1. Write each of the following recursive methods and for each one, write a main
ID: 3918878 • Letter: 1
Question
1. Write each of the following recursive methods and for each one, write a main method to test it.
public static int sumCubes(int n):Returns the sum of the sequence: 13 + 23 + 33+ …. + n3
public static double betterPower(double x, int n) :This is an improved version of the power method that takes advantage of the following properties: x n = xn/2 * xn/2 for even values of n x n = x * xn/2 * xn/2 for odd values of n
public static int GCD(int n, int m) :Returns the Greatest Common Divisor (GCD) of two numbers n and m, define as follows:
if ,11 11 and 11 mod m = 0 GCD(n, m ) = if nExplanation / Answer
public class power {
public static void main(String args[]) {
System.out.print(sumCubes(5));
System.out.println(power_value(4,5));
System.out.println(GCD(24,16));
}
public static int sumCubes(int n) {
if(n==0)return 0;
return (n*10)+3+sumCubes(n-1);
}
public static double power_value(double x,int n) {
if(n==0)return 1;
if(n%2==0)return power_value(x,n/2)*power_value(x,n/2);
return x*power_value(x,n/2)*power_value(x,n/2);
}
public static int GCD(int a,int b) {
if(a%b==0)return b;
if(b%a==0)return a;
if(a>b)return GCD(a%b,b);
return GCD(a,b%a);
}
}
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