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

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

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

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

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 how these operations are used Fundamentals of Python: From First Programs Through Data Structures

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

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: ArrayQueue and LinkedQueue q1 = ArrayQueue() q2 = LinkedQueue() Fundamentals of Python: From First Programs Through Data Structures

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

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

Simulations (continued) Simulations avoid need for 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

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

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

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

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

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 LinkedQueue are given an initial value of None size tracks number of elements currently in queue Fundamentals of Python: From First Programs Through Data Structures

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

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

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

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

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

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

Time and Space Analysis for the Two Implementations Linked implementation: Running time: __str__ is O(n); all other are O(1) Space requirement: 2n + 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

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

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

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

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

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

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

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

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

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 getItem before processing Two implementations: Sorted linked list or heap Fundamentals of Python: From First Programs Through Data Structures

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

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

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

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

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

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

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 simple implementations 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