README.md

Remove Nth Node From End of List

Question:

Given the head of a linked list, remove the nth node from the end of the list and return its head.

How to Solve:

The intuitive approach (O(2n)) is to find the length (size) of the linked list first with a single pass. Then we locate the node to remove by going again from the start to size - n - 1. We reroute the node's next to next's next, and return head.

The better approach (O(1n)) is an optimized version of the first, and requires only one pass in total. We maintain two pointers moving at the same speed except with different head-starts. The first one starts at the nth nodes from the start, and the second one starts normally at the beginning of the list. When the first pointer reaches the end, the second one must land on the node to remove (i.e. the nth node from the end), since we have maintained the same distance between the two pointers all along. The tricky thing about this approach is that we need to create a dummy pointer that points to head, because we might need to remove the head node. We need the 2 pointers to start "one step before" the head.

The code below implements the second approach.

My C++ Solution:

class Solution {
 public:
  ListNode *removeNthFromEnd(ListNode *head, int n) {
    auto sentinel = make_unique<ListNode>(0, head);
    auto ptr1 = sentinel.get(), ptr2 = sentinel.get();
    for (int i = 0; i <= n; ++i) {
      ptr1 = ptr1->next;
    }
    while (ptr1) {
      ptr1 = ptr1->next;
      ptr2 = ptr2->next;
    }
    ptr2->next = ptr2->next->next;
    return sentinel->next;
  }
};