What is the difference between O (N) + O (M) and O (N + M). Whether there is a?

Question

I solve problems for the practice of interviewing, and I cannot figure out how to answer the complexity of time and space of the following problem:

Given two sorted linked lists, combine them into a third list in sorted order. Suppose we use a descending ordering.

One of the answers I came across that is clearly not the most efficient is the following recursive solution:

Node mergeLists(Node head1, Node head2) {
    if (head1 == null) {
        return head2;
    } else if (head2 == null) {
        return head1;
    }

    Node newHead = null;
    if(head1.data < head2.data) {
        newHead = head1;
        newHead.next = mergeLists(head1.next, head2);
    } else {
        newHead = head2;
        newHead.next = mergeLists(head1, head2.next);
    }

    return newHead;
}

, , . , O(M + N) O(M) + O(N). . , O(N) + O(M) O(max(N,M)), ( ).

:

, O(N+M) O(N) + O(M)? -? , , - .

Answer 1

O(N) + O(M) , cN + dM c d.

O(N + M) , e(N + M) e.

, :

cN + dM <= (c + d)(N + M) c d.

e(N + M) <= eN + eM e.