documetnation for binary_exponent.cpp

math/binary_exponent.cpp

@@ -1,46 +1,57 @@
-/// 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.
+/**
+ * @file
+ * @brief C++ Program to find Binary Exponent Iteratively and Recursively.
+ *
+ * Calculate \f$a^b\f$ in \f$O(\log(b))\f$ by converting \f$b\f$ 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 \f$O(b)\f$ 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.
-*/
+ * </br>10 in base 2 is 1010.
+ * \f{eqnarray*}{
+ * 2^{10_d} &=& 2^{1010_b} = 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\\
+ * \f}
+ * Hence to calculate 2^10 we only need to multiply \f$2^8\f$ and \f$2^2\f$
+ * skipping \f$2^1\f$ and \f$2^4\f$.
+ */
 
-/// Recursive function to calculate exponent in O(log(n)) using binary exponent.
+#include <iostream>
+
+/// Recursive function to calculate exponent in \f$O(\log(n))\f$ 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;
+    int res = binExpo(a, b / 2);
+    if (b % 2) {
+        return res * res * a;
     } else {
-        return res*res;
+        return res * res;
     }
 }
 
-/// Iterative function to calculate exponent in O(log(n)) using binary exponent.
+/// Iterative function to calculate exponent in \f$O(\log(n))\f$ using binary
+/// exponent.
 int binExpo_alt(int a, int b) {
     int res = 1;
     while (b > 0) {
-        if (b%2) {
-            res = res*a;
+        if (b % 2) {
+            res = res * a;
         }
-        a = a*a;
+        a = a * a;
         b /= 2;
     }
     return res;
 }
 
+/// Main function
 int main() {
     int a, b;
     /// Give two numbers a, b