Delete by Value in Doubly Linked List in DSA C++ - Time & Space Complexity

Time Complexity: Delete by Value in Doubly Linked List

O(n)

Understanding Time Complexity

We want to know how long it takes to remove a node by its value from a doubly 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 deleteByValue(Node*& head, int value) {
    Node* current = head;
    while (current != nullptr && current->data != value) {
        current = current->next;
    }
    if (current == nullptr) return; // value not found
    if (current->prev != nullptr) {
        current->prev->next = current->next;
    } else {
        head = current->next;
    }
    if (current->next != nullptr) {
        current->next->prev = current->prev;
    }
    delete current;
}

This code searches for the first node with the given value and removes it from the doubly linked list.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The while loop that moves through nodes to find the value.
• How many times: Up to n times, where n is the number of nodes in the list.

How Execution Grows With Input

As the list grows, the search may take longer because it might check more nodes.

Input Size (n)	Approx. Operations
10	Up to 10 checks
100	Up to 100 checks
1000	Up to 1000 checks

Pattern observation: The number of steps grows roughly in direct proportion to the list size.

Final Time Complexity

Time Complexity: O(n)

This means the time to delete by value grows linearly with the number of nodes in the list.

Common Mistake

[X] Wrong: "Deleting a node by value always takes constant time because we just remove one node."

[OK] Correct: We must first find the node by checking nodes one by one, which can take time proportional to the list size.

Interview Connect

Understanding this helps you explain how searching affects deletion time in linked lists, a common topic in coding interviews.

Self-Check

"What if the list was sorted? How would that change the time complexity of deleting by value?"

Practice

1. What happens when you delete a node by value in a doubly linked list?

easy

A. All nodes are deleted regardless of value.

B. The node with the matching value is removed and links are updated.

C. Only the first node is deleted without checking value.

D. The list is reversed instead of deleting.

Solution

1. Step 1: Locate the node with the given value

   Traverse the list from head to tail to find the node whose data matches the value to delete.

2. Step 2: Update links to remove the node

   Adjust the previous node's next pointer and the next node's previous pointer to bypass the node to be deleted.

3. Final Answer:

   The node with the matching value is removed and links are updated. -> Option B

4. Quick Check:

   Delete by value removes matching node [OK]

Hint: Find node, update previous and next pointers [OK]

Common Mistakes:

• Not updating both previous and next pointers
• Deleting node without checking value
• Deleting all nodes instead of one

2. Which of the following is the correct syntax to delete a node by value in a doubly linked list in C++?

easy

A. void deleteNode(Node* &head, int val) { /* code */ }

B. void deleteNode(int val) { /* code */ }

C. Node deleteNode(int val) { /* code */ }

D. int deleteNode(Node* head, int val) { /* code */ }

Solution

1. Step 1: Understand parameter passing for head pointer

   Head pointer must be passed by reference to allow modification if the first node is deleted.

2. Step 2: Check function return type

   Deletion functions usually return void as they modify the list in place.

3. Final Answer:

   void deleteNode(Node* &head, int val) { /* code */ } -> Option A

4. Quick Check:

   Pass head by reference and return void [OK]

Hint: Pass head by reference to modify list [OK]

Common Mistakes:

• Passing head by value causing no list update
• Returning Node instead of void
• Missing head pointer parameter

3. What is the output of the following code snippet after deleting value 20 from the doubly linked list?

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

// List: 10 <-> 20 <-> 30
// deleteNode(head, 20);
// printList(head);

medium

A. 10 <-> null

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

C. 20 <-> 30 <-> null

D. 10 <-> 30 <-> null

Solution

1. Step 1: Identify node to delete

   Node with value 20 is in the middle of the list 10 <-> 20 <-> 30.

2. Step 2: Update links after deletion

   After deleting 20, 10's next points to 30, and 30's prev points to 10.

3. Final Answer:

   10 <-> 30 <-> null -> Option D

4. Quick Check:

   Middle node deleted, links updated [OK]

Hint: Deleting middle node links neighbors directly [OK]

Common Mistakes:

• Not updating previous pointer of next node
• Not updating next pointer of previous node
• Leaving deleted node linked

4. Identify the bug in this delete by value function for doubly linked list:

void deleteNode(Node* &head, int val) {
  Node* temp = head;
  while (temp != nullptr && temp->data != val) {
    temp = temp->next;
  }
  if (temp == nullptr) return;
  if (temp->prev != nullptr) temp->prev->next = temp->next;
  if (temp->next != nullptr) temp->next->prev = temp->prev;
  delete temp;
}

medium

A. Does not check for null head pointer

B. Deletes all nodes with matching value

C. Does not update head if first node is deleted

D. Deletes node without freeing memory

Solution

1. Step 1: Check head update when deleting first node

   If the node to delete is the head, head pointer must be updated to next node.

2. Step 2: Verify code for head update

   Code does not update head pointer when temp->prev is nullptr (first node).

3. Final Answer:

   Does not update head if first node is deleted -> Option C

4. Quick Check:

   Head update missing for first node deletion [OK]

Hint: Update head if deleting first node [OK]

Common Mistakes:

• Forgetting to update head pointer
• Not handling empty list
• Deleting without checking node existence

5. Given a doubly linked list with nodes: 5 <-> 10 <-> 15 <-> 20, what will be the list after deleting value 5 and then value 20?

hard

A. 10 <-> 15 <-> null

B. 5 <-> 10 <-> 15 <-> 20 <-> null

C. 10 <-> 15 <-> 20 <-> null

D. 15 <-> null

Solution

1. Step 1: Delete node with value 5 (head node)

   Update head to 10, set 10's prev to nullptr. List becomes 10 <-> 15 <-> 20.

2. Step 2: Delete node with value 20 (tail node)

   Update 15's next to nullptr. List becomes 10 <-> 15.

3. Final Answer:

   10 <-> 15 <-> null -> Option A

4. Quick Check:

   Deleted head and tail nodes correctly [OK]

Hint: Update head and tail pointers when deleting ends [OK]

Common Mistakes:

• Not updating head when deleting first node
• Not updating tail when deleting last node
• Leaving dangling pointers