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.
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
- Implement recursive Fibonacci: Return the nth number in the Fibonacci sequence (5 points) a. Demonstrate by printing the first 10 numbers
- 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
- Return the length of a linked list
- You will need to implement a simple link list
- Include a length function that uses recursion to count the number of elements
In: Computer Science