How can the Shunting-Yard Algorithm be used to efficiently parse mathematical expressions in C ?

Parsing Mathematical Expressions in C

To parse mathematical expressions efficiently, a structured representation, such as a parsing tree, is vital. Let's consider the problem of representing the expression "(a b)c-(d-e)f/g" as a tree.

Shunting-Yard Algorithm

The Shunting-yard algorithm is a well-known approach for parsing mathematical expressions. It follows these steps:

1. Input Scan: Scan the expression character by character and identify tokens (e.g., operators, operands, parentheses).
2. Operator Stack: Create a stack to store operators.
3. Output Queue: Create a queue to store the parsed expression.

4. Processing: For each token encountered:

   • Operand: Add the operand to the output queue.
   • Left Parenthesis: Push it onto the operator stack.
   • Right Parenthesis: Pop operators from the stack until the left parenthesis is encountered and add them to the output queue.

   • Operator:

     • If the operator stack is empty or contains only parentheses, push the operator onto the stack.
     • Otherwise, pop higher precedence operators from the stack and add them to the output queue until the operator stack is empty or the next operator has higher precedence.
     • Then, push the current operator onto the stack.
5. Flush Stack: After processing all tokens, pop all operators from the stack and add them to the output queue.

Example

Using the Shunting-yard algorithm with the expression "(a b)c-(d-e)f/g" yields the following tree:

Node(+:
  - Node(a)
  - Node(b))
- Node(*:
  - Node(c)
  - Node(-:
    - Node(d)
    - Node(e))
  - Node(/:
    - Node(f)
    - Node(g)))

Other Options

In addition to the Shunting-yard algorithm, you could also write a formal grammar and use a parsing library. Parsing-expression grammars (PEGs) are suitable for this purpose, and C/C libraries exist for PEG parsing.

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