem(3, B) insertItem(7, D) minElement() minKey() removeMin() size() minElement() removeMin() removeMin() removeMin() removeMin() isEmpty() Example

  5. The Comparator Pattern • Suppose we want a priority queue of “Appointment” objects • How do we determine that one appointment is before another? • Need to compare Appointment objects • operator overloading versus standard function

  6. Implementation • Using an array? • Using a linked list? • Running time of insertItem/removeMin?

  7. Sorting • Can you sort a list of numbers using a priority queue? • Algorithm?

  8. Heaps • A heap is a priority queue implemented with a binary tree • Heap-Order Property: In a heap T, for every node v other than the root, the key stored at v is greater than or equal to the key stored at v’s parent • Complete Binary Tree Property: A heap

  9. Heaps • Heap-Order Property: In a heap T, for every node v other than the root, the key stored at v is greater than or equal to the key stored at v’s parent

  10. Heaps • Complete Binary Tree Property: A heap T with height h is a complete binary tree, that is, levels 0,1,2,…,h-1of T have the maximum number of nodes possible and all the internal nodes are to the left of the external nodes in level h-1. • What does this give us?

  11. Example Heap root 4 9 7 56 10 15 11

  12. Heap Implementation • Insertion algorithm new_node 5 root 4 9 7 56 10 15 11

  13. Up-Heap Bubbling while new node is smaller than its parent swap parent and node • Running time?

  14. Heap Implementation • Deletion algorithm delete 4 root 4 9 5 56 10 7 11 15

  15. Down-Heap Bubbling if right child is null if left child is smaller than current swap left and current if both children not null swap current with smallest child

  16. Vector Implementation • Children are positions index*2 and index*2+1 • Implementation of insert and remove? 0 1 2 3 4 5 6 7

  17. Heap Sort • Algorithm to use a heap to sort a list of numbers • Running time?

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