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The exercise here is to implement code that is a set, without relying on the native implementation of the language of choice.

In computer science, a set is an abstract data type that can store certain values, without any particular order, and no repeated values. It is a computer implementation of the mathematical concept of a finite set. Unlike most other collection types, rather than retrieving a specific element from a set, one typically tests a value for membership in a set. — Wikipedia

In our task, we are interested in implementing and testing as many operations as we can get through in order to provide us with an idea of how you solve problems and how you work with someone while pairing on a problem.

Core Operations

Note that sets are represented mathematically with a list specified in braces ({}), such that the set of odd positive integers less than or equal to five would be written as { 1, 3, 5 }.

• Set definition constructs a Set object from a list (vector, array, range, etc.) of other objects.

• The union of two sets is a new Set containing the unique members of those sets. This is written with the symbol ∪.

  ( { 1, 3 } ∪ { 2, 4 } ) ≡ { 1, 2, 3, 4 }
  

• The intersection of two sets is a new Set of all objects that are members of both sets. This is written with the symbol ∩.

  ( { 1, 2, 3 } ∩ { 2, 3, 4 } ) ≡ { 2, 3 }
  

• The difference of two sets is a new Set of all members of the first set that are not part of the second set. This is written with \. This operation is not symmetric.

  ( { 1, 2, 3 } \ { 2, 3, 4 } ) ≡ { 1 }
  ( { 2, 3, 4 } \ { 1, 2, 3 } ) ≡ { 4 }
  

• The subset tests whether the first set is a subset of the second set. This relationship is written with the symbol ⊆.

  { 1, 2, 3 } ⊆ { 1, 2, 3, 4 }
  

Common Extended Operations

• A set contains an element x if that value is in the set.

  { 1, 2, 3 } contains 2 ≡
     { 2 } ⊆ { 1, 2, 3 }
  

• A set is empty if there are no elements in the set.

• A set can return the number of elements in itself.

• A dynamic set can have elements added to or removed from itself.

• The symmetric difference of two sets is a new Set of all objects that are members of exactly one set, but not both. This is written with the symbol ∆.

  A = { 1, 2, 3 }
  B = { 2, 3, 4 }
  A ∆ B ≡ { 1, 4 }
        ≡ (A ∪ B) \ (A ∩ B)
        ≡ (A \ B) ∪ (B \ A)
  

Licence

These exercise skeletons are available under the MIT licence.

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