32 lines
1.3 KiB
Plaintext
32 lines
1.3 KiB
Plaintext
{{data structure}}
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A '''set''' is a collection of elements, without duplicates and without order.
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;Task:
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Show each of these set operations:
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* Set creation
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* Test m ∈ S -- "m is an element in set S"
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* A ∪ B -- ''union''; a set of all elements either in set A or in set B.
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* A ∩ B -- ''intersection''; a set of all elements in ''both'' set A and set B.
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* A ∖ B -- ''difference''; a set of all elements in set A, except those in set B.
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* A ⊆ B -- ''subset''; true if every element in set A is also in set B.
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* A = B -- ''equality''; true if every element of set A is in set B and vice versa.
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<br>
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As an option, show some other set operations.
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<br>(If A ⊆ B, but A ≠ B, then A is called a true or proper subset of B, written A ⊂ B or A ⊊ B.)
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As another option, show how to modify a mutable set.
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One might implement a set using an [[associative array]] (with set elements as array keys and some dummy value as the values).
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One might also implement a set with a binary search tree, or with a hash table, or with an ordered array of binary bits (operated on with bit-wise binary operators).
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The basic test, m ∈ S, is [[O]](n) with a sequential list of elements, O(''log'' n) with a balanced binary search tree, or (O(1) average-case, O(n) worst case) with a hash table.
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{{Template:See also lists}}
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<br><br>
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