Delete Node at End in DSA C++ - Time & Space Complexity

Time Complexity: Delete Node at End

O(n)

Understanding Time Complexity

We want to understand how long it takes to remove the last node from a linked list.

How does the time needed change as the list gets bigger?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

void deleteAtEnd(Node*& head) {
    if (head == nullptr) return;
    if (head->next == nullptr) {
        delete head;
        head = nullptr;
        return;
    }
    Node* temp = head;
    while (temp->next->next != nullptr) {
        temp = temp->next;
    }
    delete temp->next;
    temp->next = nullptr;
}
    

This code removes the last node from a singly linked list by walking through the list to find the second last node.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The while loop that moves through nodes to find the second last node.
• How many times: It runs once for each node except the last two, so roughly n-2 times for a list of size n.

How Execution Grows With Input

As the list gets longer, the loop runs more times, almost one time per node.

Input Size (n)	Approx. Operations
10	About 8 steps
100	About 98 steps
1000	About 998 steps

Pattern observation: The number of steps grows roughly in a straight line with the size of the list.

Final Time Complexity

Time Complexity: O(n)

This means the time to delete the last node grows directly with the number of nodes in the list.

Common Mistake

[X] Wrong: "Deleting the last node is always quick because it's just one node."

[OK] Correct: You must find the node before the last one, which takes time proportional to the list size.

Interview Connect

Understanding this helps you explain how linked lists work and why some operations take longer than others.

Self-Check

"What if the list had a tail pointer that points directly to the last node? How would the time complexity change?"

Practice

1. What happens when you delete the last node in a singly linked list?

easy

A. The second last node's next pointer becomes null

B. The head pointer is set to null

C. The first node is deleted instead

D. All nodes are deleted

Solution

1. Step 1: Understand the linked list structure

   Each node points to the next node. The last node points to null.

2. Step 2: Effect of deleting the last node

   Deleting the last node means the previous node's next pointer must be set to null to mark new end.

3. Final Answer:

   The second last node's next pointer becomes null -> Option A

4. Quick Check:

   Last node removed, previous node points to null [OK]

Hint: Last node removal sets previous node's next to null [OK]

Common Mistakes:

• Setting head to null incorrectly
• Deleting the first node instead
• Not updating the previous node's next pointer

2. Which of the following is the correct syntax to delete the last node in a singly linked list in C++?

easy

A. delete lastNode->prev; lastNode->prev = nullptr;

B. delete lastNode; lastNode = nullptr;

C. delete head; head = nullptr;

D. delete lastNode->next; lastNode->next = nullptr;

Solution

1. Step 1: Identify the last node's pointer

   In singly linked list, last node's previous node points to it via next pointer.

2. Step 2: Delete last node and update pointer

   Deleting lastNode->next and setting lastNode->next to nullptr correctly removes last node.

3. Final Answer:

   delete lastNode->next; lastNode->next = nullptr; -> Option D

4. Quick Check:

   Delete next node and set pointer null [OK]

Hint: Delete node via previous node's next pointer [OK]

Common Mistakes:

• Deleting head instead of last node
• Using prev pointer in singly linked list
• Not setting pointer to nullptr after delete

3. What will be the output linked list after deleting the last node from the list: 10 -> 20 -> 30 -> 40 -> null?

medium

A. 10 -> 20 -> null

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

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

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

Solution

1. Step 1: Identify the last node

   The last node is 40, which points to null.

2. Step 2: Remove last node and update previous node

   Deleting 40 means 30's next pointer becomes null, ending list at 30.

3. Final Answer:

   10 -> 20 -> 30 -> null -> Option B

4. Quick Check:

   Last node 40 removed, list ends at 30 [OK]

Hint: Last node removed, previous node points to null [OK]

Common Mistakes:

• Not updating previous node's next pointer
• Deleting head node by mistake
• Outputting original list without deletion

4. Given the code snippet below, what is the error when deleting the last node?

struct Node {
  int data;
  Node* next;
};

void deleteLast(Node*& head) {
  if (head == nullptr) return;
  Node* temp = head;
  while (temp->next != nullptr) {
    temp = temp->next;
  }
  delete temp;
  temp = nullptr;
}

medium

A. Uses wrong pointer type for deletion

B. Deletes head node instead of last node

C. Does not update previous node's next pointer to null

D. No error, code works correctly

Solution

1. Step 1: Analyze traversal to last node

   The loop moves temp to last node, but does not track previous node.

2. Step 2: Identify missing pointer update

   Deleting temp frees last node but previous node's next still points to freed memory, causing dangling pointer.

3. Final Answer:

   Does not update previous node's next pointer to null -> Option C

4. Quick Check:

   Previous node's next must be null after deletion [OK]

Hint: Track previous node to update next pointer before delete [OK]

Common Mistakes:

• Not tracking previous node in traversal
• Deleting node without updating links
• Setting temp to nullptr does not fix list

5. You have a singly linked list with only one node. What should happen when you delete the last node?

hard

A. Set head pointer to null

B. Set node's next pointer to null

C. Delete node but keep head pointing to it

D. Do nothing, list remains same

Solution

1. Step 1: Identify single node list condition

   Only one node means head points to that node and node's next is null.

2. Step 2: Delete node and update head

   Deleting the only node requires setting head to null to mark empty list.

3. Final Answer:

   Set head pointer to null -> Option A

4. Quick Check:

   Single node deleted means empty list head = null [OK]

Hint: Single node deletion empties list, head = null [OK]

Common Mistakes:

• Not setting head to null after deletion
• Trying to update next pointer of deleted node
• Leaving dangling pointer in head