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What is the cost of using Arrays.asList to convert static object arrays? Assuming that the object array has N items is it just an O(N) algorithm, where all of the items are copied by reference or is it merely a facade where the original array is put behind a List facade?

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It is cheap, O(1). As you suspect the list is merely a wrapper around the array. This is confirmed by the Java API documentation:

Returns a fixed-size list backed by the specified array. (Changes to the returned list "write through" to the array.)

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When going the other direction (Collection.toArray) the array is not "write-through". Changes to the array won't affect the list the array came from.
In otherwords sam, it clones the original array.

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