Hi all,
A very popular interview question is to try implement all arithemtic
operations for integers without using all the usual suspects. After
thinking for a while I concluded that I only really need inc/dec in
order to implement everything else. And the good news is that one can
easily implement inc/dec using bit-shifts like so:
(ns interview.arithmetic
(:refer-clojure :exclude [- * / + inc dec even? odd?]))
(defn even? [x]
(== 0 (bit-and x 1)))
(defn odd? [x]
(== 1 (bit-and x 1)))
(defn- halve-int [x]
(bit-shift-right x 1))
(defn- double-int [x]
(bit-shift-left x 1))
(defn inc [x]
(cond
(even? x) (bit-xor x 1)
(== -1 x) 0
:else
(-> x
halve-int
inc
double-int)))
(defn dec [x]
(if (odd? x) (bit-xor x 1)
(-> x
bit-not
inc
bit-not)))
At this point, having this I can implement all arithmetic operations on
integers by combining 'iterate' + take/take-while. For example here is +:
(defn +
([] 0)
([x] x)
([x y]
(let [iter (if (neg? y) dec inc)]
(->> x
(iterate iter)
(take (inc (Math/abs y)))
last)))
([x y & more]
(reduce + x (cons y more))))
The same pattern applies for [- * /]. My question is, can anyone see
a better way of doing this? It seems pretty elegant to me but I'd like
to see what other people think...
many thanks :)
Jim
ps: division is indeed a bit trickier than the rest due to
positive/negative signs. Not really hard though...
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