# Write a Java program with functions for each of the following problems. Each problem should be solved by writing a recursive function. Your final program should not have any loops in it.

Recursion practice

Write a Java program with functions for each of the following problems. Each problem should be solved by writing a recursive function. Your final program should not have any loops in it.

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Write a Java program with functions for each of the following problems. Each problem should be solved by writing a recursive function. Your final program should not have any loops in it.
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All of your solutions should be in a single .java file. The main function of the file should demonstrate each of your solutions, by running several tests and producing the corresponding outputs.

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Write a recursive method to

1. calculate power of a give number

2. multiply m by n using only repeated addition

1. Implement recursive Fibonacci: Return the nth number in the Fibonacci sequence (5 points) a. Demonstrate by printing the first 10 numbers
2. Implement Euclid’s algorithm recursively.

a. Euclid’s algorithm to calculate the greatest common divisor of two positive integer

numbers a and b (gcd(a,b)) is recursively defined as:

gcd(a,b) := a if a = b

gcd(a,b) := gcd(a – b, b) if a > b

gcd(a,b) := gcd(a, b – a) if b > a

1. Return the length of a linked list
1. You will need to implement a simple link list
2. Include a length function that uses recursion to count the number of elements

In: Computer Science