Queue Definition
Ordered list with property:– All insertions take place at one end (tail)– All deletions take place at other end (head)
Queue: Q = (a0, a1, …, an-1)
a0 is the front element, an-1 is the tail, and ai is behind ai-1 for all i, 1 <= i < n
Queue Definition
Because of insertion and deletion properties,Queue is very similar to:
Line at the grocery storeCars in trafficNetwork packets….
Also called first-in first out lists
Array-Based Queue Definitiontemplate <class KeyType>class Queue{
public:Queue(int MaxQueueSize = DefaultSize);~Queue();
bool IsFull();bool IsEmpty();void Add(const KeyType& item);KeyType* Delete(KeyType& item);
private:void QueueFull(); // error handlingvoid QueueEmpty(); // error handlingint head, tail;KeyType* queue;int MaxSize;
};
Queue Implementation
Constructor:template <class KeyType>Queue<KeyType>::Queue(int MaxQueueSize): MaxSize(MaxQueueSize){
queue = new KeyType[MaxSize];head = tail = -1;
}
Queue Implementation
Destructor:template <class KeyType>Queue<KeyType>::~Queue(){
delete [] queue;head = tail = -1;
}
Queue ImplementationIsFull() and IsEmpty():
template <class KeyType>bool Queue<KeyType>::IsFull()
{return (tail == (MaxSize-1));
}
template <class KeyType>bool Queue<KeyType>::IsEmpty()
{return (head == tail);
}
Queue ImplementationAdd() and Delete():template <class KeyType>void Queue<KeyType>::Add (const KeyType& item)
{if (IsFull()) {QueueFull(); return;}else { tail = tail + 1; queue[tail] = item; }}
template <class KeyType>KeyType* Queue<KeyType>::Delete(KeyType& item)
{
if (IsEmpty()) {QueueEmpty(); return 0};else { head = head + 1; item = queue[head]; return &item; }}
Example: OS Job Scheduling
OS has to manage how jobs (programs) are executed on the processor – 2 typical techniques:-Priority based: Some ordering over of jobs based on importance
(Professor X’s jobs should be allowed to run first over Professor Y).-Queue based: Equal priority, schedule in first in first out order.
Queue Based Job ProcessingFront Rear Q[0] Q[1] Q[2] Q[3] Comments
-1 -1 Initial
-1 0 J1 Job 1 Enters
-1 1 J1 J2 Job 2 Enters
-1 2 J1 J2 J3 Job 3 Enters
0 2 J2 J3 Job 1 Leaves
0 3 J2 J3 J4 Job 4 Enters
1 3 J3 J4 Job 2 Leaves
Job Processing• When J4 enters the queue, rear is updated to 3.• When rear is 3 in a 4-entry queue, run out of space.• The array may not really be full though, if head is not
-1.• Head can be > -1 if items have been removed from
queue.
Possible Solution: When rear = (maxSize – 1) attempt to shift data forwards into empty spaces and then do Add.
Queue Shift private void shiftQueue(KeyType* queue, int &
head, int & tail){
int difference = head – (-1); // head + 1for (int j = head + 1; j < maxSize; j++){
queue[j-difference] = queue[j];}head = -1;tail = tail – difference;
}
Queue ShiftWorst Case For Queue Shift:
Full QueueAlternating Delete and Add statements
Front Rear Q[0] Q[1] Q[2] Q[3] Comments-1 3 J1 J2 J3 J4 Initial0 3 J2 J3 J4 Job 1 Leaves-1 3 J2 J3 J4 J5 Job 5 Enters0 3 J3 J4 J5 Job 2 Enters-1 3 J3 J4 J5 J6 Job 6 Leaves
Worst Case Queue Shift
• Worst Case:– Shift entire queue: Cost of O(n-1)– Do every time perform an add– Too expensive to be useful
Worst case is not that unlikely, so this suggests finding an alternative implementation.
‘Circular’ Array Implementation
Basic Idea: Allow the queue to wrap-aroundImplement with addition mod size:
tail = (tail + 1) % queueSize;
01
2
3
4
N-1
N-2J1J2
J3
J4
01
2
3
4
N-1
N-2J2J3J1
Linked Queues• Problems with implementing queues on top of
arrays– Sizing problems (bounds, clumsy resizing, …)– Non-circular Array – Data movement problem
• Now that have the concepts of list nodes, can take advantage of to represent queues.
• Need to determine appropriate way of:– Representing front and rear– Facilitating node addition and deletion at the ends.
Linked Queues
CAT
Front Rear
MATHAT
Front Rear Rear
Add(Hat) Add(Mat) Add(Cat) Delete()
Linked QueuesClass QueueNode{
friend class Queue;public:
QueueNode(int d, QueueNode * l); private:
int data;QueueNode *link;
};
Linked Queuesclass Queue{
public:Queue();~Queue();void Add(const int);int* Delete(int&);bool isEmpty();
private:QueueNode* front;QueueNode* rear;void QueueEmpty();
}
Linked QueuesQueue::Queue(){
front = 0;rear = 0;
}bool Queue::isEmpty(){
return (front == 0);}
Front Rear
0 0
Linked Queuesvoid Queue::Add(const int y){
// Create a new node that contains data y// Has to go at end// Set current rear link to new node pointer// Set new rear pointer to new node pointerrear = rear->link = new QueueNode(y, 0);
}
CAT
Front
MATHAT
Rear Rear
Linked Queuesint * Queue::Delete(int & retValue){
// handle empty caseif (isEmpty()) {return 0;}QueueNode* toDelete = front;retValue = toDelete.data;front = toDelete->link;delete toDelete;return &retValue;
}
CAT
Front
MATHAT
ReartoDelete
HAT
returnValue
Front
Queue DestructorQueue destructor needs to remove all nodes
from head to tail.
CAT
Front
MATHAT
RearFront FrontTemp Temp
0 0if (front) {QueueNode* temp;while (front != rear) {
temp = front;front = front -> link;delete temp; }
delete front;front = rear = 0; }
Front vs Delete
• Implementation as written has to remove the item from the queue to read data value.
• Some implementations provide two separate functions:– Front() which returns the data in the first
element– Delete() which removes the first element from
the queue, without returning a value.
Radix Sort and Queues
What does radix sort have to do with queues?
Each list (the master list (all items) and bins (per digit)) needs to be first in, first out ordered – perfect for a queue.
