A stack is a linear data structure that follows the Last In First Out (LIFO) principle, meaning the last element added to the stack will be the first one to be removed. This makes stacks particularly useful in scenarios where you need to reverse items or access them in a specific order, such as backtracking in algorithms, managing function calls in programming, or undo operations in software applications.

Explanation of LIFO and FILO Principles

• LIFO (Last In First Out): This principle is the core of how a stack operates. The last element added to the stack is the first one to be removed. This is akin to the behavior of a stack of plates where the last plate added is the first to be removed.
• FILO (First In Last Out): Although the terms LIFO and FILO are often used interchangeably, FILO can be thought of as a more general concept where the first element added is the last one to be removed, but in the context of stacks, it is the same as LIFO.

Real-life Examples of Stack

Stacks are used in various everyday scenarios:

• Undo/Redo in Software: Many software applications implement undo and redo functionalities using stacks. The actions are pushed onto a stack when performed, and popped when undone, allowing users to reverse their actions in the order they were performed.
• Web Browsers: The 'back' and 'forward' buttons in web browsers use stacks to manage the history of visited web pages.
• Expression Evaluation in Calculators: Stacks are used to evaluate arithmetic expressions in calculators.
• Function Call Stack: In programming, the call stack is a real-life example of a stack. When a function is called, it is pushed onto the stack, and when the function returns, it is popped from the stack. This ensures that the function that was called last is the one that finishes executing first.

Basic Operations of Stack

Stacks provide a set of basic operations to manage the data:

• Push: Adds an element to the top of the stack. If the stack is full, this operation cannot be performed.

Stack: [1, 2, 3]
Push(4)
Stack: [1, 2, 3, 4]

// Pseudocode
Procedure Push(stack, item)
    If stack is full Then
        Return "Stack Overflow"
    Else
        Increment stack's top index
        Insert item at the top index of the stack
    End If
End Procedure

• Pop: Removes the top element from the stack. If the stack is empty, this operation cannot be performed.

Stack: [1, 2, 3, 4]
Pop()
Stack: [1, 2, 3]

// Pseudocode
Procedure Pop(stack)
    If stack is empty Then
        Return "Stack Underflow"
    Else
        Decrement stack's top index
        Return the item at the new top index of the stack
    End If
End Procedure

• IsEmpty: Checks if the stack is empty. Returns true if the stack is empty, otherwise false.

Stack: []
IsEmpty() // Returns true

// Pseudocode
Procedure IsEmpty(stack)
    If stack's top index is -1 Then
        Return True
    Else
        Return False
    End If
End Procedure

• IsFull: Checks if the stack is full. This operation is not always applicable as stacks can grow dynamically.
• Peek: Returns the value of the top element without removing it from the stack. If the stack is empty, this operation cannot be performed.

Stack: [1, 2, 3, 4]
Peek() // Returns 4
Stack: [1, 2, 3, 4]

// Pseudocode
Procedure Peek(stack)
    If stack is empty Then
        Return "Stack is empty"
    Else
        Return the item at the top index of the stack
    End If
End Procedure

• Size: Returns the number of elements in the stack. This operation is useful for checking the current capacity of the stack.

Stack: [1, 2, 3, 4]
Size() // Returns 4

function size(stack)
    return stack.top + 1

• search: Finds the position of an element in the stack

function search(stack, element)
  index = 1
  for each item in stack
    if item == element
      return index
    index++
  return -1

Stack Complexity

The time complexity of basic stack operations is O(1), which means these operations can be performed in constant time, regardless of the size of the stack. The space complexity of a stack is O(n), where n is the number of elements in the stack, as each element requires a fixed amount of space.

Applications of Stack Data Structure

Stacks are used in various applications:

• Algorithm Design and Problem Solving: Stacks are used to solve problems like the Tower of Hanoi, depth-first search in graphs, and parsing expressions.
• Software Development: Stacks are used in the implementation of undo/redo functionality, managing function calls, and parsing expressions.

Advanced Stack Concepts

1. Stack Using Linked List

A stack can be implemented using a linked list, where the head of the list represents the top of the stack. This allows for dynamic resizing of the stack.

2. Monotonic Stack

A monotonic stack is a stack that contains only monotonically increasing or decreasing elements. It is used in various algorithms, such as the next greater element problem.

3. Stack in Data Structure Algorithms

Stacks are used in various algorithms, including depth-first search (DFS), breadth-first search (BFS), and backtracking algorithms.

Problem Solving with Stack

Easy Problems on Stack

• Balanced Parentheses: Check if a string of parentheses is balanced.
• Next Greater Element: Find the next greater element for every element in an array.

Medium Problems on Stack

• Largest Rectangle in Histogram: Find the largest rectangle that can be formed in a histogram.
• Minimum Stack: Implement a stack with push, pop, top, and getMin operations in O(1) time complexity.

Hard Problems on Stack

• Sliding Window Maximum: Find the maximum in each sliding window of size k.
• Trapping Rain Water: Calculate the amount of rainwater that can be trapped between the bars.

Conclusion

Stacks are a fundamental data structure that follows the LIFO principle, offering efficient operations for managing a collection of elements. They are widely used in algorithm design, problem-solving, and software development for various applications, including managing function calls, undo/redo functionality, and parsing expressions.