2023-07-01 11:58:00 -04:00
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(def ! (memoize #(apply * (range 1 (inc %)))))
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(defn catalan-numbers-direct []
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(map #(/ (! (* 2 %))
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2026-04-30 12:34:36 -04:00
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(* (! (inc %)) (! %))) (range)))
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2023-07-01 11:58:00 -04:00
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(def catalan-numbers-recursive
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#(->> [1 1] ; [c0 n1]
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2026-04-30 12:34:36 -04:00
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(iterate (fn [[c n]]
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[(* 2 (dec (* 2 n)) (/ (inc n)) c) (inc n)]) ,)
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(map first ,)))
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2023-07-01 11:58:00 -04:00
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user> (take 15 (catalan-numbers-direct))
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(1 1 2 5 14 42 132 429 1430 4862 16796 58786 208012 742900 2674440)
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user> (take 15 (catalan-numbers-recursive))
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(1 1 2 5 14 42 132 429 1430 4862 16796 58786 208012 742900 2674440)
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