Stack and Queue : Stack and Queue
Stack Overview : Stack Overview Stack ADT
Basic operations of stack
Pushing, popping etc.
Implementations of stacks using
array
linked list
The Stack ADT : The Stack ADT A stack is a list with the restriction
that insertions and deletions can only be performed at the top of the list
The other end is called bottom
Fundamental operations:
Push: Equivalent to an insert
Pop: Deletes the most recently inserted element
Top: Examines the most recently inserted element
Stack ADT : Stack ADT Stacks are less flexible
but are more efficient and easy to implement
Stacks are known as LIFO (Last In, First Out) lists.
The last element inserted will be the first to be retrieved
Push and Pop : Push and Pop Primary operations: Push and Pop
Push
Add an element to the top of the stack
Pop
Remove the element at the top of the stack top empty stack push an element push another pop
Implementation of Stacks : Implementation of Stacks Any list implementation could be used to implement a stack
Arrays (static: the size of stack is given initially)
Linked lists (dynamic: never become full)
We will explore implementations based on array and linked list
Let’s see how to use an array to implement a stack first
Array Implementation : Array Implementation Need to declare an array size ahead of time
Associated with each stack is TopOfStack
for an empty stack, set TopOfStack to -1
Push
(1) Increment TopOfStack by 1.
(2) Set Stack[TopOfStack] = X
Pop
(1) Set return value to Stack[TopOfStack]
(2) Decrement TopOfStack by 1
These operations are performed in very fast constant time
Stack class : Stack class class Stack {
public:
Stack(int size = 10); // constructor
~Stack() { delete [] values; } // destructor
bool IsEmpty() { return top == -1; }
bool IsFull() { return top == maxTop; }
double Top();
void Push(const double x);
double Pop();
void DisplayStack();
private:
int maxTop; // max stack size = size - 1
int top; // current top of stack
double* values; // element array
};
Stack class : Stack class Attributes of Stack
maxTop: the max size of stack
top: the index of the top element of stack
values: point to an array which stores elements of stack
Operations of Stack
IsEmpty: return true if stack is empty, return false otherwise
IsFull: return true if stack is full, return false otherwise
Top: return the element at the top of stack
Push: add an element to the top of stack
Pop: delete the element at the top of stack
DisplayStack: print all the data in the stack
Create Stack : Create Stack The constructor of Stack
Allocate a stack array of size. By default, size = 10.
When the stack is full, top will have its maximum value, i.e. size – 1.
Initially top is set to -1. It means the stack is empty. Stack::Stack(int size /*= 10*/) {
maxTop = size - 1;
values = new double[size];
top = -1;
} Although the constructor dynamically allocates the stack array, the stack is still static. The size is fixed after the initialization.
Push Stack : Push Stack void Push(const double x);
Push an element onto the stack
If the stack is full, print the error information.
Note top always represents the index of the top element. After pushing an element, increment top. void Stack::Push(const double x) {
if (IsFull())
cout << "Error: the stack is full." << endl;
else
values[++top] = x;
}
Pop Stack : Pop Stack double Pop()
Pop and return the element at the top of the stack
If the stack is empty, print the error information. (In this case, the return value is useless.)
Don’t forgot to decrement top double Stack::Pop() {
if (IsEmpty()) {
cout << "Error: the stack is empty." << endl;
return -1;
}
else {
return values[top--];
}
}
Stack Top : Stack Top double Top()
Return the top element of the stack
Unlike Pop, this function does not remove the top element double Stack::Top() {
if (IsEmpty()) {
cout << "Error: the stack is empty." << endl;
return -1;
}
else
return values[top];
}
Printing all the elements : Printing all the elements void DisplayStack()
Print all the elements void Stack::DisplayStack() {
cout << "top -->";
for (int i = top; i >= 0; i--)
cout << "\t|\t" << values[i] << "\t|" << endl;
cout << "\t|---------------|" << endl;
}
Using Stack : Using Stack int main(void) {
Stack stack(5);
stack.Push(5.0);
stack.Push(6.5);
stack.Push(-3.0);
stack.Push(-8.0);
stack.DisplayStack();
cout << "Top: " << stack.Top() << endl;
stack.Pop();
cout << "Top: " << stack.Top() << endl;
while (!stack.IsEmpty()) stack.Pop();
stack.DisplayStack();
return 0;
} result
Slide 16: Now let us implement a stack based on a linked list
To make the best out of the code of List, we implement Stack by inheriting List
To let Stack access private member head, we make Stack as a friend of List Implementation based on Linked List class List {
public:
List(void) { head = NULL; } // constructor
~List(void); // destructor
bool IsEmpty() { return head == NULL; }
Node* InsertNode(int index, double x);
int FindNode(double x);
int DeleteNode(double x);
void DisplayList(void);
private:
Node* head;
friend class Stack;
};
Implementation based on Linked List : Implementation based on Linked List class Stack : public List {
public:
Stack() {} // constructor
~Stack() {} // destructor
double Top() {
if (head == NULL) {
cout << "Error: the stack is empty." << endl;
return -1;
}
else
return head->data;
}
void Push(const double x) { InsertNode(0, x); }
double Pop() {
if (head == NULL) {
cout << "Error: the stack is empty." << endl;
return -1;
}
else {
double val = head->data;
DeleteNode(val);
return val;
}
}
void DisplayStack() { DisplayList(); }
}; Note: the stack implementation based on a linked list will never be full.
Balancing Symbols : Balancing Symbols To check that every right brace, bracket, and parentheses must correspond to its left counterpart
e.g. [( )] is legal, but [( ] ) is illegal
Algorithm
(1) Make an empty stack.
(2) Read characters until end of file
i. If the character is an opening symbol, push it onto the stack
ii. If it is a closing symbol, then if the stack is empty, report an error
iii. Otherwise, pop the stack. If the symbol popped is not the
corresponding opening symbol, then report an error
(3) At end of file, if the stack is not empty, report an error
Postfix Expressions : Postfix Expressions Calculate 4.99 * 1.06 + 5.99 + 6.99 * 1.06
Need to know the precedence rules
Postfix (reverse Polish) expression
4.99 1.06 * 5.99 + 6.99 1.06 * +
Use stack to evaluate postfix expressions
When a number is seen, it is pushed onto the stack
When an operator is seen, the operator is applied to the 2 numbers that are popped from the stack. The result is pushed onto the stack
Example
evaluate 6 5 2 3 + 8 * + 3 + *
The time to evaluate a postfix expression is O(N)
processing each element in the input consists of stack operations and thus takes constant time
Slide 20:
Queue Overview : Queue Overview Queue ADT
Basic operations of queue
Enqueuing, dequeuing etc.
Implementation of queue
Array
Linked list
Queue ADT : Queue ADT Like a stack, a queue is also a list. However, with a queue, insertion is done at one end, while deletion is performed at the other end.
Accessing the elements of queues follows a First In, First Out (FIFO) order.
Like customers standing in a check-out line in a store, the first customer in is the first customer served.
The Queue ADT : The Queue ADT Another form of restricted list
Insertion is done at one end, whereas deletion is performed at the other end
Basic operations:
enqueue: insert an element at the rear of the list
dequeue: delete the element at the front of the list
First-in First-out (FIFO) list
Enqueue and Dequeue : Enqueue and Dequeue Primary queue operations: Enqueue and Dequeue
Like check-out lines in a store, a queue has a front and a rear.
Enqueue
Insert an element at the rear of the queue
Dequeue
Remove an element from the front of the queue Insert (Enqueue) Remove(Dequeue) rear front
Implementation of Queue : Implementation of Queue Just as stacks can be implemented as arrays or linked lists, so with queues.
Dynamic queues have the same advantages over static queues as dynamic stacks have over static stacks
Queue Implementation of Array : Queue Implementation of Array There are several different algorithms to implement Enqueue and Dequeue
Naïve way
When enqueuing, the front index is always fixed and the rear index moves forward in the array. Enqueue(3) 3 Enqueue(6) 3 6 Enqueue(9) 3 6 9
Queue Implementation of Array : Queue Implementation of Array Naïve way
When enqueuing, the front index is always fixed and the rear index moves forward in the array.
When dequeuing, the element at the front the queue is removed. Move all the elements after it by one position. (Inefficient!!!) Dequeue() 6 9 Dequeue() Dequeue() 9 rear = -1
Queue Implementation of Array : Queue Implementation of Array Better way
When an item is enqueued, make the rear index move forward.
When an item is dequeued, the front index moves by one element towards the back of the queue (thus removing the front item, so no copying to neighboring elements is needed). XXXXOOOOO (rear)
OXXXXOOOO (after 1 dequeue, and 1 enqueue)
OOXXXXXOO (after another dequeue, and 2 enqueues)
OOOOXXXXX (after 2 more dequeues, and 2 enqueues) (front) The problem here is that the rear index cannot move beyond the last element in the array.
Implementation using Circular Array : Implementation using Circular Array Using a circular array
When an element moves past the end of a circular array, it wraps around to the beginning, e.g.
OOOOO7963 ? 4OOOO7963 (after Enqueue(4))
After Enqueue(4), the rear index moves from 3 to 4.
Empty or Full? : Empty or Full? Empty queue
back = front - 1
Full queue?
the same!
Reason: n values to represent n+1 states
Solutions
Use a boolean variable to say explicitly whether the queue is empty or not
Make the array of size n+1 and only allow n elements to be stored
Use a counter of the number of elements in the queue
Queue Implementation of Linked List : Queue Implementation of Linked List class Queue {
public:
Queue(int size = 10); // constructor
~Queue() { delete [] values; } // destructor
bool IsEmpty(void);
bool IsFull(void);
bool Enqueue(double x);
bool Dequeue(double & x);
void DisplayQueue(void);
private:
int front; // front index
int rear; // rear index
int counter; // number of elements
int maxSize; // size of array queue
double* values; // element array
};
Queue Class : Queue Class Attributes of Queue
front/rear: front/rear index
counter: number of elements in the queue
maxSize: capacity of the queue
values: point to an array which stores elements of the queue
Operations of Queue
IsEmpty: return true if queue is empty, return false otherwise
IsFull: return true if queue is full, return false otherwise
Enqueue: add an element to the rear of queue
Dequeue: delete the element at the front of queue
DisplayQueue: print all the data
Create Queue : Create Queue Queue(int size = 10)
Allocate a queue array of size. By default, size = 10.
front is set to 0, pointing to the first element of the array
rear is set to -1. The queue is empty initially. Queue::Queue(int size /* = 10 */) {
values = new double[size];
maxSize = size;
front = 0;
rear = -1;
counter = 0;
}
IsEmpty & IsFull : IsEmpty & IsFull Since we keep track of the number of elements that are actually in the queue: counter, it is easy to check if the queue is empty or full. bool Queue::IsEmpty() {
if (counter) return false;
else return true;
}
bool Queue::IsFull() {
if (counter < maxSize) return false;
else return true;
}
Enqueue : Enqueue bool Queue::Enqueue(double x) {
if (IsFull()) {
cout << "Error: the queue is full." << endl;
return false;
}
else {
// calculate the new rear position (circular)
rear = (rear + 1) % maxSize;
// insert new item
values[rear] = x;
// update counter
counter++;
return true;
}
}
Dequeue : Dequeue bool Queue::Dequeue(double & x) {
if (IsEmpty()) {
cout << "Error: the queue is empty." << endl;
return false;
}
else {
// retrieve the front item
x = values[front];
// move front
front = (front + 1) % maxSize;
// update counter
counter--;
return true;
}
}
Printing the elements : Printing the elements void Queue::DisplayQueue() {
cout << "front -->";
for (int i = 0; i < counter; i++) {
if (i == 0) cout << "\t";
else cout << "\t\t";
cout << values[(front + i) % maxSize];
if (i != counter - 1)
cout << endl;
else
cout << "\t<-- rear" << endl;
}
}
Using Queue : Using Queue int main(void) {
Queue queue(5);
cout << "Enqueue 5 items." << endl;
for (int x = 0; x < 5; x++)
queue.Enqueue(x);
cout << "Now attempting to enqueue again..." << endl;
queue.Enqueue(5);
queue.DisplayQueue();
double value;
queue.Dequeue(value);
cout << "Retrieved element = " << value << endl;
queue.DisplayQueue();
queue.Enqueue(7);
queue.DisplayQueue();
return 0;
}
Stack Implementation based on Linked List : Stack Implementation based on Linked List class Queue {
public:
Queue() { // constructor
front = rear = NULL;
counter = 0;
}
~Queue() { // destructor
double value;
while (!IsEmpty()) Dequeue(value);
}
bool IsEmpty() {
if (counter) return false;
else return true;
}
void Enqueue(double x);
bool Dequeue(double & x);
void DisplayQueue(void);
private:
Node* front; // pointer to front node
Node* rear; // pointer to last node
int counter; // number of elements
};
Enqueue : Enqueue void Queue::Enqueue(double x) {
Node* newNode = new Node;
newNode->data = x;
newNode->next = NULL;
if (IsEmpty()) {
front = newNode;
rear = newNode;
}
else {
rear->next = newNode;
rear = newNode;
}
counter++;
} 8 rear rear newNode 5 5 8
Dequeue : Dequeue bool Queue::Dequeue(double & x) {
if (IsEmpty()) {
cout << "Error: the queue is empty." << endl;
return false;
}
else {
x = front->data;
Node* nextNode = front->next;
delete front;
front = nextNode;
counter--;
}
} 8 front 5 5 8 3 front
Printing all the elements : Printing all the elements void Queue::DisplayQueue() {
cout << "front -->";
Node* currNode = front;
for (int i = 0; i < counter; i++) {
if (i == 0) cout << "\t";
else cout << "\t\t";
cout << currNode->data;
if (i != counter - 1)
cout << endl;
else
cout << "\t<-- rear" << endl;
currNode = currNode->next;
}
}
Result : Result Queue implemented using linked list will be never full based on array based on linked list