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Question: 1. Write each of the following recursive methods and for each one, write a main method to test it...

1. Write each of the following recursive methods and for each one, write a main method to
test it.

(i) public static double betterPower(double x, int n)
This is an improved version of the power method that takes advantage of the following
properties:
xn = xn/2 * xn/2 for even values of n
xn = x * xn/2 * xn/2 for odd values of n

Explanation / Answer

public class BetterPower { public static double betterPower(double x, int n) { if(n == 0) { return 1; } else { double res = betterPower(x, n/2); if(n % 2 == 0) { return res * res; } else { return res * res * x; } } } public static void main(String[] args) { System.out.println(betterPower(2, 10)); System.out.println(betterPower(3, 3)); } }

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