Re-implement median function using the quick-select algorithm
I wanted to submit a re-implementation of alexandria:median. Currently the function works by fully sorting the sequence, which has a complexity of O(n log n). This commit implements it as a special case of the quick select algorithm, which brings its complexity down to O(n).
The new implementation is more complicated, though I think it's still simpler than some other algorithms in alexandria. Anyways, the performance gains are dramatic enough that I thought I'd at least submit the patch. I did some testing via the timing code below, and observed speedups of 5-10x even on sequences with just 100 elements.
I could also provide the quick select algorithm as its own function if there's any interest, though it seems like this would have to go into the alexandria-2 branch.
;; Speed-testing function (defun test-median-speed (mag) (labels ((get-vec-median (vec) (if (oddp (length vec)) (aref vec (ash (length vec) -1)) (* 1/2 (+ (aref vec (ash (length vec) -1)) (aref vec (1- (ash (length vec) -1)))))))) (let ((arr (loop for i from 0 upto (expt 10 mag) collect (random 1000000)))) (assert (= (time (get-vec-median (sort (alexandria:copy-sequence 'vector arr) #'<))) (time (alexandria:median arr)))))))