Implement a set-like data structure that supports Insert, Remove, and GetRandomElement efficiently. Example: If you insert the elements 1, 3, 6, 8 and remove 6, the structure should contain [1, 3, 8]. Now, GetRandom should return one of 1, 3 or 8 with equal probability

setLikeDS.java

public class SetLikeDS {
	private List<Integer> list;	
	private Map<Integer, Integer> map;
	
	public SetLikeDS() {
		list = new ArrayList<>();
		map = new HashMap<>();
	}
	
	public void insert(int num) {
		if (!map.containsKey(num)) { //insert if not present only, set-like
			list.add(num); //O(1) as adding at end
			int index = list.size()-1;
			map.put(num, index); //O(1)
		}
	}
	
	public void remove(int num) {
		if (map.containsKey(num)) { //can remove if present only					
      			int index = map.get(num); //O(1)			
			int last = list.get(list.size()-1); //O(1) as accessing at known index
			list.set(index, last); //O(1) as replacing at and from known indices
			list.remove(list.size()-1); //O(1) as removing last element	
			map.remove(num); //O(1)
			map.put(last, index); //update index
		}
	}

	public int getRandom() {
		int rand = ThreadLocalRandom.current().nextInt(0, list.size()); //0 and list.size()-1 should both be inclusive
		return list.get(rand); //O(1) as accessing at known index
	}
}

For the remove(), I feel your implementation is incomplete. I modified your code to loop trough all items after the the item that is to be deleted, and update their indexes in the HashMap

	public void remove(int num) {
		if (map.containsKey(num)) { //can remove if present only					
      		       int index = map.get(num); //O(1)	
                       for( int i = index + 1; i < list.size(); i++){ // int i = index + 1  // I added one so as to not update the index of the item that is about to be deleted
                             int itemKey = list.get(i);
                             int newIndex =  i -1;
                             map.set(itemKey, newIndex);
                       }
                       list.remove(i);
                       map.remove();
                      
		}
	}

What do you think?

Your loop helps move all the elements after the removed element but the requirement doesn't state that all the elements should be moved.