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IF 200 2016

Struktur DataAntrian & Antrian Dua Arah

(Queue & Deque)

Husni

[email protected]

Agenda & Reading

•Agenda • Introduction• Queue Abstract Data Type (ADT)• Implementing a queue using a list• Using the Queue ADT to solve problems• A Circular Queue• The Deque Abstract Data Type

•Reading• Textbook: Problem Solving with Algorithms and Data

Structures• Chapter 3

2

What is a Queue?

•Queues are appropriate for many real-world situations• Example: A line to buy a movie ticket

• Computer applications, e.g. a request to print a document

•A queue is an ordered collection of items where the addition of new items happens at one end (the rear or back of the queue) and the removal of existing items always takes place at the other end (the front of the queue).• New items enter at the back, or rear, of the queue

• Items leave from the front of the queue

• First-in, first-out (FIFO) property: • The first item inserted into a queue is the first item to leave

3

More formally…

• Queues implement the FIFO (first-in first-out) policy: e.g. the printer / job queue!

4

enqueue( o )

is_empty()

peek()

dequeue()

front Rear of the

queue

ADT Queue Operations

•What are the operations which can be used with a Queue Abstract Data?•Create an empty queue: •Determine whether a queue is empty: •Add a new item to the queue: enqueue

•Remove from the queue the item that was added earliest: dequeue

•Retrieve from the queue the item that was added earliest: peek

5

The Queue Abstract Data Type

•Queue() creates a new queue that is empty. • It needs no parameters and returns an empty queue.

•enqueue(item) adds a new item to the rear of the queue. • It needs the item and returns nothing.

•dequeue() removes the front item from the queue. • It needs no parameters and returns the item. The queue

is modified.

• is_empty() tests to see whether the queue is empty. • It needs no parameters and returns a boolean value.

• size() returns the number of items in the queue. • It needs no parameters and returns an integer.

6

Queue Implementation In Python•We use a python List data structure to implement the

queue.• Remember:

• the addition of new items takes place at the beginning of the list • the removal of existing items takes place at the end of the list

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class Queue:

def __init__(self):

self.items = []

def is_empty(self):

return self.items == []

def size(self):

return len(self.items)

def enqueue(self, item):

self.items.insert(0,item)

def dequeue(self):

return self.items.pop()

Enqueue

(rear of the

queue)

Dequeue

(front of

the queue)

Code Example – Result

• Queue operations, state of the queue, values returned

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q.is_empty()

q.enqueue(4)

q.enqueue('dog')

q.enqueue(True)

q.size()

q.is_empty()

q.enqueue(8.4)

q.dequeue()

q.dequeue()

q.size()

[]

[4]

['dog',4]

[True,'dog',4]

[True,'dog',4]

[True,'dog',4]

[8.4,True,'dog',4]

[8.4,True,'dog']

[8.4,True]

[8.4,True]

True

3

False

4

'dog'

2

q = Queue()Enqueue:

(rear of the queue)

(beginning of the list)

Example Applications

•Simulation: Hot Potato

•Simulation: Printing Tasks

9

1. Simulation: Hot Potato

•Six person game of Hot Potato•Children form a circle and pass an item from

neighbour to neighbour as fast as they can. At a certain point in the game, the action is stoppedand the child who has the item (the potato) is removed from the circle. Play continues until only one child is left.

10

1. Simulation: Hot Potato

• Simulation of Hot Potato

• 1st round:• 2nd round:

• 3rd round:• Finally

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hotPotato([Bill, David, Susan, Jane], 3) Jane Susan David Bill

Bill Jane Susan David

Enqueue

(rear of the queue)dequeue

David Bill Jane Susan

0

1

2 Susan David Bill Jane

Remove

Jane

Bill Susan David

David Bill Susan

0

1

2 Susan David Bill

Remove

Bill

David Susan

Susan David

0

1

2 David Susan Remove

SusanDavid

Hot Potato- Code

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def hotPotato(namelist, num):simqueue = Queue()for name in namelist:

simqueue.enqueue(name)

while simqueue.size() > 1:for i in range(num):

simqueue.enqueue(simqueue.dequeue())

simqueue.dequeue()

return simqueue.dequeue()

Return the name when there is only

ONE name remains in the queue

Move element from the front

of the queue to the end

Simulation

•Simulation: a technique for modelling the behaviour of both natural and human-made systems

•Goal• Generate statistics summarising the performance of an

existing system• Predict the performance of a proposed system

•An example: Behaviour of a printing tasks – how to optimise? • Reduce number of complaints from our students about how

long they have to wait for service from a shared printer• Before hiring a faster printer: evaluate the approximate

average time that a student has to wait• To spend a few days and measure with a stopwatch: not an

exciting prospect! 13

2. Printing Tasks• Students send printing tasks to the shared printer, the tasks are

placed in a queue to be processed in a first-come first-served manner. • Is the printer capable of handling a certain amount of work?

• The slower printing speed could make students wait too long. What page rate should be used?

• => Build a simulation that models the laboratory:• Students submit printing tasks, we will add them to a waiting list, a queue of

print tasks attached to the printer.

• When the printer completes a task, it will look at the queue to see if there are any remaining tasks to process.

14

enqueue

Simulation

•How to determine when certain events occur?•By studying the real world, mathematicians have

learned to model events such as the arrival of tasks using techniques from probability theory

•This statistical information is incorporated into the math model of the system and is used to generate events reflecting the real world.

•A time-driven simulation•Simulated time is advanced by a single time unit•The time of an event, such as an arrival or

departure, is determined randomly and compared with a simulated clock

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2. Printing Tasks – An Example

•Simulation for a period of 1200 seconds• Rate: 5 pages per minute• 6 printing tasks have been added to the queue. • Average waiting time is 26 sec.

16

Task At (currentsecond)

Number of pages

Timelength

1 190 1 12

2 656 18 216

3 778 8 96

4 906 9 108

5 1136 2 24

6 1193 30 240

An Example

17

Printing T1

Printing

Queue

T3

new

task

190

202

656

778

872906968

1076

1136

11601193

Printing T2

Printing T3T4

Printing T4

Printing T5

Printing T6

from To description

190 Task 1 created (12 sec)Added to the printing queue

190 202 Removed T1 from the queuePrinting Task 1

202 Task1 finished











Waiting time:

872-778 = 94

968-906 = 62

Circular Queue

• What is the Big-O performance of enqueue and dequeue of the implementation using Python List?

•enqueue(…): O(n)• Shifting array elements to the right after each addition – too

Expensive!

•dequeue() : O(1)

• Another Implementation: Circular Queue

•enqueue & dequeue : O(1)• Items can be added/removed without shifting the other items in

the process

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def enqueue(self, item):


def dequeue(self):


Viewed as a circle

instead of line

Circular Queue: Set up

•Uses a Python list data structure to store the items in the queue.

•The list has an initial capacity (all elements None) •Keeps an index of the current front of the queue and

of the current back of the queue. • set front to 0, • set back to MAX_QUEUE – 1, • set count to 0

•New items are enqueued at the back index position• Items are dequeued at the front index position. •A count of the queue items to detect queue-full and

queue-empty conditions

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To initialize the

queue

Circular Queue: How To Advance• Queue-empty:

• front is one slot ahead of back

• When either front or back advances past MAX_QUEUE - 1, it wraps around to 0• The wrap-around effect: by using Modulus (%) arithmetic operator

• enqueue• If it is not full,

• dequeue• If it is not empty

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self.back = (self.back + 1) % self.MAX_QUEUE

self.items[self.back] = item

self.count += 1

item = self.items[self.front]

self.front = (self.front + 1) % self.MAX_QUEUE

self.count -= 1

return item

Circular Queue: enqueue(32)

• Before:

• After:

• New item is inserted at the position following back• back is advanced by one position• count is incremented by 1

21

self.back = (self.back + 1) % self.MAX_QUEUE

self.items[self.back] = item

self.count += 1

enqueue

Circular Queue: dequeue()

• Before:

• After:

• Value in front position is removed and returned

• front is advanced by 1

• count is decremented by 122

item = self.items[self.front]

self.front = (self.front + 1) % self.MAX_QUEUE

self.count -= 1

return item

Two spaces left!dequeue

Circular Queue: enqueue(8) & enqueue(50)

• Before:

• After:

• After running the first enqueue, back = 6• After running the second enqueue, back = 0

• as the “Back” is wrapped around the list23

Two spaces left!enqueue

Circular Queue: Empty ? Full?

• front and back cannot be used to distinguish between queue-full and queue-empty conditions for a circular array

• Case 1:

24

q = Queuecircular(8)

q.enqueue(5)

q.enqueue(2)

q.enqueue(1)

q.enqueue(7)

q.enqueue(9)

q.dequeue()

q.dequeue()

q.dequeue()

q.dequeue()

52

q.dequeue()

front = 5

back = 4

Circular Queue: Empty ? Full?

• Case 2:

• is_empty()

• is_full()

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...

q.enqueue(2)

q.enqueue(4)

q.enqueue(1)

q.enqueue(7)

q.enqueue(6)

q.enqueue(3)

q.enqueue(8)

q.enqueue(9) front = 5

back = 4

(Same as before)!

return self.count == 0

return self.MAX_QUEUE <= self.count

Deque : Abstract Data Type

•Deque - Double Ended Queue•A deque is an ordered collection of items where items are added and removed from either end, either front or back.

•The newest item is at one of the ends

26

ADT Deque Operations

•What are the operations which can be used with a Deque Abstract Data?•Create an empty deque: •Determine whether a deque is empty: •Add a new item to the deque:

•add_front()

•add_rear()

•Remove from the deque the item that was added earliest:

• remove_front()

• remove_rear() 27

Deque In Python

•We use a python List data structure to implement the deque.

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class Deque:

def __init__(self):

self.items = []

...

def add_front(self, item):

self.items.append(item)

def add_rear(self, item):


def remove_front(self):


def remove_rear(self):

return self.items.pop(0)

(rear of the

deque)

(front of

the deque)

Deque: Code Example – Result

• Deque operations, state of the deque, values returned

29

d = Deque()

d.is_empty()

d.add_rear(4)

d.add_rear('dog')

d.add_front('cat')

d.add_front(True)

d.size()

d.is_empty()

d.add_rear(8.4)

d.remove_rear()

d.remove_front()

[]

[4]

['dog',4,]

['dog',4,'cat']

['dog',4,'cat',True]



[8.4,'dog',4,'cat',True]


['dog',4,'cat']

True

4

False

8.4

True

(rear of the

deque)

(front of

the deque)

Deque: Big-O Performance

• O(1)

• add_front() • remove_front()

• O(n)

• add_rear() • remove_rear()

30

def add_front(self, item):

self.items.append(item)

def add_rear(self, item):


def remove_front(self):


def remove_rear(self):

return self.items.pop(0)

(rear of the

deque)

(front of

the deque)

Deque Application: Palindrome Checker

•A string which reads the same either left to right, or right to left is known as a palindrome• radar•deed•A dog, a plan, a canal: pagoda.

31

Palindrome Checker - Algorithm

•Create a deque to store the characters of the string• The front of the deque will hold the first character of the

string and the rear of the deque will hold the lastcharacter

•Remove both of them directly, we can compare them and continue only if they match. • If we can keep matching first and the last items, we will

eventually either run out of characters or be left with a deque of size 1 • In either case, the string must be a palindrome.

32

Summary

•The definition of the queue operations gives the ADT queue first-in, first-out (FIFO) behaviour

•To distinguish between the queue-full and queue-empty conditions in a queue implementation that uses a circular array, • count the number of items in the queue

•Models of real-world systems often use queues

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