Implementing a Simple Calculator Using the Shunting Yard Algorithm in Python

Solving mathematical expressions in Python can be a complex task, especially when dealing with intricate operations such as 33 / 6 - 7. This article explores the implementation of a simple calculator using the Shunting Yard algorithm, a popular technique for parsing mathematical expressions specified in infix notation. We will delve into a naive and possibly over-engineered version of this algorithm, complete with detailed explanations and examples.

Introduction to the Shunting Yard Algorithm

The Shunting Yard algorithm, developed by Edsger W. Dijkstra, is an efficient method for parsing mathematical expressions implemented in infix notation. This algorithm leverages a stack to convert the infix notation to postfix notation (also known as Reverse Polish Notation), which is easier to evaluate. The key steps involve tokenizing the input expression, using operator and operand stacks, and converting expressions between different notations.

Tokenization and Evaluation in Python

We begin by implementing a basic tokenization function to break down the mathematical expression into tokens. This function will identify operators and numbers, helping us prepare for the conversion to postfix notation.

    import operator    operator_set  {"^": 3, "/": 2, "*": 2, " ": 1, "-": 1, "(": 0, ")": 0}    float_value_pattern  r"[- ]?d*.d |[- ]?d "    def tokenize_expression(expression):        number  ""        for position, character in enumerate(expression):            if character  " ":                continue            if character in operator_set:                if number:                    yield float(number) if "." in number else int(number), position                yield character, operator_set[character], position                number  ""                continue            if () or character  ".":                number   character                continue            if character  ".":                if "." in number:                    raise SyntaxError(f"Only one decimal point allowed in a number at column {position}")            raise SyntaxError(f"Unknown operator {character} at column {position}")        else:            if number:                yield float(number) if "." in number else int(number), position    

Implementing the Shunting Yard Algorithm

Once the expression is tokenized, we can proceed with the Shunting Yard algorithm. This involves both a stack for operators and a stack for operands. The algorithm ensures that operators are applied in the correct order by comparing their precedence and associativity.

    def evaluate_expression(expression):        operator_stack  []        data_stack  []        def consume_upto(upto_tokenNone):            if upto_token:                token_type, token_priority, token_callable, token_position  upto_token            else:                token_type, token_priority, token_callable  ^, -500, None                operator_("(")            if token_type  ")":                operator_untilconsume_upto()                return            if token_type  "number":                operand_value, operand_position  token                data_(operand_value)                return            else:                operator_info, operator_position  token                if operator_stack:                    operator_untilconsume_upto()                operator_(operator_info)        for token in tokenize_expression(expression):            token_type, token_priority, token_callable, position  token            if token_type  "number":                value, position  token                data_(value)            else:                operator_info, position  token                consume_upto()        while operator_stack:            consume_upto(None)        return data_stack[-1]    

Issues and Features of the Implementation

This solution has several issues and features worth noting:

Issues

Not Fully Tested: The code may not cover all edge cases and need proper testing. WhiteSpace Handling: Expressions with spaces are currently ignored, which can lead to incorrect evaluations. No Support for Unary Operators: Operations such as negative numbers are not supported in this implementation. No Support for Multi-Character Operators: Operations like multiplication (or division) using the '×' or '/' symbol are not supported.

Features

Supports Integers and Floating Point Numbers: The implementation can handle both integer and floating point numbers. Correctly Handles Floating Point Numbers: It correctly traps floating point numbers with multiple decimal points. Complexity: The solution might be too complex for production use.

Conclusion

Implementing a calculator using the Shunting Yard algorithm in Python is a valuable exercise for understanding expression parsing and evaluation. While this solution may have some limitations, it provides a solid foundation for building more robust calculators. By addressing the identified issues and enhancing the features, we can create a more comprehensive and efficient calculator application.

To improve this implementation, you might want to:

Add proper whitespace handling and support for negative numbers and multi-character operators. Refactor the code to make it more modular and easier to maintain. Implement error handling and edge case handling to ensure a more robust evaluation process.

By following these steps, you can create a more comprehensive and efficient implementation of a Python calculator using the Shunting Yard algorithm.