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Built-in sorting algorithms from standard libraries are considered to cost O(1) auxiliary space as heapsort[1] exists, even though major implementations, such as Java's Arrays.sort[2,3]'s dual-pivot quicksort[4] and Python's list.sort[5,6]'s powersort[7] actually need O(log n). [1] https://dl.acm.org/doi/pdf/10.1145/512274.3734138 [2] https://docs.oracle.com/en/java/javase/24/docs/api/java.base/java/util/Arrays.html#sort(int%5B%5D) [3] https://github.com/openjdk/jdk/blob/c62223a5af747bc5cbdd3d970dd994f74aa08834/src/java.base/share/classes/java/util/DualPivotQuicksort.java#L242-L394 [4] https://www.kriche.com.ar/root/programming/spaceTimeComplexity/DualPivotQuicksort.pdf [5] https://docs.python.org/3/library/stdtypes.html#list.sort [6] https://github.com/python/cpython/blob/8e8786f8986353e20c1c4406c34409a6139fa073/Objects/listobject.c#L2874-L3163 [7] https://www.wild-inter.net/publications/munro-wild-2018.pdf
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