Question

What is the recurrence of the power2() function? What is its running time? Is it faster than the iterative way?

int power(int base, int n)
{
        int result = 1;
        for (int i = 1; i <= n; i++)
        {
                result *= base;
        }
        return result;
}

int power2(int base, int n)
{
        int result;

        if (n == 0)
                return 1;

        if (n % 2 == 0) // 3^10
        {
                result = power2(base, n / 2); // 3^5
                return result * result; // 3^5 * 3^5 
        }
        else // 3^11
        {
                result = power2(base, n / 2); // 3^5
                return result * result * base; // 3^5 * 3^5 * 3
        }
}

Answer 1