// 1A
function compute_e(lst) {
    function helper_acc(xs, n, current){
        if(is_empty_list(xs)) {
            return current;
        } else {
            if (n % 2 === 0){
                return helper_acc(tail(xs), n + 1, current + head(xs)); //if index is even (so number is at odd i), just add it to the sum
            } else {
                return helper_acc(tail(xs), n + 1, current + head(xs) * 3); //if index is odd (so number is at even i), multiply by 3 and then add to sum
            }
        }
    }
    const result = helper_acc(lst, 0, 0); //this gives the sum with weights
    return result % 10; //returns remainder upon division by 10.
}

compute_e(list(4,9,2,7,1,8,2,0,9,3,7,5)); //returns 1.

//1B

function add_e(lst) {
    return append(lst, list(compute_e(lst)));
}

//1C
function get_index_of_largest(is, current_index, largest_so_far, index_of_largest_so_far){
  if(is_empty_list(is)){
    return index_of_largest_so_far;
  } else {
    if (head(is) > largest_so_far){
      return get_index_of_largest(tail(is), current_index + 1, head(is), current_index);
    } else {
      return get_index_of_largest(tail(is), current_index + 1, largest_so_far, index_of_largest_so_far);
    }
  }
}

function index_of_largest(is) {
    return get_index_of_largest(is, 0, -Infinity, NaN);
}

index_of_largest(list(42,34,65,22,5,19)); //returns 2

//2A

function get_index_of_largest(is, current_index, largest_so_far, index_of_largest_so_far){
  if(is_empty_list(is)){
    return index_of_largest_so_far;
  } else {
    if (head(is) > largest_so_far){
      return get_index_of_largest(tail(is), current_index + 1, head(is), current_index);
    } else {
      return get_index_of_largest(tail(is), current_index + 1, largest_so_far, index_of_largest_so_far);
    }
  }
}

function index_of_largest(is) {
    return get_index_of_largest(is, 0, -Infinity, NaN);
}

index_of_largest(list(42,34,65,22,5,19)); //returns 2

//2B

function remove_specified_element_from_tail(lst, n){
  if(length(lst) < n + 2) {
    return NaN;
  } else {
    const result = list_ref(tail(lst), n);//index of largest element specified in args
    const new_list = remove(result, tail(lst));//removes all elements that are equal to that element
    set_tail(lst, new_list);//mutate original list to set its tail to the new list
    return result;
  }
}

var example1 = list(1,2,3,4,5,6);
remove_specified_element_from_tail(example1 , 3);
example1;