Past exam of the year 1 of the computer science course of the University of Oxford / 2022 / Functional programming, design and analysis of algorithms (resit) / 4 / c / Solution 2026-10-25
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Interleave equal halves, or collect the first and second components of adjacent pairs:
riffle :: [a] -> [a]
riffle = unpairs . uncurry zip . halve

unriffle :: [a] -> [a]
unriffle = unhalve . unzip . pairs
For halves as and bs of equal length, pairs (riffle xs) = zip as bs, and unzip (zip as bs) = (as,bs). Therefore unriffle (riffle xs) = xs. Conversely, starting from the adjacent pairs of any even list, separating the components, halving their concatenation and zipping them restores those same pairs. Hence riffle (unriffle xs) = xs too. Every stage takes linear time. This perfect out-shuffle leaves the first and last positions fixed.
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