How can the Shunting-Yard Algorithm and Tree Representation be used to Parse Mathematical Expressions in C ?

Parsing Mathematical Expressions in C

In the realm of programming, parsing complex mathematical expressions into tree structures is a fundamental task. Consider an expression string such as "(a b)c-(d-e)f/g." Constructing a hierarchical representation of this expression aids in its evaluation and manipulation.

Shunting-Yard Algorithm

The Shunting-yard algorithm proves to be a robust approach to this problem. By iteratively processing the input string, the algorithm generates an output queue and an operator stack. Operators encountered in the string are either pushed onto the stack or processed immediately, based on their precedence rules.

Tree Representation

The resulting output queue forms the basis of a parsing tree. Each element of the queue represents a node in the tree. The Exp class serves as the base class, while leaf nodes are represented by the Term class, containing an integer value.

Internal nodes, known as Node objects, contain two child nodes (loperator_ and roperator_) and an operation symbol (operation). By carefully constructing the tree in this manner, we accurately capture the mathematical expression's structure and semantics.

Additional Approaches

Alternatively, one could employ formal grammar and a parsing tool to generate a parser. Parsing-expression grammar (PEG) is a notable choice, and several C/C libraries support PEG parsing.

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