Remove Nth Node from End of List in DSA Go - Time & Space Complexity

Time Complexity: Remove Nth Node from End of List

O(n)

Understanding Time Complexity

We want to understand how the time needed to remove the nth node from the end of a linked list changes as the list grows.

Specifically, how many steps does the program take when the list gets bigger?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

func removeNthFromEnd(head *ListNode, n int) *ListNode {
    dummy := &ListNode{Next: head}
    first, second := dummy, dummy
    for i := 0; i <= n; i++ {
        first = first.Next
    }
    for first != nil {
        first = first.Next
        second = second.Next
    }
    second.Next = second.Next.Next
    return dummy.Next
}
    

This code removes the nth node from the end of a singly linked list by using two pointers moving through the list.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Two loops that move pointers through the list.
• How many times: The first loop runs n+1 times; the second loop runs (length of list - n - 1) times.

How Execution Grows With Input

As the list gets longer, the total steps grow roughly in a straight line with the list size.

Input Size (n)	Approx. Operations
10	About 10 steps
100	About 100 steps
1000	About 1000 steps

Pattern observation: The steps increase directly with the list size, so doubling the list roughly doubles the work.

Final Time Complexity

Time Complexity: O(n)

This means the time to remove the nth node from the end grows linearly with the list size.

Common Mistake

[X] Wrong: "Because we only move pointers a few times, the time is constant O(1)."

[OK] Correct: The loops move through the list nodes, so the number of steps depends on the list length, not fixed.

Interview Connect

Understanding this linear time complexity helps you explain why two-pointer techniques are efficient for linked lists and shows your grasp of pointer traversal.

Self-Check

"What if we used a single pass with extra memory to store nodes? How would the time complexity change?"

Practice

1. What does the problem "Remove Nth Node from End of List" ask you to do with a linked list?

easy

A. Reverse the linked list

B. Add a new node at the Nth position from the start

C. Remove the node that is the Nth from the end of the list

D. Find the value of the Nth node from the start

Solution

1. Step 1: Understand the problem statement

   The problem requires removing the node that is Nth from the end, not from the start or adding nodes.

2. Step 2: Clarify the operation on the linked list

   We must delete the node counting from the end, which is different from reversing or finding a value.

3. Final Answer:

   Remove the node that is the Nth from the end of the list -> Option C

4. Quick Check:

   Remove Nth from end = Remove Nth node from end [OK]

Hint: Focus on 'Nth from end' means counting backwards [OK]

Common Mistakes:

• Confusing Nth from end with Nth from start
• Thinking the problem asks to add nodes
• Assuming the list should be reversed

2. Which of the following Go code snippets correctly declares a singly linked list node struct for this problem?

easy

A. type ListNode struct { Val int; Next *ListNode }

B. type ListNode struct { Value int; NextNode *ListNode }

C. struct ListNode { int Val; ListNode* Next; }

D. class ListNode { int Val; ListNode Next; }

Solution

1. Step 1: Identify Go struct syntax

   In Go, structs use 'type Name struct { fields }' and pointers use '*Type'.

2. Step 2: Match correct field names and types

   type ListNode struct { Val int; Next *ListNode } uses 'Val int' and 'Next *ListNode' which is the standard for singly linked list nodes in Go.

3. Final Answer:

   type ListNode struct { Val int; Next *ListNode } -> Option A

4. Quick Check:

   Go struct with pointer field = type ListNode struct { Val int; Next *ListNode } [OK]

Hint: Go structs use 'type' and pointers with '*' [OK]

Common Mistakes:

• Using C/C++ or Java syntax in Go code
• Missing pointer '*' for Next field
• Incorrect field names or types

3. What will be the linked list after removing the 2nd node from the end in this list: 1 -> 2 -> 3 -> 4 -> 5 -> null?

medium

A. 1 -> 3 -> 4 -> 5 -> null

B. 1 -> 2 -> 3 -> 5 -> null

C. 1 -> 2 -> 4 -> 5 -> null

D. 2 -> 3 -> 4 -> 5 -> null

Solution

1. Step 1: Identify the 2nd node from the end

   Counting from the end: 5 (1st), 4 (2nd). So node with value 4 is to be removed.

2. Step 2: Remove node with value 4 and link previous node to next

   Node 3's next should point to node 5, skipping node 4.

3. Final Answer:

   1 -> 2 -> 3 -> 5 -> null -> Option B

4. Quick Check:

   Remove 2nd from end (4) = 1->2->3->5 [OK]

Hint: Count nodes from end to find which to remove [OK]

Common Mistakes:

• Removing the wrong node counting from start
• Breaking links incorrectly causing list corruption
• Off-by-one errors in counting nodes

4. Given this Go function snippet to remove the Nth node from end, what is the bug?

func removeNthFromEnd(head *ListNode, n int) *ListNode {
    dummy := &ListNode{0, head}
    first, second := dummy, dummy
    for i := 0; i < n; i++ {
        first = first.Next
    }
    for first.Next != nil {
        first = first.Next
        second = second.Next
    }
    second.Next = second.Next.Next
    return head
}

medium

A. Missing check for empty list before loops

B. The loop runs n times instead of n+1 times

C. second pointer is not initialized correctly

D. Returns head instead of dummy.Next, so removal of first node fails

Solution

1. Step 1: Understand dummy node usage

   Dummy node helps handle edge cases like removing the first node. The result list starts at dummy.Next.

2. Step 2: Check return statement

   Returning 'head' ignores changes if first node was removed. Should return dummy.Next instead.

3. Final Answer:

   Returns head instead of dummy.Next, so removal of first node fails -> Option D

4. Quick Check:

   Return dummy.Next to handle first node removal [OK]

Hint: Always return dummy.Next after removal [OK]

Common Mistakes:

• Returning original head ignoring dummy node
• Not using dummy node for edge cases
• Incorrect loop bounds causing panic

5. You have a linked list: 10 -> 20 -> 30 -> 40 -> 50 -> null. You want to remove the 5th node from the end. What will be the resulting list?

hard

A. 20 -> 30 -> 40 -> 50 -> null

B. 10 -> 20 -> 30 -> 40 -> null

C. 10 -> 20 -> 30 -> 40 -> 50 -> null

D. 30 -> 40 -> 50 -> null

Solution

1. Step 1: Identify the 5th node from the end

   The list length is 5, so the 5th from end is the first node with value 10.

2. Step 2: Remove the first node and link dummy to second node

   Removing node 10 means the new head is node 20, so list becomes 20 -> 30 -> 40 -> 50 -> null.

3. Final Answer:

   20 -> 30 -> 40 -> 50 -> null -> Option A

4. Quick Check:

   Remove 5th from end (first node) = 20->30->40->50 [OK]

Hint: Nth from end equals list length means remove head [OK]

Common Mistakes:

• Removing wrong node when N equals list length
• Not updating head pointer after removal
• Confusing node positions counting from start vs end