## Solution

#### Approach 1: Two pass algorithm

Intuition

We notice that the problem could be simply reduced to another one : Remove the th node from the beginning in the list , where is the list length. This problem is easy to solve once we found list length .

Algorithm

First we will add an auxiliary "dummy" node, which points to the list head. The "dummy" node is used to simplify some corner cases such as a list with only one node, or removing the head of the list. On the first pass, we find the list length . Then we set a pointer to the dummy node and start to move it through the list till it comes to the th node. We relink next pointer of the th node to the th node and we are done.

Figure 1. Remove the L - n + 1 th element from a list.

Complexity Analysis

• Time complexity : .

The algorithm makes two traversal of the list, first to calculate list length and second to find the th node. There are operations and time complexity is .

• Space complexity : .

We only used constant extra space.

#### Approach 2: One pass algorithm

Algorithm

The above algorithm could be optimized to one pass. Instead of one pointer, we could use two pointers. The first pointer advances the list by steps from the beginning, while the second pointer starts from the beginning of the list. Now, both pointers are exactly separated by nodes apart. We maintain this constant gap by advancing both pointers together until the first pointer arrives past the last node. The second pointer will be pointing at the th node counting from the last. We relink the next pointer of the node referenced by the second pointer to point to the node's next next node.

Figure 2. Remove the nth element from end of a list.

Complexity Analysis

• Time complexity : .

The algorithm makes one traversal of the list of nodes. Therefore time complexity is .

• Space complexity : .

We only used constant extra space.