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 understand how long it takes to delete a node by value in 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.

public void DeleteByValue(int value) {
    Node current = head;
    while (current != null) {
        if (current.Data == value) {
            if (current.Prev != null) current.Prev.Next = current.Next;
            else head = current.Next;
            if (current.Next != null) current.Next.Prev = current.Prev;
            return;
        }
        current = current.Next;
    }
}
    

This code searches the list for the first node with the given value and removes it by adjusting links.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Traversing the list nodes one by one 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 time to find the value grows roughly in direct proportion.

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

Pattern observation: The number of steps grows linearly with the list size.

Final Time Complexity

Time Complexity: O(n)

This means the time to delete by value grows linearly as the list gets longer.

Common Mistake

[X] Wrong: "Deleting by value is always fast because we just remove the node."

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

Interview Connect

Understanding this helps you explain how searching affects deletion speed in linked lists, a common topic in 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 if the value is not found?

easy

A. An error is thrown and the program stops.

B. The first node is deleted regardless of the value.

C. All nodes are deleted from the list.

D. The list remains unchanged because no node matches the value.

Solution

1. Step 1: Search for the node with the given value

   Traverse the list from head to tail to find a node matching the value.

2. Step 2: Check if node is found

   If no node matches the value, no deletion occurs and the list stays the same.

3. Final Answer:

   The list remains unchanged because no node matches the value. -> Option D

4. Quick Check:

   Delete by value with no match = no change [OK]

Hint: If value not found, list stays same [OK]

Common Mistakes:

• Assuming deletion happens even if value not found
• Trying to delete head without checking value
• Expecting an error instead of no action

2. Which of the following is the correct way to update the previous pointer when deleting a middle node in a doubly linked list in C#?

easy

A. nodeToDelete.Next.Prev = nodeToDelete.Prev;

B. nodeToDelete.Prev.Next = nodeToDelete.Next.Prev;

C. nodeToDelete.Next = nodeToDelete.Prev.Next;

D. nodeToDelete.Prev = nodeToDelete.Next.Prev;

Solution

1. Step 1: Understand pointers in doubly linked list

   When deleting a node, the next node's previous pointer must point to the deleted node's previous node.

2. Step 2: Correct pointer update

   Setting nodeToDelete.Next.Prev = nodeToDelete.Prev correctly links the next node back to the previous node.

3. Final Answer:

   nodeToDelete.Next.Prev = nodeToDelete.Prev; -> Option A

4. Quick Check:

   Update next node's Prev to deleted node's Prev [OK]

Hint: Next node's Prev points to deleted node's Prev [OK]

Common Mistakes:

• Mixing up Next and Prev pointers
• Assigning Prev to Next's Prev incorrectly
• Not updating both Next and Prev pointers

3. Given the doubly linked list: 10 <-> 20 <-> 30 <-> 40 <-> null, what is the list after deleting the node with value 30?

medium

A. 10 <-> 20 <-> 30 <-> 40 <-> null

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

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

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

Solution

1. Step 1: Locate node with value 30

   Traverse the list and find the node containing 30 between 20 and 40.

2. Step 2: Remove node 30 and update pointers

   Set 20's Next to 40 and 40's Prev to 20, skipping 30.

3. Final Answer:

   10 <-> 20 <-> 40 <-> null -> Option B

4. Quick Check:

   Deleted 30, linked 20 and 40 directly [OK]

Hint: Remove node, link previous and next nodes [OK]

Common Mistakes:

• Not updating both Prev and Next pointers
• Leaving deleted node in the list
• Deleting wrong node by mistake

4. Consider this code snippet for deleting a node by value in a doubly linked list:

if (current == null) return;
if (current.Prev != null) current.Prev.Next = current.Next;
if (current.Next != null) current.Next.Prev = current.Prev;
if (current == head) head = current.Next;

What is the bug in this code?

medium

A. It may cause a null reference if current is null before checks.

B. It does not update the head when deleting the first node.

C. It does not handle deleting the last node correctly.

D. It does not remove the node from memory.

Solution

1. Step 1: Verify null safety

   The initial check if (current == null) return; and conditional pointer accesses prevent null references.

2. Step 2: Check head and pointer updates

   Head is updated correctly when deleting the first node, and pointers are linked properly for middle nodes.

3. Step 3: Identify the issue with last node

   The code sets current.Prev.Next = null but does not update a potential tail pointer to current.Prev, leaving the tail pointing to the deleted node.

4. Final Answer:

   It does not handle deleting the last node correctly. -> Option C

5. Quick Check:

   Missing tail update for last node deletion [OK]

Hint: Update tail pointer when deleting last node [OK]

Common Mistakes:

• Ignoring null checks before pointer access
• Not updating head when deleting first node
• Assuming garbage collection removes node immediately

5. You have a doubly linked list with nodes: 5 <-> 10 <-> 15 <-> 20 <-> 25 <-> null. You want to delete all nodes with values greater than 15. Which approach correctly deletes these nodes by value?

hard

A. Traverse from head, delete nodes with value > 15, updating pointers carefully.

B. Delete nodes by value without updating pointers, then reset head.

C. Only delete the first node with value > 15 and stop.

D. Traverse from tail, delete nodes with value < 15.

Solution

1. Step 1: Traverse list from head to tail

   Visit each node and check if its value is greater than 15.

2. Step 2: Delete matching nodes and update pointers

   For each node with value > 15, remove it by linking its previous node to its next node, updating both Next and Prev pointers.

3. Step 3: Continue traversal carefully

   After deletion, continue traversal without skipping nodes to delete all matching nodes.

4. Final Answer:

   Traverse from head, delete nodes with value > 15, updating pointers carefully. -> Option A

5. Quick Check:

   Delete all matching nodes with pointer updates [OK]

Hint: Traverse and delete nodes carefully, update pointers [OK]

Common Mistakes:

• Deleting nodes without updating pointers
• Stopping after first deletion
• Deleting wrong nodes by incorrect condition