$.(30$ marks$)$ Given an array A of n elements that are integers from $0$ to n$-1,$ with any

of these numbers appearing any number of times.

$($a$)(10$ marks$)$ Design an algorithm that finds the repeating numbers in A$.$ For

example, let n be $7$ and array A be $1,2,3,1,3,6,6,$ the answer should be $1,3$

and $6.$ Give the pseudo code description of your algorithm and analyze its time

complexity.

$($b$)(10$ marks$)$ Implement your algorithm using Java. Your program takes any sequence of numbers as the input, outputs the repeating number$($s$).$

$($c$)(10$ marks$)$ Design an efficient algorithm for this task with time complexity O$($n$)$

and space complexity O$(1).$