n-th last element in the list

Given a singly linked list, find n-th element from the last.

The most obvious way is to traverse the list once and get its length say L. Then traverse again first L-n nodes to get to the n-th last node. This is linear in complexity but we need to traverse the list twice. Can we eliminate this?

We can, using extra pointer. Let's have a pointer to the list say *first and one more say *second. We traverse the list using *first till n nodes are traversed. Now imagine that at this moment we start traversing the list with second pointer, say *second. Then, by the time *first reaches towards the end of the list, *second will fall short by n nodes from the end of the list. That's precisely the node we want - n-th node from the end. So the solution is clear. After *first reaches the n-th node, start traversing with *second and continuing with *first till *first reached the last node.

Note: This will take care of the error in input when n > length of the list as *first will reach NULL sooner than expected.