On the surface, implementing a calculator in C++ might seem like a straightforward task, but the project quickly revealed its complexity, especially in terms of parsing and interpreting mathematical expressions. This undertaking significantly deepened my understanding of tree structures, particularly the Abstract Syntax Tree (AST).

The development of this calculator involved designing a system that could take a string input representing a mathematical equation and break it down into a manageable form that the computer could process to perform calculations. The core of this challenge lay in constructing an effective AST, a tree representation of the syntactic structure of the source code, where each node represented a construct occurring within the expression.

Creating an AST involved several steps: lexical analysis, parsing, and finally the evaluation. During the lexical analysis phase, the program transformed the input string of characters into a sequence of tokens, which included numbers, operators, and parentheses. Parsing these tokens required a deep dive into recursive parsing techniques, which helped me understand how to process expressions and subexpressions based on the precedence and associativity of operators.

This project not only enhanced my programming skills in C++ but also provided me with a practical application of compiler theory, specifically in how expressions are parsed and evaluated in programming languages. The construction of the AST was particularly intricate, as it needed to correctly represent the hierarchical structure of mathematical operations to ensure the calculator’s accuracy.