A stack is a linear data structure that follows the Last In, First Out (LIFO) principle. This means that the last element added to the stack will be the first one to be removed. Stacks are used in many applications, including function call management, expression evaluation, and backtracking algorithms. The simplicity and efficiency of stacks make them an essential tool in computer science.

Components of a Stack

1. Elements

The elements are the data items stored in the stack. They can be of any data type, including integers, characters, or complex objects. The order in which these elements are added and removed follows the LIFO principle, ensuring that the most recently added item is the first to be taken out.

2. Top

The top is a pointer or index that indicates the most recently added element in the stack. It is crucial for both the push and pop operations. When the stack is empty, the top is typically set to a sentinel value like -1, indicating no elements are present.

3. Stack Size

The stack size refers to the maximum number of elements the stack can hold. This is particularly relevant for stacks implemented using arrays, which have a fixed size. In contrast, dynamic stacks, often implemented using linked lists, do not have a predefined size and can grow or shrink as needed.

4. Push Operation

The push operation adds an element to the top of the stack. Before performing this operation, the stack checks if it has reached its maximum capacity (for fixed-size stacks). If the stack is full, an overflow condition occurs, and the push operation is aborted. If there is space, the element is placed at the position indicated by the top pointer, and the top is incremented.

5. Pop Operation

The pop operation removes the top element from the stack and returns it. If the stack is empty, an underflow condition occurs, indicating that there are no elements to pop. When an element is successfully removed, the top pointer is decremented. This operation is critical in maintaining the LIFO order of the stack.

6. Peek/Top Operation

The peek (or top) operation allows access to the top element without removing it from the stack. This is useful for checking the most recent entry without altering the stack’s state. It simply returns the element located at the position indicated by the top pointer.

7. isEmpty Operation

The isEmpty operation checks whether the stack contains any elements. It returns a boolean value: true if the stack is empty (i.e., the top pointer is at its sentinel value) and false if there are elements in the stack. This operation is crucial for avoiding underflow errors during pop operations.

8. isFull Operation

The isFull operation applies to fixed-size stacks, checking whether the stack has reached its maximum capacity. It returns true if the stack is full and false otherwise. This helps in preventing overflow errors during push operations.

Implementation Methods

1. Array-Based Implementation:

– Simple and fast.

– Fixed size, which can lead to overflow issues.

– Direct access to elements via index.

2. Linked List-Based Implementation:

– Dynamic size, so no overflow.

– Each element (node) contains data and a reference to the next node.

– More memory overhead due to pointers.

Applications of Stack

1. Expression Evaluation: Used in parsing and evaluating mathematical expressions, especially those in postfix notation.

2. Function Call Management: Manages function calls and recursion through the call stack, maintaining order and state.