Priority QueueData Structures

CS322Prepared By: L.Fatimah Alanizi

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Priority Queue

Course Priority Due dayDatabase Systems 2 October 3

UNIX 4 October 10

Data Structure & Algorithm

1 September 29

Structured Systems Analysis

3 October 7

Suppose that you have a few assignments from different courses .Which assignment will you want to work on first?

You set your priority based on due days. Due days are called keys.

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a priority queue is an abstract data type which is like a regular queue or stack data structure, but where additionally each element has a "priority" associated with it.

An entry in a priority queue is simply a (key, value) pair

In a priority queue, an entry with high priority is served before an entry with low priority, So the order is determined by key. Exe: Highest priority entry will served first ,so it is in the first order: kmin

The smallest key: If we have a finite number of entries , then the smallest key, is the key that satisfies kmin< k for any other key k

If two entries have the same key value, they are served according to their arrival in the queue.

What is Priority Queue?

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Stacks and Queues:• Removal order determined by order of inserting (stack LIFO, Queue FIFO)Sequences:• User chooses exact placement when inserting and explicitly chooses removal orderPriority Queue• Removal order determined by key• Key may be part of element data or separate

Examples: Processes scheduled by CPU Hospital Emergency Rooms College admissions process for students

What’s so different?

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insertItem(k,e): insert element e with key k extractMin( )/ removeMin() : return element with

minimum key and remove from queue minElement( ): Return (but do not remove) an element

with the smallest key; an error condition occurs if the priority queue is empty.

minKey( ): Return a smallest key; an error condition occurs if the priority queue is empty

size( ): return number of elements isEmpty( ): size == 0?

Priority Queue ADT

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1) Implementing PQ with Unsorted Sequence: Keys in the sequence are not sorted

Each call to insertItem(k, e) inserts element in the last of Sequence O(1) time

Each call to extractMin( ) )/ removeMin() traverses the entire sequence to find the minimum, then removes element O(n) time

What about other operations?

Priority Queue implementation

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1) Implementing PQ with Unsorted Sequence:Example: Assume we have the elements stored in an unsorted sequence show here.

To perform the extractMin()/ removeMin() operation, we have to inspect all elements to find the element (0,0) that has the smallest key.

Priority Queue implementation

(8,8) (7,7) (0,0) (4,4) (1,1)

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2) Implementing PQ with Sorted Sequence: Keys in the sequence are sorted

Each call to insertItem(k, e) traverses sorted sequence to find correct position, then does insert O(n) worst case

Each call to extractMin( )/removeMin() does remove first element O(1) time

What about other operations?

Priority Queue implementation

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2) Implementing PQ with Sorted Sequence:Example:To insert the pair (6,6), we have to scan through the sequence until we find the right place (between (4,4) and (7,7)).

Priority Queue implementation

(8,8) (7,7) (4,4) (1,1) (0,0)

(6,6)