added binary_exponent.cpp

math/binary_exponent.cpp

@@ -0,0 +1,25 @@
+/// C++ Program to find Binary Exponent recursively.
+
+#include<iostream>
+/*
+ * Calculating a^b in O(log(b)) by converting b in binary no.
+ * Binary exponentiation (also known as exponentiation by squaring)
+ * is a trick which allows to calculate an using only O(logn) multiplications
+ * (instead of O(n) multiplications required by the naive approach).
+*/
+
+int binExpo(int a,int b) {
+    if (b == 0) return 1;
+    int res = binExpo(a,b/2);
+    if (b%2) return res*res*a;
+    else return res*res;
+}
+
+int main() {
+    int a,b;
+    /// Give two nos as a^b (where '^' denotes power exponent operation
+    std::cin >> a >> b;
+    ///Result of a^b
+    std::cout << binExpo(a,b) << endl;
+}
+