Added Modular Binary Exponentiation (Recursive) (#337)

Maths/ModularBinaryExponentiationRecursive.js

@@ -0,0 +1,31 @@
+/*
+  Modified from:
+    https://github.com/TheAlgorithms/Python/blob/master/maths/binary_exp_mod.py
+
+  Explaination:
+    https://en.wikipedia.org/wiki/Exponentiation_by_squaring
+*/
+
+const modularBinaryExponentiation = (a, n, m) => {
+  // input: a: int, n: int, m: int
+  // returns: (a^n) % m: int
+  if (n === 0) {
+    return 1
+  } else if (n % 2 === 1) {
+    return (modularBinaryExponentiation(a, n - 1, m) * a) % m
+  } else {
+    const b = modularBinaryExponentiation(a, n / 2, m)
+    return (b * b) % m
+  }
+}
+
+const main = () => {
+  // binary_exponentiation(2, 10, 17)
+  // > 4
+  console.log(modularBinaryExponentiation(2, 10, 17))
+  // binary_exponentiation(3, 9, 12)
+  // > 3
+  console.log(modularBinaryExponentiation(3, 9, 12))
+}
+
+main()