How Do You Parse Complex Mathematical Expressions in C ?

Parsing Complex Mathematical Expressions in C

In this article, we address the task of parsing intricate mathematical expressions into tree structures for efficient evaluation and manipulation.

The sought algorithm should convert an expression string such as "(a b)c-(d-e)f/g" into a tree of nodes representing operations and operands. The tree structure facilitates both syntactic analysis and subsequent calculations.

Algorithm for Expression Parsing

The Shunting-yard algorithm, also known as the Dijsktra algorithm, is a reliable method for parsing mathematical expressions.

The algorithm operates by iterating through the expression string, classifying each character as an operator (*, , -, /) or operand (a, b, ..., z). Operators are handled accordingly, with parentheses considered for precedence.

The resulting output is a postfix notation, where operands precede operators. This allows for straightforward tree construction where each node represents a single operation or operand.

Implementation Considerations

When implementing the algorithm in C , consider utilizing classes like "Exp" for abstract expressions, "Term" for operands, and "Node" for operators.

Alternative Methods

Alternatively, formal grammars such as parsing-expression grammars (PEGs) can be employed. Tools exist to generate parsers based on these grammars. For C/C , several PEG libraries are available.

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