Queues

1
Queues

• Linear list.
• One end is called front.
• Other end is called rear.
• Additions are done at the rear only.
• Removals are made from the front only.

2
Bus Stop Queue
front
rear
rear
rear
rear
rear
3
Bus Stop Queue
front
rear
rear
rear
4
Bus Stop Queue
front
rear
rear
5
Bus Stop Queue
front
rear
rear
6
Revisit Of Stack Applications

• Applications in which the stack cannot be
  replaced with a queue.
• Parentheses matching.
• Towers of Hanoi.
• Switchbox routing.
• Method invocation and return.
• Try-catch-throw implementation.
• Application in which the stack may be replaced
  with a queue.
• Rat in a maze.
• Results in finding shortest path to exit.

7
Wire Routing
8
Lees Wire Router
Label all reachable squares 1 unit from start.
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Lees Wire Router
1
1
Label all reachable unlabeled squares 2 units
from start.
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Lees Wire Router
2
2
1
1
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2
Label all reachable unlabeled squares 3 units
from start.
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Lees Wire Router
3
3
2
2
1
1
2
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3
Label all reachable unlabeled squares 4 units
from start.
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Lees Wire Router
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3
3
2
2
1
1
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4
Label all reachable unlabeled squares 5 units
from start.
13
Lees Wire Router
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1
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Label all reachable unlabeled squares 6 units
from start.
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Lees Wire Router
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1
1
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End pin reached. Traceback.
15
Lees Wire Router
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1
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End pin reached. Traceback.
16
Queue Operations

• IsFullQ return true iff queue is full
• IsEmptyQ return true iff queue is empty
• AddQ add an element at the rear of the queue
• DeleteQ delete and return the front element of
  the queue

17
Queue in an Array

• Use a 1D array to represent a queue.
• Suppose queue elements are stored with the front
  element in queue0, the next in queue1, and so
  on.

18
Queue in an Array

• DeleteQ() gt delete queue0
• O(queue size) time
• AddQ(x) gt if there is capacity, add at right end
• O(1) time

19
O(1) AddQ and DeleteQ

• to perform each opertion in O(1) time (excluding
  array doubling), we use a circular representation.

20
Circular Array

• Use a 1D array queue.

• Circular view of array.

21
Circular Array

• Possible configuration with 3 elements.

22
Circular Array

• Another possible configuration with 3 elements.

23
Circular Array

• Use integer variables front and rear.
• front is one position counterclockwise from first
  element
• rear gives position of last element

24
Add An Element

• Move rear one clockwise.

25
Add An Element

• Move rear one clockwise.

• Then put into queuerear.

D
26
Delete An Element

• Move front one clockwise.

27
Delete An Element

• Move front one clockwise.

• Then extract from queuefront.

28
Moving rear Clockwise

• rear
• if (rear capacity) rear 0

• rear (rear 1) capacity

29
Empty That Queue
30
Empty That Queue
front
31
Empty That Queue
front
32
Empty That Queue
front

• When a series of removes causes the queue to
  become empty, front rear.
• When a queue is constructed, it is empty.
• So initialize front rear 0.

33
A Full Tank Please
34
A Full Tank Please
D
C
A
B
35
A Full Tank Please
rear
D
E
C
A
B
36
A Full Tank Please
D
E
C
F
A
B
rear

• When a series of adds causes the queue to become
  full, front rear.
• So we cannot distinguish between a full queue and
  an empty queue!

37
Ouch!!!!!

• Remedies.
• Dont let the queue get full.
• When the addition of an element will cause the
  queue to be full, increase array size.
• This is what the text does.
• Define a boolean variable lastOperationIsAddQ.
• Following each AddQ set this variable to true.
• Following each DeleteQ set to false.
• Queue is empty iff (front rear)
  !lastOperationIsAddQ
• Queue is full iff (front rear)
  lastOperationIsAddQ

38
Ouch!!!!!

• Remedies (continued).
• Define an integer variable size.
• Following each AddQ do size.
• Following each DeleteQ do size--.
• Queue is empty iff (size 0)
• Queue is full iff (size arrayLength)
• Performance is slightly better when first
  strategy is used.