Hi friends, in this article we going to see how to remove the Nth node from end of the list. Here is our given problem,

Given a linked list, remove the *n*-th node from the end of list and return its head.

**Example:**

Given linked list:1->2->3->4->5, and. After removing the second node from the end, the linked list becomesn= 21->2->3->5.

**Note:**

Given *n* will always be valid.

**Follow up:**

Could you do this in one pass?

Before moving into the solution, I ask, you guys try to come up with your own approach. Take 5 to 10 minutes time, try to solve the problem.

If you really has done, I appreciate your work, you are great😇

#### Basic knowledge

#### How can we APPROACH this problem?

In our given question, they mentioned **Could you do this in one pass? **That is we have to solve this problem with O(n) time complexity.

### BEst way

**Slow and Fast Pointer Approach**

#### Do you know?

If you know Slow and Fast Pointer approach, you can able to solve most of the Linked List Problems easily.

See my previous articles, I have solved most of the linked list problems in O(n) time complexity with Slow and Fast pointer approach.

### Steps to Solve

```
Input:
head = 1->2->3->4->5->null
n = 2;
```

**Create a dummy newHead node**

```
ListNode newHead = new ListNode(0);
newHead = 0->null;
```

**Assign head, next to the newHead**

```
newHead.next = head;
newHead = 0>1->2->3->4->5->null;
```

**Assign newHead node to the fast and slow pointers**

```
ListNode fast = newHead;
fast = 0->1->2->3->4->5->null;
ListNode slow = newHead;
slow = 0->1->2->3->4->5->null;
```

**Now move fast pointer 0 to n positions, so that the gap between slow and fast becomes n**

```
while(n > 0)
{
fast = fast.next;
n--;
}
```

**In our case, n = 2**

```
Iteration first time, n = 2
fast = fast.next;
fast = 1->2->3->4->5->null;
n--;
n = 1;
Iteration second time, n = 1
fast = fast.next;
fast = 2->3->4->5->null;
n--;
n = 0;
Iteration third time, n = 0
Since n is equal to 0, it breaks and comes out of the while loop.
```

**Still now we have,**

```
fast = 2->3->4->5->null;
slow = 0->1->2->3->4->5->null;
```

We maintained a gap between fast and slow is n.

Now, move fast and slow pointer simultaneously, still fast.next becomes null;

It indicates that, when fast.next becomes null, slow pointer is standing infront of the nth node.

Therefore, slow.next = slow.next.next;

By assigning slow’s next’s next pointer to slow’s next, removes the nth node.

```
while(fast.next != null)
{
fast = fast.next;
slow = slow.next;
}
```

```
In our case,
fast = 2->3->4->5->null;
slow = 0->1->2->3->4->5->null;
```

```
Iteration first time, fast.next != null
fast = fast.next;
fast = 3->4->5->null;
slow = slow.next;
slow = 1->2->3->4->5->null;
Iteration second time, fast.next != null
fast = fast.next;
fast = 4->5->null;
slow = slow.next;
slow = 2->3->4->5->null;
Iteration third time, fast.next != null
fast = fast.next;
fast = 5->null;
slow = slow.next;
slow = 3->4->5->null;
Iteration fourth time, fast.next == null.
Breaks the condition, comes out of the while loop.
```

**Still now we have,**

```
fast = 5->null;
slow = 3->4->5->null;
```

```
slow.next = slow.next.next;
By assigning slow's next's next pointer to slow's next, removes the nth node.
slow = 3->5->null;
```

Hence, we remove the nth node.

**Already, slow pointer reference is with newHead.newHead = 0->1->2->3->5->null;**

When I return, newHead.next, I will get my desired list

## Solution

/** * Definition for singly-linked list. * public class ListNode { * int val; * ListNode next; * ListNode(int x) { val = x; } * } */ class Solution { public ListNode removeNthFromEnd(ListNode head, int n) { ListNode newHead = new ListNode(0); newHead.next = head; ListNode fast = newHead; ListNode slow = newHead; while(n > 0) { fast = fast.next; n--; } while(fast.next != null) { slow = slow.next; fast = fast.next; } slow.next = slow.next.next; return newHead.next; } }

**Time Complexity : O(n)**

**Space Complexity: O(1)**

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