Understanding Stacks: How to Build a Custom Stack in Pseudocode

· 6 min read

Hey everyone, it’s alanturrr1703 back again! 😄 Today, we’re going to dive into another fundamental data structure: the Stack. Stacks are widely used in programming for a variety of applications, from reversing data to managing function calls. In this blog, we’ll break down what a stack is, how it works, and how to implement common operations like push, pop, and peek using pseudocode. Plus, we’ll cover both array-based and linked-list-based implementations.

Let’s get started! 🚀

What is a Stack?

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. You can think of a stack like a pile of books: the last book you put on top is the first one you take off.

Basic Operations:

  • Push: Add an element to the top of the stack.
  • Pop: Remove the element from the top of the stack.
  • Peek (Top): Look at the top element without removing it.
  • isEmpty: Check if the stack is empty.

Key Features:

  • LIFO: Last In, First Out.
  • No random access: You can only access the top element.

Applications of Stacks:

  • Expression Evaluation: Stacks are used to evaluate arithmetic expressions and reverse polish notation.
  • Function Call Management: Stacks are used in memory to manage function calls and recursive functions.
  • Undo Mechanism: Many applications like text editors use stacks to manage undo operations.
  • Backtracking: Stacks are useful for algorithms like Depth-First Search (DFS).

Types of Stack Implementations

Stacks can be implemented in two main ways:

  1. Array-based implementation
  2. Linked-list-based implementation

Let’s look at how to implement stacks using these methods, complete with pseudocode for each operation.

Array-Based Stack Implementation

In the array-based implementation, we use an array to store stack elements. The stack has a fixed size, and we use an integer top to keep track of the index of the topmost element in the stack.

(a) Initialize Stack

Function InitializeStack(size):
    Create an array of size 'size'
    Set top = -1  # Indicates the stack is empty

(b) Push Operation

Function Push(stack, top, size, data):
    If top == size - 1:
        Print "Stack Overflow"
        Return
    top = top + 1
    stack[top] = data

(c) Pop Operation

Function Pop(stack, top):
    If top == -1:
        Print "Stack Underflow"
        Return NULL
    data = stack[top]
    top = top - 1
    Return data

(d) Peek Operation

Function Peek(stack, top):
    If top == -1:
        Print "Stack is empty"
        Return NULL
    Return stack[top]

(e) isEmpty Operation

Function isEmpty(top):
    Return top == -1

Array-Based Example:

Stack = [1, 2, 3]  # Top element is 3
top = 2

In the array-based implementation, we need to be cautious of stack overflow (trying to push when the stack is full) and stack underflow (trying to pop from an empty stack).

Linked-List-Based Stack Implementation

In the linked-list-based implementation, the stack is dynamic in size. Each element is represented as a node with two fields: data and a pointer to the next node. The top pointer points to the topmost element of the stack.

Node Structure

Structure Node:
    data
    next

(a) Initialize Stack

Function InitializeStack():
    Set top = NULL  # Empty stack

(b) Push Operation

Function Push(top, data):
    Create newNode with data
    newNode.next = top
    top = newNode
    Return top

(c) Pop Operation

Function Pop(top):
    If top == NULL:
        Print "Stack Underflow"
        Return NULL
    data = top.data
    top = top.next
    Return data

(d) Peek Operation

Function Peek(top):
    If top == NULL:
        Print "Stack is empty"
        Return NULL
    Return top.data

(e) isEmpty Operation

Function isEmpty(top):
    Return top == NULL

Linked-List-Based Example:

Let’s visualize the stack as a linked list:

top → [data: 3, next: → [data: 2, next: → [data: 1, next: NULL]]]

Here, the top element is 3.

Circular Stack Implementation

In some cases, you might want to implement a circular stack, where the stack behaves like a circular queue, wrapping around when it reaches the end of the array. While this is less common, it can be useful in scenarios like fixed-size circular buffers.

(a) Push Operation (Circular Stack)

Function PushCircular(stack, top, size, data):
    nextIndex = (top + 1) % size
    If nextIndex == 0 and top == size - 1:
        Print "Stack Overflow"
        Return
    top = nextIndex
    stack[top] = data

(b) Pop Operation (Circular Stack)

Function PopCircular(stack, top, size):
    If top == -1:
        Print "Stack Underflow"
        Return NULL
    data = stack[top]
    top = (top - 1 + size) % size
    Return data

Circular stacks are a bit trickier and require proper handling of indices, but they are useful when you have a fixed memory space, like when implementing a ring buffer.

Stack Operations and Time Complexity

  • Push: O(1) – We simply insert an element at the top.
  • Pop: O(1) – We remove the top element.
  • Peek: O(1) – We retrieve the top element.
  • isEmpty: O(1) – We check if the stack is empty.

All of these operations are highly efficient and take constant time.

Real-World Applications of Stacks

1. Function Call Management (Call Stack)

Stacks are used to manage function calls in programming languages. When a function is called, its details (return address, parameters, etc.) are pushed onto the stack, and when the function returns, the details are popped from the stack.

2. Expression Evaluation

Stacks are used to evaluate expressions like infix, postfix (reverse Polish notation), and prefix notation. Stacks help in converting between these notations and evaluating the expressions efficiently.

3. Backtracking Algorithms

In algorithms like Depth-First Search (DFS), stacks are used to keep track of the nodes to visit and backtrack when needed.

4. Undo Mechanisms

Many applications, such as text editors, use stacks to store the history of operations. When the user presses “Undo,” the latest operation is popped from the stack.

5. Balancing Parentheses

Stacks are often used to check if parentheses or brackets in an expression are balanced, making sure every opening bracket has a corresponding closing bracket.

Wrapping It Up

Stacks are a foundational data structure that is incredibly useful in various applications, from managing function calls to evaluating expressions. Whether you choose to implement stacks using arrays or linked lists depends on your use case, but understanding both implementations will make you a stronger programmer.

I hope this post gave you a clear understanding of how stacks work, and how to implement their basic operations in pseudocode. Whether you’re building an undo feature or working with recursion, stacks will undoubtedly come in handy!

That’s all for today! Until next time, happy coding! 🚀