C++ Program to find Binary Exponent Iteratively and Recursively. More...

#include <iostream>

Include dependency graph for binary_exponent.cpp:

Functions
int	binExpo (int a, int b)

int	binExpo_alt (int a, int b)

int	main ()
	Main function.

Detailed Description

C++ Program to find Binary Exponent Iteratively and Recursively.

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.

\begin{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\\ \end{eqnarray*}

Hence to calculate 2^10 we only need to multiply \(2^8\) and \(2^2\) skipping \(2^1\) and \(2^4\).

Function Documentation

◆ binExpo()

int binExpo	(	int	a,
		int	b )

Recursive function to calculate exponent in \(O(\log(n))\) using binary exponent.

                          {
    if (b == 0) {
        return 1;
    }
    int res = binExpo(a, b / 2);
    if (b % 2) {
        return res * res * a;
    } else {
        return res * res;
    }
}

Here is the call graph for this function:

◆ binExpo_alt()

int binExpo_alt	(	int	a,
		int	b )

Iterative function to calculate exponent in \(O(\log(n))\) using binary exponent.

                              {
    int res = 1;
    while (b > 0) {
        if (b % 2) {
            res = res * a;
        }
        a = a * a;
        b /= 2;
    }
    return res;
}

◆ main()

int main ( void )

Main function.

Give two numbers a, b

int resIterate = binExpo_alt(a, b);

Result of a^b (where '^' denotes exponentiation)

std::cout << resIterate << std::endl;