2016 Update

Task/Modular-inverse/Clojure/modular-inverse.clj

@@ -0,0 +1,43 @@
+(ns test-p.core
+  (:require [clojure.math.numeric-tower :as math]))
+
+(defn extended-gcd
+  "The extended Euclidean algorithm--using Clojure code from RosettaCode for Extended Eucliean
+  (see http://en.wikipedia.orwiki/Extended_Euclidean_algorithm)
+  Returns a list containing the GCD and the Bézout coefficients
+  corresponding to the inputs with the result: gcd followed by bezout coefficients "
+  [a b]
+  (cond (zero? a) [(math/abs b) 0 1]
+        (zero? b) [(math/abs a) 1 0]
+        :else (loop [s 0
+                     s0 1
+                     t 1
+                     t0 0
+                     r (math/abs b)
+                     r0 (math/abs a)]
+                (if (zero? r)
+                  [r0 s0 t0]
+                  (let [q (quot r0 r)]
+                    (recur (- s0 (* q s)) s
+                           (- t0 (* q t)) t
+                           (- r0 (* q r)) r))))))
+
+(defn mul_inv
+  " Get inverse using extended gcd.  Extended GCD returns
+    gcd followed by bezout coefficients. We want the 1st coefficients
+   (i.e. second of extend-gcd result).  We compute mod base so result
+    is between 0..(base-1) "
+  [a b]
+  (let [b (if (neg? b) (- b) b)
+        a (if (neg? a) (- b (mod (- a) b)) a)
+        egcd (extended-gcd a b)]
+      (if (= (first egcd) 1)
+        (mod (second egcd) b)
+        (str "No inverse since gcd is: " (first egcd)))))
+
+
+(println (mul_inv 42 2017))
+(println (mul_inv 40 1))
+(println (mul_inv 52 -217))
+(println (mul_inv -486 217))
+(println (mul_inv 40 2018))