Comparisons per element to find the median, n = 4,001, 30 seeds

Comparisons per element to find the median, n = 4,001, 30 seeds

For each pivot rule: the range of comparisons per element over 30 independent runs (the bar), with the mean marked. randomised pivot averages 2.96 and ranges from 1.56 to 4.12 — a factor of 2.6 on identical data, decided entirely by the coins. median of medians averages 7.94, spends no randomness, and varies by 1.7%. What derandomisation buys is not a lower cost; it is a cost that does not move.

Drawn at 700 × 192, wide on the page. Everything above is what select-constants returns with no arguments; the caption is the generator's own, computed from the numbers in the drawing rather than written beside it.

2 essays call select-constants. The drawing above is what it returns with no arguments at all; every call below passes it something, because a placement that passes nothing draws whichever member of the family the generator happens to default to rather than the one its essay argues about — which is what optcheck and figfill exist to catch.