[4Clojure]解题记录-#75

Euler's Totient Function

 

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Difficulty:	Medium
Topics:

Two numbers are coprime if their greatest common divisor equals 1. Euler's totient function f(x) is defined as the number of positive integers less than x which are coprime to x. The special case f(1) equals 1. Write a function which calculates Euler's totient function.

 

(= (__ 1) 1)

 

(= (__ 10) (count '(1 3 7 9)) 4)

 

(= (__ 40) 16)

 

(= (__ 99) 60)

 

解长度100：
#(count 

   (for [i (range %)  

        :let [j (+ 1 i) 

               g ((fn f [x y](let [r (mod x y) q (quot x y)](if (= 0 r) y (f y r)))) j %)]      :when (= g 1)] j))
中间过程：

先写最大公约数，gcd，是递归的

(defn gcd [x y](let [r (mod x y) q (quot x y)](if (= 0 r) y (gcd y r))))

user=> (gcd 3 6);3 

user=> (gcd 4 6);2 

for从1到n，把里面和n互质的找出来(= 1 (gcd i n))

最后count个数，把gcd变成匿名函数，以及最外层的匿名函数用写成语法糖形式。