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Data Structures

Applications of Stacks

 


Applications of Stacks

Stacks, following the Last-In, First-Out (LIFO) principle, play a crucial role in several core computing applications. Here is an in-depth look at four classic stack applications:

1. Balancing Symbols

Purpose:
To verify that pairs of symbols—such as parentheses (), curly braces {}, and square brackets []—are properly opened and closed in code or expressions.

How it works:

  • Process each symbol in order (typically left to right).

  • On encountering an opening symbol, push it onto the stack.

  • On seeing a closing symbol:

    • Pop the top of the stack and check if it matches the closing symbol's type.

    • If it doesn't, or if the stack is empty when a closing symbol is found, the expression is unbalanced.

  • At the end, if the stack is empty, all symbols are balanced.

What It Is:
Stacks are used to verify that all parentheses, braces, and brackets are correctly paired and nested in source code or mathematical expressions.

Real-World Example:

  • Code Editors (IDEs): When you write code in Visual Studio Code or IntelliJ, the editor instantly checks for matching brackets or braces, highlighting them or warning you if something is unbalanced. This check is efficiently executed using stack operations internally.

2. Evaluating Arithmetic Expressions

Purpose:
To compute the result of arithmetic expressions, especially when expressions include nested operations and parentheses.

How it works:

  • Stacks are used to store operators and operands temporarily.

  • For postfix (Reverse Polish Notation) evaluation:

    • Scan from left to right.

    • Push operands (numbers) to the stack.

    • On encountering an operator, pop required operands, perform the operation, and push the result back.

  • For infix expressions, stacks can help handle operator precedence and associativity during evaluation.

What It Is:
Stacks help compute the value of mathematical expressions, particularly those with nested parentheses and multiple operators.

Real-World Example:

  • Scientific Calculators: Advanced calculators, including those on smartphones, can process complex expressions with parentheses and operator precedence by converting infix notation (e.g., 3 + 4 * (2 - 1)) to postfix, then evaluating the result using stacks.

  • Spreadsheet Formula Parsing: Programs like Microsoft Excel parse and evaluate formulas with nested operations using stack-based parsing and calculation.

3. Infix to Postfix Conversion

Purpose:
To convert standard arithmetic notation (infix: e.g., A + B) to postfix notation (AB+) for easier computation by machines.

How it works:

  • Use a stack to store operators:

    • Read operands and print/add them to output directly.

    • Push operators on the stack; pop them to output when you encounter an operator of lower or equal precedence or a right parenthesis.

    • At the end, pop all remaining operators.

  • The result: a postfix expression with no parentheses, ready for efficient evaluation.

What It Is:
Stacks convert traditional arithmetic expressions (which humans write as infix, like A + B * C) into postfix (Reverse Polish Notation, like A B C * +) for easier computerized evaluation.

Real-World Example:

  • Interpreter and Compiler Design: Languages like Python and Java convert user-written expressions into postfix (or other forms) internally using stacks, allowing efficient automated calculation or bytecode generation.


4. Function Call Tracking (Call Stack)

Purpose:
To manage the sequence of active function calls in programming languages, especially for recursion and nested calls.

How it works:

  • Each new function call pushes execution context (local variables, return address) onto the stack.

  • When a function returns, the stack is popped to restore the previous context.

  • This allows programs to return to the correct place after a function finishes and supports recursive operations.

What It Is:
Stacks track active function calls, their local variables, and the point to return to after a function finishes.

Real-World Example:

  • Web Browsers’ Scripting Engines: When you call a function in JavaScript (for example, a button click handler that itself calls another function), each call is pushed onto the browser’s call stack. When a function returns, the stack unwinds to restore the previous state.

  • Gaming Applications: In games, scripts trigger actions that may call other scripts or routines recursively — the game engine manages these using a call stack, ensuring actions are completed in the right sequence.

Summary Table

ApplicationWhy Stacks Are Used
Balancing SymbolsTrack opening/closing pairs LIFO
Evaluating Arithmetic Expr.Manage operands/operators as subexpressions are solved
Infix to Postfix ConversionEnsure operators appear in output in correct order of precedence
Function Call TrackingMaintain sequence/context for nested and recursive function invocations

Stacks offer a powerful, simple mechanism for managing temporary data, making them indispensable in both algorithms and practical software tools.