How to Build a PHP Calculator Using the Shunting Yard Algorithm?

How to Build a Calculator in PHP Using the Shunting Yard Algorithm

Introduction:

Creating a calculator that can handle simple algebraic expressions entered in normal notation presents a challenge, as PHP does not have built-in functionality for expression parsing. To address this, we can leverage the powerful and efficient Shunting Yard Algorithm.

Implementation:

1. Tokenization: Split the input string into individual tokens using word boundary and token boundaries (e.g., digits, parentheses, operators).
2. Shunting Yard Algorithm: Convert the tokens into Reverse Polish Notation (RPN) using a stack. Operators are pushed and popped based on their precedence and associativity, ensuring proper ordering.
3. Evaluation: Process the RPN stack by popping operators and evaluating them. Push the results back onto the stack.
4. Handling Operators and Parentheses: Implement classes that encapsulate operators and parentheses, allowing them to operate on the stack and handle special cases.

Example Code:

Implementing the Shunting Yard Algorithm requires a series of classes and functions that represent the various components. Here's an overview:

class TerminalExpression {
    // Represents operands and operators
}

class Number extends TerminalExpression {
    // Represents numeric values
}

class Operator extends TerminalExpression {
    // Represents arithmetic operators (+, -, *, /, ^)
}

class Parenthesis extends TerminalExpression {
    // Represents parentheses ((), used for grouping)
}

class Stack {
    // A simple stack data structure
}

class Math {
    // Contains the logic for evaluation and parsing
}

Example Usage:

Once implemented, you can use the calculator as follows:

$math = new Math();
$result = $math->evaluate("(2 + 3) * 4");
echo $result; // Output: 20

Benefits of the Shunting Yard Algorithm:

• Efficient and accurate parsing of algebraic expressions
• Supports operator precedence and associativity
• Avoids the need for costly string manipulation or complex regular expressions
• Handles complex expressions involving parentheses and nested calculations
• Can be extended to support more complex mathematical operations

By utilizing the Shunting Yard Algorithm, you can create a PHP calculator that can evaluate simple algebraic expressions in a robust and performant manner.

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