Implement a custom list with iterator and map

You are asked to implement a simple generic list type without using any built-in collection classes (e.g., no ArrayList, LinkedList, Vector, etc.). You may use primitive arrays / custom nodes.

Part 1 — Implement a List

Design and implement MyList<T> with at least the following operations:

• void add(T value)
• T get(int index)
• void set(int index, T value) (or return a new value)
• T remove(int index)
• int size()

Requirements:

• Handle invalid indices (define behavior: throw an exception or return a sentinel).
• Aim for reasonable time complexity (state your choice of underlying structure: dynamic array or linked list).

Part 2 — Implement an Iterator

Extend MyList<T> so it is iterable.

• Implement an iterator type with standard iterator methods (e.g., hasNext() and next() ; optionally remove() if you support it).
• The iterator should traverse the list from index 0 to size()-1 .

Part 3 — Implement a map function

Add a map-style higher-order function:

• MyList<R> map(Function<T, R> f) (or equivalent in your language)

It should:

• Apply f to each element in order
• Return a new MyList<R> containing the mapped results
• Not modify the original list

Clarifications

• Assume single-threaded use.
• You may assume elements can be null unless you choose to forbid it (but document your choice).