Rossella Lau Lecture 11, DCO20105, Semester A,2005-6 DCO 20105 Data structures and algorithms Lecture 11: Queue & Priority Queue Basic operations.

Rossella Lau Lecture 11, DCO20105, Semester A,2005-6

DCO20105 Data structures and algorithms

Lecture 11: Queue & Priority Queue

Basic operations of a queue Applications of a queue Priority queue and the STL’s priority queue

-- By Rossella Lau


Queue

Queue is an ordered list of items, ordered in the input sequence

Basically, items are deleted at one end (the front/head of the queue) and added at the other end (the rear/tail of the queue)

An example:A B CDThe original queue

Take an itemAdd an item

B C


Operations of a queue

Basic: push() – to add an item; formerly called enqueue() pop() – to remove an item; formerly called dequeue()

Assistance: size() – returns the number of items in a queue empty() – to check if a queue is empty front() – returns the first element of a queue


ExercisesFord’s 8:9

queue<int> q;int x = 5, y = 3;

q.push(8);q.push(9);q.push(y);X = q.fron();q.pop();q.push(18);x = q.front();q.push(22);while (!q.empty()) { y = q.front(); q.pop(); cout << y << “ “;}cout << x << endl;

Ford’s 8:10: List the elements in intQ after each of the following operations:

queue<int> intQ; intQ.push(18);intQ.push(2);intQ.push(intQ.front());intQ.push(intQ.front());intQ.pop();


Typical applicationsA real life application – check out queues in a

super market (Ford’s slide: 8.2) When a customer goes to a cashier – push()

• If there is a cashier available, check out at that cashier• Line up a queue at the end and wait for checking out

When a cashier is working – pop()• Perform check out for the first customer on her/his

line one by one


Services for othersAs a service for other data structures and

algorithms Radix sort Traverse a binary tree in a breadth first order; i.e.,

from top to bottom and at each level, from left to right


Re-visit the Radix sort

25 57 48 37 12 92 86 33

12 92 33 25 86 57 37 48

25

5748

37

12 92

86

33

12

92

3325

86

57

3748

12 25 33 37 48 57 86 92

0123456789

0123456789

push(ni) to qs[k]

for (i=0;i<10,i++) while (!qs[i].empty()) qs[i].pop();


Breadth First Search (BFS) order

A BT’s Breadth First Search order is similar to the implicit array index

E.g., The BFS order for the BT on the right hand side is: 92, 37, 86, 33, 12, 48, 57, 25

92

8637

33 12 48 57

25


#include <queue>……void bfs(void) const { queue <BSTNode<T> *> children;

children.push(root); while (! children.empty()) { if (children.front()->left) children.push(children.front()->left); if (children.front()->right) children.push(children.front()->right); cout << children.front()->getItem() << " "; children.pop(); } cout << endl;}

BFS traversal


Implementation of a queue

When using a vector: As elements grow (shift) in one direction, slots in the

beginning become useless while new elements may be required to re-size the array frequently

Another approach is to use an array in a cyclic method -- calculation of the index becomes a bit more complicated and care should be taken in how to determine the front and the rear of the queue and an empty queue


Using a cyclic vector for implementing queue

A B C0 1 2 3 4

front rear

pop(): B C D0 1 2 3 4

front rear

push(): C D0 1 2 3 4

front rear

pop():

C D E0 1 2 3 4

front rear

push(): F C D E0 1 2 3 4

frontrear

push(): F D E0 1 2 3 4

frontrear

pop():

B C0 1 2 3 4

front rear

Initial:


Test of empty()

When front points to the first element of a queue, it is difficult to test if a queue is empty or has a single element

Initial or empty: 0 1 2 3 4

front rear

0 1 2 3 4

front rear

single element: A0 1 2 3 4

front rear


Modification of front

A special way is to make the front point to the vector index immediately preceding the first element.

B C0 1 2 3 4

front rear

pop(): B C D0 1 2 3 4

front rear

push(): C D0 1 2 3 4

front rear

pop():

C D E0 1 2 3 4

front rear

push(): F C D E0 1 2 3 4

frontrear

push(): F D E0 1 2 3 4

frontrear

pop():


list-based queue

Seems a more natural way to implement queue

But the cost of the operation new/delete makes a list-based container not favorable


Implementation of a queue using a list

// Queue.htemplate<class T>class Queue { private: list<T> queue;

public: T const & front() const { return queue.front();} void push(T const & item) {queue.push_back(item);} T & pop() {T t(front()); queue.pop_front(); return t;} size_t size() const { return queue.size();} bool empty() const { return queue.empty();}};


Execution time for operations of a queue

No matter which basic container is used to build a queue,

a push() is actually a push_back() a pop() is similar to a pop_front()

• Although pop_front() is not allowed in a STL’s vector, it can use a self-defined index to remember its head and move it forward to represent a pop() operation

• It can also use deque<T>Both operations are at O(1)Operations of a STL’s queue: Ford’s slides: 8.4-6


Priority Queue

Many applications need elements to queue up with priority.

Queues in bank: general a/c holders, priority a/c holders Task queues: jobs assigning a higher priority can be

executed earlier


ExercisesFord’s 8:15

priority_queue<int> pq;int arr[] = {10,50,30,40,60};int i, x, y;

for (i=0; i< 5; i++) pq.push(arr[i]);

pq.push(25);x = pq.top(); pq.pop();pq.push(35);y = pq.top(); pq.pop();cout << x << “ “ << y << endl;

while (!pq.empty()) { cout << pq.top() << “ “; pq.pop();}cout << endl;

Ford’s 8:16: priority_queue<int> intPQ;

intPQ.push(5);intPQ.push(27);intPQ.push(25);intPQ.pop();

intPQ.push(intPQ.top()*2);intPQ.push(intPQ.top()*5);

While (!intPQ.empty()) { cout<< intPQ.top() << “ “;

intPQ.opp();}cout << endl;


priority_queue<T>

The STL provides the class priority_queue E.g.,

• push(taskA,5), push(taskB,5), push(taskC,8), push(taskD,2), push(taskE,5), push(taskF,8)

• pop() returns (taskC, 8) priority_queue uses a heap to insert an item

• A heap works quite efficiently on vector and the STL uses a vector to implement priority_queue by default

The templated class of the priority_queue must provide the comparison operator <() for the heap construction


An example application

class task { string taskName, int priority; …}

operator< must be overloaded bool task::operator<(task const & rhs) const { return priority < rhs.priority;}

The application: priority_queue<task> taskQ; …… taskQ.push(taskObj); …… resultTask=taskQ.front(); taskQ.pop();


Summary

Queue can use different kinds of sequential containers with restricted operations as adaptor containers in the STL

Both the basic operations of a queue are at O(1) and make a queue one of the favored data structures being used in many other algorithms

Priority queue, in addition to the behaviors of a queue having a priority, uses a heap with a comparison method built on a vector or a deque


Reference

Ford: 8

STL online references http://www.sgi.com/tech/stl http://www.cppreference.com/

-- END --

Rossella Lau Lecture 11, DCO20105, Semester A,2005-6 DCO 20105 Data structures and algorithms Lecture 11: Queue & Priority Queue Basic operations.

Documents

queue queue

queue slide

queue applications

original queue

queue q int x

stls priority queue

children children

rossella lau slide