Lecture 7 data structures and algorithms
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A queue is a first-in, first-out (FIFO) data structure that can be implemented using either a linear array or linked list. Elements are added to the rear of the queue and removed from the front. A priority queue is a collection of elements where each element has a priority and higher priority elements are processed before lower priority ones. A priority queue can be implemented using a one-way linked list where each node stores the element, priority, and link. Elements are deleted from the front of the list and inserted in order of descending priority.
![Queue
• Queue is assumed to be circular
• QUEUE[1] comes after QUEUE[N]
• Instead of increasing REAR to N +1, we
reset REAR = 1 and then assign
QUEUE[REAR] = ITEM](https://image.slidesharecdn.com/lecture7-m-131122062250-phpapp02/85/Lecture-7-data-structures-and-algorithms-8-320.jpg)
![Algorithm to Insert in Q
[1] If FRONT = 1 and REAR = N or if FRONT =
REAR + 1 then Print: Overflow and Exit
[2] If FRONT = NULL then
Set FRONT = 1 and REAR = 1
Else If REAR = N then
Set REAR = 1
Else
Set REAR = REAR + 1
[3] Set QUEUE[REAR] = ITEM
[4] Exit](https://image.slidesharecdn.com/lecture7-m-131122062250-phpapp02/85/Lecture-7-data-structures-and-algorithms-11-320.jpg)
![Queue
FRONT: 7
REAR: 6
AA BB CC DD EE FF
1
2
3
4
5
6
FRONT = REAR + 1 [FULL QUEUE]
XX …
7
ZZ
N](https://image.slidesharecdn.com/lecture7-m-131122062250-phpapp02/85/Lecture-7-data-structures-and-algorithms-12-320.jpg)
![Algorithm to Delete from Q
[1] If FRONT = NULL then Print: Underflow and
Exit
[2] Set ITEM = QUEUE[FRONT]
[3]
If FRONT = REAR then
Set FRONT = NULL and REAR = NULL
Else If FRONT = N then
Set FRONT = 1
Else
Set FRONT = FRONT + 1
[4] Exit](https://image.slidesharecdn.com/lecture7-m-131122062250-phpapp02/85/Lecture-7-data-structures-and-algorithms-13-320.jpg)
![Insertion
[1] NEW -> INFO = ITEM
NEW -> LINK = NULL
[2] If (FRONT = NULL) then
FRONT = REAR = NULL
else
Set REAR -> LINK = NEW
REAR = NEW
[3] Exit](https://image.slidesharecdn.com/lecture7-m-131122062250-phpapp02/85/Lecture-7-data-structures-and-algorithms-21-320.jpg)
![Deletion
[1] If (FRONT = NULL) then
Print: Overflow, and Exit
[2] FRONT = FRONT -> LINK
[3] Exit](https://image.slidesharecdn.com/lecture7-m-131122062250-phpapp02/85/Lecture-7-data-structures-and-algorithms-22-320.jpg)
![Variation of deque
• There are two variation of deque
[1] Input-restricted queue: Deque which
allows insertions at only one end of the list
but allows deletion at both ends of the list
[2] Output-restricted queue: Deque which
allows deletion at only one end of the list
but allows insertion at both ends of the
list](https://image.slidesharecdn.com/lecture7-m-131122062250-phpapp02/85/Lecture-7-data-structures-and-algorithms-25-320.jpg)
![Priority Queue
• A priority queue is a collection of elements
such that each elements has been assigned
a priority and such that the order in which
elements are deleted and processed comes
from the following rules:
[1] Elements of higher priority is processed
before any elements of lower priority
[2] Two elements with the same priority are
processed according to the order in which
they were added to the queue](https://image.slidesharecdn.com/lecture7-m-131122062250-phpapp02/85/Lecture-7-data-structures-and-algorithms-29-320.jpg)
![Priority Queue
• There are different ways a priority
queue can be represented such as
[1] One-way List
[2] Multiple queue](https://image.slidesharecdn.com/lecture7-m-131122062250-phpapp02/85/Lecture-7-data-structures-and-algorithms-30-320.jpg)
![One-Way List Representation of
a Priority Queue
[1] Each node in the list will contain three
items of information: an information
field INFO, a priority number PRN,
and a link number LINK
[2] A node X precedes a node Y in the list
(a) when X has higher priority than Y or
(b) when both have same priority but X
was added to the list before Y](https://image.slidesharecdn.com/lecture7-m-131122062250-phpapp02/85/Lecture-7-data-structures-and-algorithms-31-320.jpg)
![Insertion and Deletion
• Deletion : Delete the first node in the
list.
• Insertion: Find the location of Insertion
Add an ITEM with priority number N
[a] Traverse the list until finding a node X
whose priority exceeds N. Insert ITEM
in front of node X
[b] If no such node is found, insert ITEM
as the last element of the list](https://image.slidesharecdn.com/lecture7-m-131122062250-phpapp02/85/Lecture-7-data-structures-and-algorithms-33-320.jpg)
![Deletion Algorithm [outline]
[1] Find the smallest K such that
FRONT[K] NULL
[2] Delete and process the front element
in row K of QUEUE
[3] Exit](https://image.slidesharecdn.com/lecture7-m-131122062250-phpapp02/85/Lecture-7-data-structures-and-algorithms-36-320.jpg)
![Insertion Algorithm [outline]
[1] Insert ITEM as the rear element in
row M of QUEUE
[2] Exit](https://image.slidesharecdn.com/lecture7-m-131122062250-phpapp02/85/Lecture-7-data-structures-and-algorithms-37-320.jpg)
Lecture 7 data structures and algorithms
- 1. Data Structure and Algorithm (CS 102) Ashok K Turuk
- 2. Queue • A queue is a linear list of elements in which – deletion can take place only at one end called Front, and – Insertion takes place at one end called Rear • Queues are also known as First-InFirst-Out (FIFO) list
- 3. Queue • Queue are represented in two-ways – Linear Array – One-way Linked List
- 4. Array representation of Queue • A queue is maintained by a – linear array QUEUE – Two pointer variable • FRONT : Containing the location of the front element of the queue • REAR : Containing • FRONT == NULL indicates that the queue is empty
- 5. Queue FRONT: 1 REAR: 4 AA BB CC DD 1 2 3 4 5 … 6 7 N Delete an element FRONT: 2 REAR: 4 1 BB CC DD 2 3 4 5 … 6 7 N Whenever an element is deleted from the queue, the value of FRONT is increased by 1 FRONT = FRONT + 1
- 6. Queue FRONT: 2 REAR: 4 BB CC DD 1 2 3 4 … 5 6 7 N Insert an element FRONT: 2 REAR: 5 1 BB CC DD EE 2 3 4 5 6 … 7 Whenever an element is inserted into the queue, the value of REAR is increased by 1 REAR = REAR + 1 N
- 7. Queue • REAR = N and Insert an element into queue FRONT: 7 REAR: N 1 2 3 4 5 6 XX … 7 Move the entire queue to the beginning of the array Change the FRONT and REAR accordingly Insert the element This procedure is too expensive ZZ N
- 8. Queue • Queue is assumed to be circular • QUEUE[1] comes after QUEUE[N] • Instead of increasing REAR to N +1, we reset REAR = 1 and then assign QUEUE[REAR] = ITEM
- 9. Queue • FRONT = N and an element of QUEUE is Deleted FRONT: N REAR: 1 2 3 4 5 6 XX … 7 We reset FRONT = 1, instead of increasing FRONT to N + 1 ZZ N
- 10. Queue • QUEUE contain one element FRONT = REAR NULL FRONT: 7 REAR: 7 1 2 3 4 5 6 FRONT = NULL and REAR = NULL XX … 7 N
- 11. Algorithm to Insert in Q [1] If FRONT = 1 and REAR = N or if FRONT = REAR + 1 then Print: Overflow and Exit [2] If FRONT = NULL then Set FRONT = 1 and REAR = 1 Else If REAR = N then Set REAR = 1 Else Set REAR = REAR + 1 [3] Set QUEUE[REAR] = ITEM [4] Exit
- 12. Queue FRONT: 7 REAR: 6 AA BB CC DD EE FF 1 2 3 4 5 6 FRONT = REAR + 1 [FULL QUEUE] XX … 7 ZZ N
- 13. Algorithm to Delete from Q [1] If FRONT = NULL then Print: Underflow and Exit [2] Set ITEM = QUEUE[FRONT] [3] If FRONT = REAR then Set FRONT = NULL and REAR = NULL Else If FRONT = N then Set FRONT = 1 Else Set FRONT = FRONT + 1 [4] Exit
- 14. Linked List Representation of Queue • A linked queue is a queue implemented as linked list with two pointer variable FRONT and REAR pointing to the nodes which is in the FRONT and REAR of the queue
- 15. Linked List Representation of Queue FRONT CC BB AA X REAR 15
- 16. Insertion in a Queue FRONT AA BB NEW CC X REAR DD 16
- 17. Insertion in a Queue FRONT AA BB CC X DD REAR 17
- 18. Delete from a Queue FRONT CC BB AA X REAR 18
- 19. Delete from a Queue FRONT BB AA X REAR 19
- 20. Linked Queue • No need to check for overflow condition during insertion • No need to view it as circular for efficient management of space
- 21. Insertion [1] NEW -> INFO = ITEM NEW -> LINK = NULL [2] If (FRONT = NULL) then FRONT = REAR = NULL else Set REAR -> LINK = NEW REAR = NEW [3] Exit
- 22. Deletion [1] If (FRONT = NULL) then Print: Overflow, and Exit [2] FRONT = FRONT -> LINK [3] Exit
- 23. Deque • A deque is a linear list in which elements can be added or removed at either end but not in the middle • Deque is implemented by a circular array DEQUE with pointers LEFT and RIGHT which points to the two end of the deque
- 24. Deque • LEFT = NULL indicate deque is empty LEFT: 4 RIGHT: 7 LEFT: 4 RIGHT: 7 1 2 YY 1 3 ZZ 2 3 AA BB CC DD 4 5 6 7 8 4 5 6 WW XX 7 8
- 25. Variation of deque • There are two variation of deque [1] Input-restricted queue: Deque which allows insertions at only one end of the list but allows deletion at both ends of the list [2] Output-restricted queue: Deque which allows deletion at only one end of the list but allows insertion at both ends of the list
- 26. Deque LEFT: 2 RIGHT: 4 1 A 2 C 3 D 4 5 6 F is added to the right LEFT: 2 RIGHT: 5 1 A 2 C 3 D 4 F 5 6
- 27. Deque LEFT: 2 RIGHT: 5 1 A 2 C 3 D 4 F 5 6 Two Letters on right is deleted LEFT: 2 RIGHT: 3 1 A 2 C 3 4 5 6
- 28. Deque LEFT: 2 RIGHT: 3 1 A 2 C 3 4 5 6 K, L and M are added to the Left LEFT: 5 RIGHT: 3 K 1 A 2 C 3 4 M 5 L 6
- 29. Priority Queue • A priority queue is a collection of elements such that each elements has been assigned a priority and such that the order in which elements are deleted and processed comes from the following rules: [1] Elements of higher priority is processed before any elements of lower priority [2] Two elements with the same priority are processed according to the order in which they were added to the queue
- 30. Priority Queue • There are different ways a priority queue can be represented such as [1] One-way List [2] Multiple queue
- 31. One-Way List Representation of a Priority Queue [1] Each node in the list will contain three items of information: an information field INFO, a priority number PRN, and a link number LINK [2] A node X precedes a node Y in the list (a) when X has higher priority than Y or (b) when both have same priority but X was added to the list before Y
- 33. Insertion and Deletion • Deletion : Delete the first node in the list. • Insertion: Find the location of Insertion Add an ITEM with priority number N [a] Traverse the list until finding a node X whose priority exceeds N. Insert ITEM in front of node X [b] If no such node is found, insert ITEM as the last element of the list
- 34. Array representation of Priority Queue • Separate queue for each level of priority • Each queue will appear in its own circular array and must have its own pair of pointers, FRONT and REAR • If each queue is given the same amount space then a 2D queue can be used
- 36. Deletion Algorithm [outline] [1] Find the smallest K such that FRONT[K] NULL [2] Delete and process the front element in row K of QUEUE [3] Exit
- 37. Insertion Algorithm [outline] [1] Insert ITEM as the rear element in row M of QUEUE [2] Exit