The subject matter concerns the design and implementation of an algorithm to evaluate arithmetic expressions represented as strings. These expressions typically involve integers, addition, subtraction, multiplication, and division operators. The challenge resides in correctly interpreting the operator precedence rules, specifically multiplication and division taking precedence over addition and subtraction. A sample input string might be “3+2*2”, which should evaluate to 7, illustrating the necessity for a solution that adheres to operator precedence.
The practical significance of solving this type of problem lies in its relevance to compiler design, interpreter construction, and general-purpose expression evaluation. Accurate and efficient expression evaluation is fundamental in numerous software applications, ranging from scientific computing and financial modeling to scripting languages and data analysis tools. Historically, various techniques, such as shunting-yard algorithms and recursive descent parsers, have been employed to address this problem, each with its own trade-offs in terms of complexity and performance.
