The previous linked list has a forward link only. Thus, at any point we can find out what the next node is with relative ease but to find the previous node, you would need to start at the beginning and search for a node who's next pointer has the same value as curr_.
One improvement that you could make to your list is to create a doubly linked list. A doubly linked list is a linked list where every node has both a forward and backwards
The advantage of a doubly linked list
No need to search entire list to find previous pointer