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memory and time: What I had in mind was the solution of an array in tandem with a hashtable. The array receives items as they are created, and so it keeps the order of insertion. And the hashtable stores data with key to facilitate search-by-key. However deleting by key is not efficient as it needs to search the array too. Introducing more values to the hash (e.g. the corresponding array index) increases memory. Inserting also needs updating 2 data structures.
10 min edit: also deleting from middle of array is inefficient.
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You will always need to update two data structures if you reuse Perl structures.
The OP suggested using sort, so how efficient is that without caching the result?
Maybe B-Trees are better suited here, though this certainly depends on the use case.
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