Download Priority Queue - Data structure cs322

Priority Queue
Data Structures
CS322
Prepared By: L.Fatimah Alanizi
Priority Queue
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.
Priority
Due day
Database Systems
2
October 3
UNIX
4
October 10
Data Structure & Algorithm
1
September 29
Structured Systems Analysis
3
October 7
Course
2
What is Priority Queue?
 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.
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What’s so different?
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 order
Priority 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
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Priority Queue ADT
 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?
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Priority Queue implementation
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?
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Priority Queue implementation
1) Implementing PQ with Unsorted Sequence:
Example: Assume we have the elements stored in an unsorted
sequence show here.
(1,1)
(4,4)
(0,0)
(7,7)
(8,8)
To perform the extractMin()/ removeMin() operation, we have to
inspect all elements to find the element (0,0) that has the
smallest key.
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Priority Queue implementation
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?
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Priority Queue implementation
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)).
(0,0)
(1,1)
(4,4)
(7,7)
(6,6)
9
(8,8)