In Java

1. Create a class Point with coordinate (x, y, z). Calculate the distance between two points p1 and p2 by using the class Point. (30 pts)

2. Write a method that accepts two arguments into the parameters x and y. Assume x and y hold positive nonzero integers, the method should return the value of x times y. Multiplication can be performed as repeated addition as follows: 5 6 = 6 + 6 + 6 + 6 + 6

a. Solve the problem by using recursion and recursion with memoization

b. Analyze the time and space complexity of each solution. (20 pts)

Ackermanns Function is a recursive mathematical algorithm that can be used to test how well a system optimizes its performance of recursion. The two-argument Ackermanns function, is defined as follows for nonnegative integers m and n:

a. Given the arguments m and n, write a method that solves the Ackermanns function by using Recursion

b. Given the arguments m and n, write a method that solves the Ackermanns function by using Recursion with memoization

c. Analyze the time and space complexity of each method.