Here are some question-based titles that fit the content of your article: Simple and direct: * How to Parse Mathematical Expressions in C : Shunting-Yard Algorithm and Formal Grammars * Parsing Mat

Parsing Mathematical Expressions in C

Question:

Given a mathematical expression string, how can you construct a parse tree to represent the expression?

Solution:

1. Shunting-Yard Algorithm:

The Shunting-yard algorithm is a two-pass approach that converts an infix expression into postfix (Reverse Polish Notation) and then builds the parse tree.

• Infix to Postfix:

  • Create two stacks: operator stack and output stack.
  • Scan the infix expression from left to right.
  • If an operand is encountered, push it onto the output stack.
  • If a left parenthesis is encountered, push it onto the operator stack.
  • If a right parenthesis is encountered, pop operators from the operator stack and push them onto the output stack until a left parenthesis is found.
  • If an operator is encountered, push it onto the operator stack if its precedence is higher than the top operator on the stack, otherwise, pop operators with higher precedence from the operator stack and push them onto the output stack.

• Postfix to Parse Tree:

  • Create a root node for the parse tree.
  • Pop operands from the output stack and create leaf nodes for them.
  • Pop operators from the output stack and create internal nodes with children pointing to the nodes created for the operands.
  • Attach the children to the root node.

2. Formal Grammar:

Alternatively, you can define a formal grammar for mathematical expressions and use a parsing tool to generate a parser. A typical Parsing-Expression Grammar (PEG) for mathematical expressions looks like this:

Expr:   Term '+' Expr | Term '-' Expr | Term;
Term:   Factor '*' Term | Factor '/' Term | Factor;
Factor: Number | '(' Expr ')';

Several C/C libraries support PEG parsing, such as:

• boost::spirit
• pyPEG2
• PCRE

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