### Problem description, from Project Euler

There exists exactly one Pythagorean triplet for which a + b + c = N. (N is known.) Find the product abc.

### Solution

This was a quick once since I just brute-forced it. I think there are some optimizations possible related to the idea that a^2 + b^2 < c^2.

; flattens a nested list (defn flatten [x] (let [s? #(instance? clojure.lang.Sequential %)] (filter (complement s?) (tree-seq s? seq x)))) ; returns the result of the pythagorean equation (defn pythagorean-triplet-c [a b] (. java.lang.Math (sqrt (+ (* a a) (* b b) ) ) ) ) ; returns the c term of a pythagorean triple ; nil if natural term does not exist (defn pythagorean-triplet-c-natural [a b] (def result (pythagorean-triplet-c a b)) (if (zero? (- result (int result))) (int result) nil ) ) (defn problem09 [sum]<br /> (def res<br /> (map (fn [a] (map (fn [b] (def c (pythagorean-triplet-c-natural a b)) (if (and (not (nil? c)) (= sum (+ a b c)) ) (* a b c) nil ) ) (range 100 sum) ) ) (range 100 sum) ) ) (first (distinct (filter #(not (nil? %)) (flatten res)))) )

Blog: Project Euler Problem 9 Solution: Clojure /programming/project-euler-problem-9-clojure/

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