Data Structure & Algo, Exercises of Data Analysis & Statistical Methods

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Stack

Engr. Usman Raza

Stack

• Suppose that you have functions A, B, C, and D in your program.
• Now suppose that function A calls function B, function B calls function C,

and function C calls function D.

• When function D terminates, control goes back to function C; when function

C terminates, control goes back to function B; and when function B

terminates, control goes back to function A.

• During program execution, how do you think the computer keeps track of the

function calls? What about recursive functions? How does the computer

keep track of the recursive calls?

• This section discusses the data structure called the stack, which the

computer uses to implement function calls.

• Stacks have numerous applications in computer science.
• After developing the tools necessary to implement a stack, we will examine

some applications of stacks.

Stack (cont.)

• A Stack is a special kind of list in which all insertions and deletions take

place at one end, called the Top ”.

• It is also known as LIFO or Push-down List:
  • The elements at the bottom of the stack have been in the stack the longest.
  • The top element of the stack is the last element added to the stack.
  • Because the elements are added and removed from one end (that is, the top), it follows that the item that is added last will be removed first.
  • For this reason, a stack is also called a Last In First Out (LIFO) data structure.

• Operations:

1. MAKENULL(S): Make Stack S be an empty stack.

2. TOP( S ): Return the element at the top of stack S.

3. POP( S ): Remove the top element of the stack.

4. PUSH( S ): Insert the element x at the top of the stack.

5. ISEMPTY( S ): Return true if S is an empty stack; return false otherwise.

6. ISFULL( S ): If the stack is full, returns true; otherwise, it returns false.

push, top, and pop operations

Stack Implementation and Operations

Engr. Usman Raza

Stack Implementation

• For simplicity, assume the data is an integer type.
• Main stack operations
  • Push (int data): Inserts data onto stack.
  • int Pop(): Removes and returns the last inserted element from the stack.
• Auxiliary stack operations
  • int Top(): Returns the top element without removing it.
  • int Size(): Returns the number of elements stored in the stack.
  • int IsEmptyStack(): Indicates whether any elements are stored in the stack or not.
  • int IsFullStack(): Indicates whether the stack is full or not.
• Exceptions
  • Attempting the execution of an operation may sometimes cause an error condition, called an exception. Exceptions are said to be “thrown” by an operation that cannot be executed.
  • In the Stack ADT, operations pop and top cannot be performed if the stack is empty.
  • Underflow : Attempting the execution of pop() on an empty stack throws an exception.
  • Overflow : Trying to push an element in a full stack throws an exception.

Initialize Stack

• Let us consider the initializeStack operation. Because the value

of stackTop indicates whether the stack is empty or not, we can

simply set stackTop to - 1 to initialize the stack.

An Array Implementation of Stacks

 Anchor the bottom of the stack at the bottom of the array.

 Let the stack grow towards the top of the array.

 Top indicates the current position of the first stack element.

Defining Stack Class

• Constructor

stack(){

top = - 1 ;

Defining Stack Class (cont.)

• Suppose STACK[SIZE] is a one dimensional array for implementing the stack, which will hold the data items.
• TOP points to the top most element of the stack.
• Item is the pushed (or inserted) data item on the top of the stack. Push (item)

1. IF (TOP == MAX-1)

a) PRINT “ The Stack is FULL” b) EXIT

2. ELSE

a) TOP=TOP+ b) STACK[TOP]=item c) EXIT

Defining Stack Class (cont.)

• Suppose STACK[SIZE] is a one dimensional array for implementing the stack, which will hold the data items.
• TOP points to the top most element of the stack.
• Item is the popped (or deleted) data item from the top of the stack. POP (item)

1. IF (TOP < 0)

a) PRINT “ The Stack is EMPTY” b) EXIT

2. ELSE

a) Item=STACK[TOP] b) TOP=TOP - 1 c) EXIT

POP Implementation

void pop(int &item){ if(top==-1) print "Stack Is Empty. No item to pop"<<endl; else{ item=a[top]; top--; print item<<" is Popped"<<endl; } }

Defining Stack Class (cont.)

• Suppose STACK[SIZE] is a one dimensional array for implementing the stack, which will hold the data items.
• TOP points to the top most element of the stack.
• Implement it yourself as a practice Size (item)

1. IF (TOP < 0)

a) PRINT “ The

Stack is EMPTY”

b) EXIT

2. ELSE

a) RETURN TOP+

b) EXIT

Defining Stack Class (cont.)

• Suppose STACK[SIZE] is a one dimensional array for implementing the stack, which will hold the data items.
• TOP points to the top most element of the stack.
• Implement it yourself as a practice IsFull (item)

1. IF (TOP == SIZE - 1)

a) RETURN TRUE

2. ELSE

a) RETURN FALSE