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Complete the following exercises:

1) prepare a function that uses recursion that converts a decimal number to octal (base 8). The function should accept a single integer and return a String containing the base 8 equivalent.

2) prepare a recursive function that implement the following functions:

a)  x0 = 1
xn = x * xn-1 if n > 0

b) x0 = 1
xn = (xn/2)2 if n > 0 and n is even
xn = x * (xn/2)2 if n> 0 and n is odd

3) How many multiplications will the functions you wrote in problem 2 perform when computing 319? 332?
How many recursive calls will the functions make when computing 319? 332?

4) prepare a recursive function that implements the following function:
f(1) = 1; f(2) = 1; f(3) = 1; f(4) = 3; f(5) = 5
f(n) = f(n-1) + 3 * f(n-5) for all n > 5

Make the function as efficient as possible.

5) Compute f(n) for n = 6, 7, 12, 15

Java, Programming

• Category:- Java
• Reference No.:- M9995

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