Data structures are essential tools in computer science and programming. They allow for the efficient storage and manipulation of data, which is crucial in developing software applications. One of the most widely used data structures is the stack, which is an abstract data type that operates in a last-in, first-out (LIFO) manner. In this article, we will take a detailed look at the stack data structure, including its definition, operations, implementation, and applications.

Definition of a Stack

A stack is a collection of elements, where only two main operations are allowed: pushing an element onto the top of the stack, and popping an element off the top of the stack. The elements in a stack are usually of the same type, and they are stored in a linear data structure, which can be implemented using an array or a linked list.

The push operation adds an element to the top of the stack, while the pop operation removes the top element from the stack. Other operations that can be performed on a stack include peeking (viewing the top element without removing it), checking whether the stack is empty, and determining its size.

The stack operates in a LIFO manner, which means that the last element added to the stack is the first one to be removed. This is similar to a stack of plates, where the last plate added is the first one to be removed. The term \”stack\” is derived from this physical analogy.

Operations on a Stack

As mentioned earlier, the stack supports two main operations: push and pop. Let us look at these operations in more detail.

Push: The push operation adds an element to the top of the stack. When a new element is pushed onto the stack, it becomes the top element, and all other elements move down one position. If the stack is already full, the push operation results in a stack overflow error.

Pop: The pop operation removes the top element from the stack. When an element is popped from the stack, all other elements move up one position, and the next element becomes the new top element. If the stack is empty, the pop operation results in a stack underflow error.

Peek: The peek operation allows you to view the top element of the stack without removing it. This is useful in situations where you need to check the value of the top element before deciding to pop it off the stack.

Size: The size operation returns the number of elements in the stack.

Empty: The empty operation checks whether the stack is empty. If the stack is empty, it returns true, otherwise it returns false.

Implementation of a Stack

The stack can be implemented using two main data structures: arrays and linked lists. Let us look at each of these implementations in more detail.

Array Implementation: The elements of the array implementation of the stack are kept in a single, continuous block of memory, and an index variable is used to keep track of the top element. The index variable is increased during the push operation, and the new element is then stored at the appropriate index. When performing a pop operation, the element at the current index is retrieved, the index variable is decreased, and then the element is returned. By returning the element at the current index, the peek operation retrieves an element. In the size operation, the index variable\’s value is returned, whereas in the empty operation, the index variable\’s value is verified to be zero.

The benefit of using an array to implement the stack is that it enables random access to the elements, which may be useful in some applications. The array\’s size must be predetermined, though, and memory waste may occur if the stack doesn\’t use all of its allotted space.

Linked List Implementation: In the linked list implementation of the stack, the elements are stored as nodes, each of which contains the element value and a reference to the next node. An identifier for the list\’s root node serves as a pointer for keeping track of the top element. The push operation entails creating a new node with the updated element value, updating the top pointer to point to the new node, setting the node\’s next reference to the existing top node. In order to perform the pop operation, the top pointer must be updated to point to the subsequent node, and the value of the top node must be returned. Returning the value of the current top node is what the peek operation entails. While the empty operation simply checks to see if the top pointer is null, the size operation involves moving through the list and counting how many nodes there are.

Using a linked list to implement the stack has the benefit of allowing for dynamic memory allocation, which enables the stack\’s size to change as needed. However, linked lists use more memory than arrays because each node must store both the value of the element and the reference to the element after it.

Applications of a Stack

The stack data structure has many practical applications in computer science and programming. Let us look at some of the common applications of the stack.

1. Function Calls: The stack is often used to implement the call stack in programming languages. When a function is called, its arguments and local variables are pushed onto the stack, and a return address is stored. When the function returns, the stack is popped to restore the previous state.
2. Expression Evaluation: The stack is also used to evaluate arithmetic expressions, such as infix, postfix, and prefix expressions. In postfix notation, also known as Reverse Polish notation, the operands are pushed onto the stack, and the operators are popped off the stack and applied to the top two operands.
3. Browser History: The stack can be used to implement the back and forward buttons in a web browser. Each time a new page is visited, its URL is pushed onto the stack. When the back button is pressed, the previous URL is popped off the stack and displayed.
4. Undo/Redo Operations: The stack can also be used to implement undo and redo operations in a text editor or graphics program. Each time a change is made, a new state is pushed onto the stack. When the undo button is pressed, the previous state is popped off the stack and restored.
5. Symbol Matching: The stack is also used to match brackets, parentheses, and other symbols in programming languages. Each opening symbol is pushed onto the stack, and each closing symbol is popped off the stack and checked against the corresponding opening symbol.

Conclusion

The stack is a basic data structure in computer science and programming, to sum up. It supports fundamental operations like push, pop, peek, size, and empty and operates according to the last-in, first-out principle. Arrays or linked lists can be used to implement the stack, each with their own benefits and drawbacks. Function calls, expression evaluation, browser history, undo/redo operations, and symbol matching are just a few of the useful uses for the stack. Any programmer or computer scientist must understand the stack data structure because it offers a potent tool for addressing a variety of issues.

In conclusion, the stack is a well-known data structure in programming and computer science that is straightforward but incredibly effective. It is a flexible tool for a variety of applications, ranging from function calls and program execution to graph traversal and algorithmic problem-solving, thanks to its efficient memory usage and simplicity of implementation. It is crucial to comprehend stacks and how they are used if you are a programmer or a student of computer science.