From 70ac13f4a0fc15f987d3874112dfdeab0af388ac Mon Sep 17 00:00:00 2001
From: Mann Mehta <44433995+mann2108@users.noreply.github.com>
Date: Thu, 2 Apr 2020 04:03:22 +0530
Subject: [PATCH] added binary_exponent.cpp

---
 math/binary_exponent.cpp | 25 +++++++++++++++++++++++++
 1 file changed, 25 insertions(+)
 create mode 100644 math/binary_exponent.cpp

diff --git a/math/binary_exponent.cpp b/math/binary_exponent.cpp
new file mode 100644
index 000000000..0f9d442a5
--- /dev/null
+++ b/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;
+}
+