The document discusses priority queues, which are data structures that allow elements to be inserted and removed based on priority. Elements with higher priority are served before those with lower priority. There are two main types - ascending order queues prioritize lower numbers, while descending order queues prioritize higher numbers. Priority queues can be implemented using linked lists, arrays, binary heaps, and binary search trees. Common applications include shortest path algorithms, heap sorting, and operating system processes.

1. Priority Queue
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2. Priority Queue
 Definition:
 The priority queue is an abstract data-type similar to a regular queue or stack
data structure in which each element additionally has a "priority" associated with it.
In a priority queue, an element with high priority is served before an element with
low priority.
 A priority queue ADT is a data structure that supports the operations Insert and
Delete Min (which returns and removes the minimum element) or Delete Max
(which returns and removes the maximum element) and peeking the element(find
min or find max).
 Difference between Priority Queue and Normal Queue:
 In a queue, the first-in-first-out rule is implemented whereas, in a priority queue,
the values are removed on the basis of priority. The element with the highest
priority is removed first.

3. Types of Priority Queue:
 There are two types in Priority Queue:
1. Ascending Order
2. Descending order
1. Ascending Order Priority Queue:
 An ascending order priority queue gives the highest priority to the lower number in that
queue.
Example:
 you have six numbers in the priority queue that are 15, 35, 10, 40, 6, 5. Firstly, you will
arrange these numbers in ascending order.
The new list is as follows:
 5, 6, 10, 15, 35, 40. In this list, 5 is the smallest number. Hence, the ascending order
priority queue treats number 5 as the highest priority.
 Before applying of ascending order table like this.
 After applying of ascending order table like this.
 In the above table 5 has the highest priority, and 40 has the lowest priority.
15 35 10 40 6 5
5 6 10 15 35 40

4. Continue…
2. Descending Order Priority Queue:
 A descending order priority queue gives the highest priority to the highest number
in that queue.
Example:
 you have six numbers in the priority queue that are 15, 35, 10, 40, 6, 5. Firstly, you
will arrange these numbers in ascending order.
The new list is as follows:
 40, 35, 15, 10, 6, 5. In this list, 40 is the highest number. Hence, the descending
order priority queue treats number 40 as the highest priority.
 Before applying of ascending order table like this.
 After applying of ascending order table like this.
 In the above table 40 has the highest priority, and 5 has the lowest priority.
15 35 10 40 6 5
40 35 15 10 6 5

5. Applications of Priority Queue:
 Prim's algorithm implementation can be done using priority queues.
 Dijkstra's shortest path algorithm implementation can be done using priority
queues.
 A* Search algorithm implementation can be done using priority queues.
 Priority queues are used to sort heaps.
 Priority queues are used in operating system for load balancing and interrupt
handling.
 Priority queues are used in huffman codes for data compression.
 In traffic light, depending upon the traffic, the colors will be given priority.

6. Characteristics of a Priority Queue:
 A queue is termed as a priority queue if it has the following characteristics:
 Each item has some priority associated with it.
 An item with the highest priority is moved at the front and deleted first.
 If two elements share the same priority value, then the priority queue follows the first-in-
first-out principle for de queue operation.
 Implementation of the Priority Queue in Data Structure:
 You can implement the priority queues in one of the following ways:
1. Linked list.
2. Binary heap.
1. Min heap.
2. Max heap.
3. Arrays.
1. Unordered Array.
2. Ordered Array.
4. Binary search tree.

7. Priority Queue using Linked list:

8. Algorithm for Implementing Priority Queue
using linked list in C :(enqueue(int))
enqueue(int d)
Create a new node of structure node type.
new_node->data = entered data.
new_node->Priority = priority.
IF(Front == NULL)||(Entered priorityPriority)
new_node->next = Front.
Front = new_node.
End IF.
ELSE
Temp = Front
WHILE((Temp->next!=NULL)&&(Temp->Priority<=Entered Priority)
Temp = Temp->next
new_node->next = temp->next
temp->next = new_node
End ELSE

9. Algorithm for Implementing Priority Queue
using linked list in C :(dequeue())
dequeue()
Create a temporary pointer temp of node structure type
IF(Front == NULL)
Print ‘Underflow Condition’
End IF
ELSE
Temp = Front
Front = Front->Next
Print(data and priority)
Free(temp)
End ELSE

10. Algorithm for Implementing Priority Queue
using linked list in C :(print())
STRUCT NODE* TEMP
IF((FRONT == NULL)&&(REAR == NULL))
RETURN
ELSE
TEMP = FRONT
WHILE(TEMP)
RETURN TEMP->DATA
TEMP = TEMP->NEXT

11. Priority Queue using unordered Array :

12. Priority Queue using ordered Array :

13. Algorithm for Implementing Priority Queue
using Array in C :(enqueue(int))
Enqueue()
IF((Front == 0)&&(Rear == N-1))
PRINT “Overflow Condition”
Else
IF(Front == -1)
Front = Rear =0
Queue[Rear] = Data
Priority[Rear] = Priority
ELSE IF(Rear ==N-1)
FOR (i=Front;i<=Rear;i++)
FOR(i=Front;i<=Rear;i++)
Q[i-Front] =Q[i]
Pr[i-Front] = Pr[i]
Rear = Rear-Front
Front = 0
FOR(i = r;i>f;i–)
IF(p>Pr[i])
Q[i+1] = Q[i] Pr[i+1] = Pr[i]
ELSE
Q[i+1] = data Pr[i+1] = p
Rear++

14. Algorithm for Implementing Priority Queue
using Array in C :(dequeue(),print())
Dequeue()
IF(Front == -1)
PRINT “Queue Under flow condition”
ELSE
PRINT”Q[f],Pr[f]”
IF(Front==Rear)
Front = Rear = -1
ELSE
FRONT++
Print()
FOR(i=Front;i<=Rear;i++)
PRINT(Q[i],Pr[i])

15. Comparative analysis of priority queue:
Operation
Unordered
Array
Ordered
Array
Linked list Binary Heap Binary Search Tree
Insert 0(1) 0(N) 0(1) 0(log(N)) 0(log(N))
Peek 0(N) 0(1) 0(N) 0(1) 0(1)
Delete 0(N) 0(1) 0(1) 0(log (N)) 0(log(N))