Fundamentals of Python From First Programs Through Data

Fundamentals of Python: From First Programs Through Data Structures Chapter 15 Linear Collections: Queues

Objectives After completing this chapter, you will be able to: • Describe the behavior of a queue from a user’s perspective • Explain how a queue can be used to support a simulation • Describe the use of a queue in scheduling processes for computational resources Fundamentals of Python: From First Programs Through Data Structures 2

Objectives (continued) • Explain the difference between a queue and a priority queue • Describe a case where a queue would be used rather than a priority queue • Analyze the performance trade-offs between an array-based implementation of a queue and a linked implementation of a queue Fundamentals of Python: From First Programs Through Data Structures 3

Overview of Queues Fundamentals of Python: From First Programs Through Data Structures 4

Overview of Queues (continued) • • • Insertions are restricted to one end (rear) Removals are restricted to one end (front) Queues supports a first-in first-out (FIFO) protocol Fundamental operations: enqueue and dequeue Item dequeued, or served next, is always the item that has been waiting the longest • Priority queue: Higher-priority items are dequeued first; equal priority items dequeued in FIFO order • Most queues in CS involve scheduling access to shared resources: CPU/Disk/Printer access Fundamentals of Python: From First Programs Through Data Structures 5

The Queue Interface and Its Use • You can use a Python list to emulate a queue – Use append to add an element to rear of queue – Use pop to remove an element from front of queue – Drawback: Queue can be manipulated by all of the other list operations as well • Violate spirit of queue as ADT • We define a more restricted interface, or set of operations, for any queue implementation and show these operations are used Fundamentals of Python: From First Programs Through Data Structures 6

The Queue Interface and Its Use (continued) Fundamentals of Python: From First Programs Through Data Structures 7

The Queue Interface and Its Use (continued) • Assume that any queue class that implements this interface will also have a constructor that allows its user to create a new queue instance • Later, we’ll consider two different implementations: – Array. Queue and Linked. Queue q 1 = Array. Queue() q 2 = Linked. Queue() Fundamentals of Python: From First Programs Through Data Structures 8

Two Applications of Queues • We now look briefly at two applications of queues: – One involving computer simulations – The other involving round-robin CPU scheduling Fundamentals of Python: From First Programs Through Data Structures 9

Simulations • Computer simulations are used to study behavior of real-world systems, especially if it is impractical or dangerous to experiment with these systems directly – Example: Mimic traffic flow on a busy highway • Another example: Manager of supermarket wants to determine number of checkout cashiers to schedule at various times of the day and must consider: – – Frequency with which new customers arrive Number of checkout cashiers available Number of items in a customer’s shopping cart Period of time considered Fundamentals of Python: From First Programs Through Data Structures 10

Simulations (continued) • Simulations avoid need formulas by imitating actual situation and collecting pertinent statistics • Simple technique to mimic variability: – Suppose new customers are expected to arrive on average once every four minutes – During each minute of simulated time, a program can generate a random number between 0 and 1 – If number is less than 1/4, program adds a new customer to a checkout line; otherwise, it does not • Probability distribution functions produce more realistic results Fundamentals of Python: From First Programs Through Data Structures 11

Simulations (continued) • Examples presented involve service providers and service consumers – We associate each service provider with a queue of service consumers • Simulations operate by manipulating these queues – At each tick of an imaginary clock, add consumer(s) to the queues and give consumers at the head of each queue another unit of service • OO methods can be used to implement simulations Fundamentals of Python: From First Programs Through Data Structures 12

Simulations (continued) • Example: Supermarket simulation – A Customer object keeps track of when the customer starts standing in line, when service is first received, and how much service is required – A Cashier object has a queue of customer objects – A simulator object coordinates customer/cashier activities by doing the following at each clock tick: • Generates new customer objects as appropriate • Assigns customers to cashiers • Tells each cashier to provide one unit of service to the customer at the head of the queue Fundamentals of Python: From First Programs Through Data Structures 13

Round-Robin CPU Scheduling • Each process on the ready queue is dequeued in turn and given a slice of CPU time • Improvement: Can use a priority queue Fundamentals of Python: From First Programs Through Data Structures 14

Implementations of Queues • Our approach to the implementation of queues is similar to the one we used for stacks • The structure of a queue lends itself to either an array implementation or a linked implementation – The linked implementation is somewhat more straight-forward Fundamentals of Python: From First Programs Through Data Structures 15

A Linked Implementation • enqueue adds a node at the end – For fast access to both ends of a queue’s linked structure, provide external pointers to both ends • Instance variables front and rear of Linked. Queue are given an initial value of None • size tracks number of elements currently in queue Fundamentals of Python: From First Programs Through Data Structures 16

A Linked Implementation (continued) Fundamentals of Python: From First Programs Through Data Structures 17

An Array Implementation • Array implementations of stacks and queues have less in common than the linked implementations • Array implementation of a queue must access items at the logical beginning and the logical end – Doing this in computationally effective manner is complex – We approach problem in a sequence of three attempts Fundamentals of Python: From First Programs Through Data Structures 18

A First Attempt • Fixes front of queue at position 0 • rear variable points to last item at position n – 1 – n is the number of items in queue • Analysis: – enqueue is efficient – dequeue entails shifting all but first item O(n) Fundamentals of Python: From First Programs Through Data Structures 19

A Second Attempt • Maintain a second index (front) that points to item at front of queue – Starts at 0 and advances as items are dequeued • Analysis: – dequeue is O(1) – Maximum running time of enqueue is O(n) Fundamentals of Python: From First Programs Through Data Structures 20

A Third Attempt • Use a circular array implementation – rear starts at – 1; front starts at 0 – front chases rear pointer through the array – When a pointer is about to run off the end of the array, it is reset to 0 • Running times of enqueue and dequeue are O(1) Fundamentals of Python: From First Programs Through Data Structures 21

A Third Attempt (continued) • What happens when the queue becomes full? – Maintain a count of the items in the queue – When this count equals the size of the array: Resize – After resizing, we would like queue to occupy initial segment of array, with front pointer set to 0 • If front pointer is less than rear pointer – Copy positions 0 through size-1 in new array • If rear pointer is less than front pointer – Copy positions 0 through size-front and size – front + 1 through size-1 in new array – Resizing process is linear Fundamentals of Python: From First Programs Through Data Structures 22

Time and Space Analysis for the Two Implementations • Linked implementation: – Running time: __str__ is O(n); all other are O(1) – Space requirement: 2 n + 3, n: size of queue • Circular array implementation: – Static array: Maximum running time of all methods other than __str__ is O(1) – Dynamic array: enqueue/dequeue are O(n) when array is resized, but are O(1) on average – Space utilization: For load factors above 1⁄2, array implementation makes more efficient use of memory than a linked implementation Fundamentals of Python: From First Programs Through Data Structures 23

Case Study: Simulating a Supermarket Checkout Line • Request: – Write program that allows user to predict behavior of supermarket checkout line under various conditions • Analysis: Fundamentals of Python: From First Programs Through Data Structures 24

Case Study: Simulating a Supermarket Checkout Line (continued) • The Interface: • Classes and responsibilities: – We divide the system into a main function and several model classes Fundamentals of Python: From First Programs Through Data Structures 25

Case Study: Simulating a Supermarket Checkout Line (continued) Fundamentals of Python: From First Programs Through Data Structures 26

Case Study: Simulating a Supermarket Checkout Line (continued) Fundamentals of Python: From First Programs Through Data Structures 27

Case Study: Simulating a Supermarket Checkout Line (continued) Fundamentals of Python: From First Programs Through Data Structures 28

Priority Queues • A priority queue is a specialized type of queue – Items added to queue are assigned an order of rank – Items of higher priority are removed before those of lower priority – Items of equal priority are removed in FIFO order – Item A has a higher priority than item B if A < B – Objects that recognize the comparison operators can be ordered in priority queues • If not, object can be wrapped with a priority number in another object that does recognize these operators Fundamentals of Python: From First Programs Through Data Structures 29

Priority Queues (continued) Fundamentals of Python: From First Programs Through Data Structures 30

Priority Queues (continued) • Wrapper class used to build a comparable item from one that is not already comparable: Fundamentals of Python: From First Programs Through Data Structures 31

Priority Queues (continued) • During insertions, a priority queue does not know whether it is comparing items in wrappers or just items • When a wrapped item is accessed (e. g. , with peek or dequeue), it must be unwrapped with the method get. Item before processing • Two implementations: Sorted linked list or heap Fundamentals of Python: From First Programs Through Data Structures 32

Priority Queues (continued) Search is linear, so enqueue is now O(n) Fundamentals of Python: From First Programs Through Data Structures 33

Case Study: An Emergency Room Scheduler • Request: – Write a program that allows a supervisor to schedule treatments for patients coming into emergency room – Patients are assigned a priority when admitted • Higher priority patients receive attention first • Analysis: – Patient priorities: critical, serious, and fair Fundamentals of Python: From First Programs Through Data Structures 34

Case Study: An Emergency Room Scheduler (continued) Fundamentals of Python: From First Programs Through Data Structures 35

Case Study: An Emergency Room Scheduler (continued) Fundamentals of Python: From First Programs Through Data Structures 36

Case Study: An Emergency Room Scheduler (continued) • Classes: • Design and Implementation: – Patient and Condition classes maintain a patient’s name and condition – Patients can be compared (according to their conditions) and viewed as strings Fundamentals of Python: From First Programs Through Data Structures 37

Case Study: An Emergency Room Scheduler (continued) Fundamentals of Python: From First Programs Through Data Structures 38

Summary • A queue is a linear collection that adds elements to the “rear” and removes them from the “front” • Queues are used in applications that manage data items in a first-in, first-out order (FIFO) – Example: Scheduling items for processing or access to resources • Arrays and singly linked structures support simplementations of queues • Priority queues schedule their elements using a rating scheme as well as a FIFO order Fundamentals of Python: From First Programs Through Data Structures 39