Add Binary Exponentiation in math/

Add Binary Exponentiation in the math directory

math/binary_exponent.cpp

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+/// C++ Program to find Binary Exponent Iteratively and Recursively.
+
+#include<iostream>
+/*
+ * Calculate a^b in O(log(b)) by converting b to a binary number.
+ * Binary exponentiation is also known as exponentiation by squaring.
+ * NOTE : This is a far better approach compared to naive method which provide O(b) operations.
+ * Example:
+ * 10 in base 2 is 1010.
+ * 2^10 = 2^(1010) = 2^8 * 2^2
+ * 2^1 = 2
+ * 2^2 = (2^1)^2 = 2^2 = 4
+ * 2^4 = (2^2)^2 = 4^2 = 16
+ * 2^8 = (2^4)^2 = 16^2 = 256
+ * Hence to calculate 2^10 we only need to multiply 2^8 and 2^2 skipping 2^1 and 2^4.
+*/
+
+/// Recursive function to calculate exponent in O(log(n)) using binary exponent.
+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;
+    }
+}
+
+/// Iterative function to calculate exponent in O(log(n)) using binary exponent.
+int binExpo_alt(int a, int b) {
+    int res = 1;
+    while (b > 0) {
+        if (b%2) {
+            res = res*a;
+        }
+        a = a*a;
+        b /= 2;
+    }
+    return res;
+}
+
+int main() {
+    int a, b;
+    /// Give two numbers a, b
+    std::cin >> a >> b;
+    if (a == 0 && b == 0) {
+        std::cout << "Math error" << std::endl;
+    } else if (b < 0) {
+        std::cout << "Exponent must be positive !!" << std::endl;
+    } else {
+        int resRecurse = binExpo(a, b);
+        /// int resIterate = binExpo_alt(a, b);
+
+        /// Result of a^b (where '^' denotes exponentiation)
+        std::cout << resRecurse << std::endl;
+        /// std::cout << resIterate << std::endl;
+    }
+}