Parsing Mathematical Expressions in C Using the Shunting-yard Algorithm
In the realm of programming, expressing complex mathematical calculations in code often requires parsing text strings into an internal tree representation. This facilitates subsequent evaluation and manipulation of these expressions.
Consider the task of parsing the following math expression string: "(a b)c-(d-e)f/g". The goal is to construct a tree structure using C classes to represent this expression.
Using the Shunting-yard Algorithm
The Shunting-yard algorithm provides an effective strategy for parsing mathematical expressions into trees. This algorithm operates in two phases:
Build the Tree: Use two stacks: an operator stack and an output stack. Process the tokens one at a time:
Defining the Tree Structure
To represent the tree structure, define the following C classes:
Example Parsing Process
For the expression "(a b)c-(d-e)f/g", the parsing process would proceed as follows:
Operator Stack | Output Stack --------------|-------------- | a b + | a b + | a b + c * | a b + c * | a b + c * d - | a b + c * d - | a b + c * d - e | a b + c * (d - e) * | a b + c * (d - e) f | a b + c * (d - e) f / | (a + b) * c - (d - e) * f / g
The resulting tree structure would have the following form:
* / \ (a + b) * (d - e) / \ / \ c / \ f / g
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