I was presented with the question "How many gifts, total, are
mentioned in the song 'The 12 Days of Christmas'?" I thought, "Aha!
I'll use clojure to figure it out." But I wanted to do it
idiomatically, using some functional constructs (with which I'm not
very familiar). First, I needed to know how many presents were given
on day n:
(defn sum-up-to [n]
"returns the sum of the positive integers from 1 to n"
(apply + 0
(map #(+ 1 %) (range n))))
(As an aside, yes, I know this is the same series from the apocryphal
story about Gauss as a child, and that the result is n+1/(n/2), but
using that would defeat the purpose of learning these functional
constructs).
The "apply + 0" is a little wonky, though, yes? I think that
reduce would be better, right? So I change the function:
(defn sum-up-to [n]
"returns the sum of the positive integers from 1 to n"
(reduce + (map #(+ 1 %) (range n))))
Then we need to find the sum of each of those days, from 1 to 12;
first, let's get that sequence (just to make sure I'm doing it right),
then let's add it up:
user> (map sum-up-to (range 1 13))
(1 3 6 10 15 21 28 36 45 55 66 78)
user> (reduce + (map sum-up-to (range 1 13)))
364
(Originally, I didn't know about the 2-argument version of range,
so I was using map and an anonymous inline function to add 1 to each
result from range, like:
(map #(sum-up-to (inc %)) (range 12))
Then I thought "This can't be right, there has to be a way to do this
already", and looked at the docs for range. It's nice when you find
something you want already exists - thanks, Rich!)
Fun times - thanks, clojure!
-Matt
PS I'm sure there are versions of this that are shorter (1 line?) or
perform better (e.g., by caching previous sums or something) - but
I'll leave those as an exercise for somebody else. ;)
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