Delete from Beginning of Doubly Linked List in DSA Go - Time & Space Complexity

Time Complexity: Delete from Beginning of Doubly Linked List

O(1)

Understanding Time Complexity

We want to understand how long it takes to remove the first item from a doubly linked list.

How does the time needed change when the list grows bigger?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

// Node represents a doubly linked list node
 type Node struct {
     data int
     prev *Node
     next *Node
 }

// DeleteFromBeginning removes the first node
 func DeleteFromBeginning(head **Node) {
     if *head == nil {
         return
     }
     *head = (*head).next
     if *head != nil {
         (*head).prev = nil
     }
 }

This code removes the first node from a doubly linked list by updating the head pointer and adjusting links.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Updating pointers of the first node and head reference.
• How many times: This happens only once per deletion, no loops or recursion.

How Execution Grows With Input

Removing the first node always takes the same steps, no matter how big the list is.

Input Size (n)	Approx. Operations
10	5
100	5
1000	5

Pattern observation: The number of steps stays constant as the list grows.

Final Time Complexity

Time Complexity: O(1)

This means deleting the first node takes the same amount of time no matter how large the list is.

Common Mistake

[X] Wrong: "Deleting the first node takes longer if the list is bigger because we have to check all nodes."

[OK] Correct: We only change a few pointers at the start, so the list size does not affect the time.

Interview Connect

Knowing that deleting from the start of a doubly linked list is quick helps you explain efficient list operations clearly.

Self-Check

"What if we changed to deleting from the end of the doubly linked list? How would the time complexity change?"

Practice

1. What happens to the head pointer when you delete the first node from a doubly linked list?

easy

A. It moves to the second node in the list

B. It becomes null immediately

C. It points to the last node

D. It remains unchanged

Solution

1. Step 1: Understand the head pointer role

   The head pointer always points to the first node in the list.

2. Step 2: Effect of deleting the first node

   When the first node is deleted, the head pointer must move to the next node, which becomes the new first node.

3. Final Answer:

   It moves to the second node in the list -> Option A

4. Quick Check:

   Head points to new first node after deletion [OK]

Hint: Head always points to the first node [OK]

Common Mistakes:

• Thinking head becomes null without checking list emptiness
• Assuming head points to last node after deletion
• Not updating head pointer after deletion

2. Which of the following Go code snippets correctly deletes the first node from a doubly linked list named dll?

easy

A. dll.head.prev = nil; dll.head = dll.head.next

B. dll.head = dll.head.next; if dll.head != nil { dll.head.prev = nil }

C. dll.head.next.prev = nil; dll.head = dll.head.next

D. dll.head = nil; dll.tail = nil

Solution

1. Step 1: Move head to next node

   Set dll.head = dll.head.next to remove first node reference.

2. Step 2: Update new head's prev pointer

   If new head exists, set dll.head.prev = nil to detach backward link.

3. Final Answer:

   dll.head = dll.head.next; if dll.head != nil { dll.head.prev = nil } -> Option B

4. Quick Check:

   Correct pointer updates for deletion [OK]

Hint: Update head then clear new head's prev [OK]

Common Mistakes:

• Setting prev pointer before moving head
• Not checking if new head is nil
• Clearing head and tail without condition

3. Given the following doubly linked list with nodes 10 <-> 20 <-> 30, what will be the list after deleting the first node?

type Node struct {
  data int
  prev *Node
  next *Node
}

head := &Node{data: 10}
second := &Node{data: 20}
third := &Node{data: 30}
head.next = second
second.prev = head
second.next = third
third.prev = second

// Delete from beginning
head = head.next
head.prev = nil

// Print list
curr := head
for curr != nil {
  fmt.Print(curr.data)
  if curr.next != nil {
    fmt.Print(" <-> ")
  }
  curr = curr.next
}

medium

A. 20 <-> 30

B. 10 <-> 20 <-> 30

C. 30

D. nil

Solution

1. Step 1: Initial list setup

   List is 10 <-> 20 <-> 30 with head at 10.

2. Step 2: Delete first node

   Head moves to 20, and 20's prev is set to nil, detaching 10.

3. Final Answer:

   20 <-> 30 -> Option A

4. Quick Check:

   First node removed, list starts at 20 [OK]

Hint: Head moves to next, prev cleared [OK]

Common Mistakes:

• Not clearing prev pointer of new head
• Printing old head node
• Confusing next and prev pointers

4. Identify the error in this Go code snippet that tries to delete the first node from a doubly linked list:

if dll.head != nil {
  dll.head = dll.head.next
  dll.head.prev = nil
}

medium

A. It should assign dll.head.prev to dll.head.next

B. It should set dll.head.next.prev to nil instead

C. No error, code is correct

D. It does not check if dll.head.next is nil before accessing prev

Solution

1. Step 1: Check condition before accessing pointers

   The code moves head to next node without checking if next node exists.

2. Step 2: Accessing prev of nil causes runtime error

   If dll.head.next is nil, then dll.head becomes nil and accessing dll.head.prev causes panic.

3. Final Answer:

   It does not check if dll.head.next is nil before accessing prev -> Option D

4. Quick Check:

   Always check for nil before pointer access [OK]

Hint: Check nil before accessing pointers [OK]

Common Mistakes:

• Assuming next node always exists
• Not handling empty list after deletion
• Confusing prev and next pointers

5. You have a doubly linked list with nodes 5 <-> 15. You want to delete the first node and then insert a new node with value 10 at the beginning. Which sequence of operations correctly updates the list?

hard

A. Delete first node by moving head to next; create new node with prev = head, next = nil; set head.next to new node

B. Delete first node by setting head to nil; create new node with next = nil, prev = nil; set head to new node

C. Delete first node by moving head to next and clearing prev; then create new node with next = head, prev = nil; update head.prev to new node; finally set head to new node

D. Delete first node by moving head to next; create new node with next = nil, prev = nil; set head to new node

Solution

1. Step 1: Delete first node properly

   Move head to next node and set new head's prev to nil to detach old first node.

2. Step 2: Insert new node at beginning

   Create new node with next pointing to current head and prev nil; update current head's prev to new node; update head pointer to new node.

3. Final Answer:

   Delete first node by moving head to next and clearing prev; then create new node with next = head, prev = nil; update head.prev to new node; finally set head to new node -> Option C

4. Quick Check:

   Proper delete then insert at head [OK]

Hint: Delete then insert by updating head and pointers [OK]

Common Mistakes:

• Not updating prev pointer of old head after insertion
• Setting new node's prev incorrectly
• Overwriting head without linking new node