Power
Details
Write the recursive function power(int base, int exponent), that returns base raised to the exponent power.
Example
The function calls:
power(2, 2)
power(2, 3)
power(2, 10)
power(3, 3)Would produce the output:
4
8
1024
27More Power
Details
Write the recursive function more_power(int base, int exponent) again. This time use the following recursive definition:
\(x^1 = x\)
\(x^y = x^{y / 2} \cdot x^{y / 2}\) (if y is even and greater than 1)
\(x^y = x \cdot x^{(y - 1) / 2} \cdot x^{(y - 1) / 2}\) (if y is odd and greater than 2)
Example
The function calls:
more_power(2, 2)
more_power(2, 3)
more_power(2, 10)
more_power(3, 3)Would produce the output:
4
8
1024
27Even More Power
Details
Modify both of your power functions so that they print multiply every time they perform a multiplication. If they multiply twice on one line, they should print multiply twice.
Count the number of times that each function multiplies when you call them with an exponent of 4. If the more_power function doesn’t print multiply fewer times, fix it so that it does.
Example
The function calls:
std::cout << power(2, 10) << std::endl;
std::cout << "-----------------" << std::endl;
std::cout << more_power(2, 10) << std::endl;Would produce the output:
multiply
multiply
multiply
multiply
multiply
multiply
multiply
multiply
multiply
1024
---------
multiply
multiply multiply
multiply
1024