Time complexity in terms of big O for a reverse vector

Question

template <typename T>
void reverseVector(vector<T> &vec, int start, int end) {
   if(start < end) {
       char temp = vec[start];
       vec[start] = vec[end];
       vec[end] = temp; 
       reverseVector(vec, start + 1, end – 1); }
   }
}

Assuming N = vec.size() what would be the time complexity of this method?

Assuming I am correct, a getting and setting a vector has time O(1). Thus, the first 3 lines in the if statement are all O(1) each. Then, the method recursively calls itself and each time the function becomes smaller, iterating n(n-1)(n-2)... times. So my answer would be O(n!) for this method. Am I correct?

edit: similar syntax, but with linked list

template <typename T>
void reverseLinkedList(list<T> &lst, int start, int end) {
  if(start < end) {
    char temp = lst[start];
    lst[start] = lst[end];
    lst[end] = temp;
    reverseLinkedList(lst, start + 1, end – 1);
  }
}

Answer 1

That is O(n) .

You swap elements n/2 times: (0 with n-1), (1 with n-2), ... (n/2 - 1 with n/2 + 1)