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A collection of all things for prime numbers that are fun...
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| (def is-prime? | |
| (memoize | |
| (fn [^Number num] | |
| ^Boolean | |
| (cond | |
| (<= num 1) false | |
| (<= num 3) true | |
| (or (zero? (mod num 2)) (zero? (mod num 3))) false | |
| :else (reduce #(if (<= (* %2 %2) num) | |
| (reduced true) | |
| (if (or (zero? (mod num %2)) (zero? (mod num (+ %2 2)))) | |
| (reduced false) %)) | |
| true | |
| (range 1 (inc num))))))) | |
| (def sieve-of-eratosthenes | |
| (memoize (fn [^Number num] (when (> num 1) | |
| (loop [v (into [] (map not (boolean-array num))) | |
| i 2] | |
| (if (<= i (Math/sqrt num)) | |
| (if (true? (get v i)) | |
| (recur (loop [vv v | |
| j (* i i)] | |
| (if (<= j num) | |
| (recur (assoc vv j false) (+ j i)) | |
| vv)) | |
| (inc i)) | |
| (recur v (inc i))) | |
| (remove nil? | |
| (map-indexed | |
| (fn [ind value] (when (and (> ind 1) (true? value)) ind)) v)))))))) | |
| (defn sieve-of-eratosthenes-revisited | |
| [n] | |
| (let [erathostenes (transient (vec (replicate n true)))] | |
| (doseq [i (range 2 (Math/sqrt n)) | |
| :let [b (nth erathostenes i)]] | |
| (if b | |
| (loop [j (* i i) k 1] | |
| (if (< j n) | |
| (do | |
| (assoc! erathostenes j false) | |
| (recur (+ (* i i) (* k i)) (inc k))))))) | |
| (filter some? (map-indexed #(if %2 % nil) (drop 2 (persistent! erathostenes)))))) | |
| (def sieve-of-sundaram | |
| (memoize (fn [^Number n] | |
| (let [top (inc n)] | |
| (map (comp inc (partial * 2)) | |
| (sort | |
| (clojure.set/difference (set (range 1 top)) | |
| (set (for [i (range 1 top) j (range i top) | |
| :let [x (+ i j (* 2 i j))] | |
| :while (<= x top)] | |
| x))))))))) | |
| ;; TODO - Optimize... |
Author
Thanks to @rssole for optimizing is-prime? and adding sieve-of-sundaram.
https://github.com/rssole/clojureplayground/blob/master/src/clojureplayground/prime_numbers_fun.clj
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(def is-prime?
(memoize
(fn [^Number num] ^Boolean
(cond
(<= num 1) false
(<= num 3) true
(or (zero? (mod num 2)) (zero? (mod num 3))) false
:else (reduce #(if (<= (* %2 %2) num)
(reduced true)
(if (or (zero? (mod num %2)) (zero? (mod num (+ %2 2))))
(reduced false) %))
true
(range 1 (inc num)))))))