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I have the implemented a calculator that is very similar to the following UML diagram. The only new thing is a new class, a Recognizer class, that says if the expression is written correctly or not.

https://i.stack.imgur.com/IxYa5.jpg

I have applied a factory design pattern for the operations Add,Sub,Extract,Division but I'm also interested in applying a structural pattern aswell(Adapter,Bridge,Filter,Composite,Decorator,Facade,Flyweight or Proxy). What would fit the diagram?

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    You're looking at it backward. Design patterns are not building blocks, you can't design an architecture by trying to fit as many design patterns as you can. – Vincent Savard Nov 13 '18 at 18:28
  • @VincentSavard I understand this, however it's for a project where I'm asked to add a structural pattern, alongside a creational and behaviour pattern. So I'm pretty much trying to get the best thing that can fit inside this, even if it looks horrible. – Shury Nov 13 '18 at 18:35
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If you are obliged to chose a structural pattern, I'd suggest to revisit the Expression and its derivates with the Composite pattern:

  • every expression can be composed themselves of sub-expressions
  • some expressions can be binary (e.g. those that you already identified)
  • some expressions can be leafs (e.g. a variable or a constant literal used in an expression)

For this to work, you need to refactor evaluate to take no argument (or a map of variables with their values as argument).

Edit: this article has a nice (although simplified) example of a composite used for expressions. This question about expressions data structures has some answer using the composite pattern.

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