C-Plus-Plus/math/binary_exponent.cpp

///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).
*/

///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;
}

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) << std::endl;
}