Schwartzian transform

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In computer programming, the Schwartzian transform is a technique used to improve the efficiency of sorting a list of items. This idiom^[1] is appropriate for comparison-based sorting when the ordering is actually based on the ordering of a certain property (the key) of the elements, where computing that property is an intensive operation that should be performed a minimal number of times. The Schwartzian transform is notable in that it does not use named temporary arrays.

The Schwartzian transform is a version of a Lisp idiom known as decorate-sort-undecorate, which avoids recomputing the sort keys by temporarily associating them with the input items. This approach is similar to memoization, which avoids repeating the calculation of the key corresponding to a specific input value. By comparison, this idiom assures that each input item's key is calculated exactly once, which may still result in repeating some calculations if the input data contains duplicate items.

The idiom is named after Randal L. Schwartz, who first demonstrated it in Perl shortly after the release of Perl 5 in 1994. The term "Schwartzian transform" applied solely to Perl programming for a number of years, but it has later been adopted by some users of other languages, such as Python, to refer to similar idioms in those languages. However, the algorithm was already in use in other languages (under no specific name) before it was popularized among the Perl community in the form of that particular idiom by Schwartz. The term "Schwartzian transform" indicates a specific idiom, and not the algorithm in general.

For example, to sort the word list ("aaaa","a","aa") according to word length: first build the list (["aaaa",4],["a",1],["aa",2]), then sort it according to the numeric values getting (["a",1],["aa",2],["aaaa",4]), then strip off the numbers and you get ("a","aa","aaaa"). That was the algorithm in general, so it does not count as a transform. To make it a true Schwartzian transform, it would be done in Perl like this:

@sorted = map  { $_->[0] }
          sort { $a->[1] <=> $b->[1] or $a->[0] cmp $b->[0] } # Use numeric comparison, fall back to string sort on original
          map  { [$_, length($_)] }    # Calculate the length of the string
               @unsorted;