Data structure and algorithms

STACK
A stack is an Abstract Data Type (ADT), commonly used in most programming
languages. It is named stack as it behaves like a real-world stack, for example – a deck of cards
or a pile of plates, etc.

A real-world stack allows operations at one end only. For example, we can place or remove a
card or plate from the top of the stack only. Likewise, Stack ADT allows all data operations at
one end only. At any given time, we can only access the top element of a stack.

This feature makes it LIFO data structure. LIFO stands for Last-in-first-out. Here, the element
which is placed (inserted or added) last, is accessed first. In stack terminology, insertion
operation is called PUSH operation and removal operation is called POP operation.

STACK REPRESENTATION

The following diagram depicts a stack and its operations −




A stack can be implemented by means of Array, Structure, Pointer, and Linked List. Stack can
either be a fixed size one or it may have a sense of dynamic resizing. Here, we are going to
implement stack using arrays, which makes it a fixed size stack implementation.

Basic Operations

Stack operations may involve initializing the stack, using it and then de-initializing it. Apart
from these basic stuffs, a stack is used for the following two primary operations −

, • push() − Pushing (storing) an element on the stack.
• pop() − Removing (accessing) an element from the stack.

When data is PUSHed onto stack.

To use a stack efficiently, we need to check the status of stack as well. For the same purpose,
the following functionality is added to stacks −

• peek() − get the top data element of the stack, without removing it.
• isFull() − check if stack is full.
• isEmpty() − check if stack is empty.

At all times, we maintain a pointer to the last PUSHed data on the stack. As this pointer always
represents the top of the stack, hence named top. The top pointer provides top value of the
stack without actually removing it.

First we should learn about procedures to support stack functions −

peek ()

Algorithm of peek() function −

begin procedure peek
return stack[top]
end procedure

Implementation of peek() function in C programming language −

Example
int peek() {
return stack[top];
}
isfull()
Algorithm of isfull() function −
begin procedure isfull

if top equals to MAXSIZE
return true
else
return false
endif

end procedure
Implementation of isfull() function in C programming language −

, Example
bool isfull() {
if(top == MAXSIZE)
return true;
else
return false;
}


isempty()
Algorithm of isempty() function −
begin procedure isempty

if top less than 1
return true
else
return false
endif

end procedure
Implementation of isempty() function in C programming language is slightly different. We
initialize top at -1, as the index in array starts from 0. So we check if the top is below zero or -
1 to determine if the stack is empty. Here's the code −

Example
bool isempty() {
if(top == -1)
return true;
else
return false;
}

PUSH OPERATION

The process of putting a new data element onto stack is known as a Push Operation. Push
operation involves a series of steps −

• Step 1 − Checks if the stack is full.
• Step 2 − If the stack is full, produces an error and exit.
• Step 3 − If the stack is not full, increments top to point next empty space.
• Step 4 − Adds data element to the stack location, where top is pointing.
• Step 5 − Returns success.