I am working on the following problem:
Find the only Pythagorean triplet, {a, b, c}, for which a + b + c =
1000
My strategy is to produce a series of triplets of a^2 + b^2 and then
filter out the ones where the c^2 is a perfect square, in order to
determine Pythagorean triplets.
I wrote a function to produce triplets that takes a range as input:
(use '[clojure.contrib.math :only (sqrt)])
(defn trips [coll]
(loop [a (first coll) b (rest coll) trip []]
(cond (seq b)
(recur (first b) (rest b) (conj trip (map #(vector a % (sqrt (+ (*
a a) (* % %)))) b)))
true trip)))
,so if I want to see all triplets over the range of 1-7, I just do:
(trips (range 1 7)), which yields the following;
[([1 2 2.23606797749979] [1 3 3.1622776601683795] [1 4
4.123105625617661] [1 5 5.0990195135927845] [1 6 6.082762530298219])
([2 3 3.605551275463989] [2 4 4.47213595499958] [2 5
5.385164807134504] [2 6 6.324555320336759]) ([3 4 5] [3 5
5.830951894845301] [3 6 6.708203932499369]) ([4 5 6.4031242374328485]
[4 6 7.211102550927978]) ([5 6 7.810249675906654])]
Obviously the only Pythagorean triplet burried in there is 3, 4, 5.
Now, I can easily test a single vector for integers as follows:
(map integer? [5 6 7])
However, the output of my trips function yields multiple collections
of vectors inside of a larger vector. I am completely befuddled as to
how to process this behemoth.
I guess I need to use some functions for merging collections?
Any help apprectiated. thanks!!
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