Delete by Value in Doubly Linked List in DSA Rust - 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 remove a value from a doubly linked list.

The question is: how does the time grow as the list gets bigger?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

fn delete_by_value(head: &mut Option>, value: i32) {
    let mut current = head.as_mut();
    while let Some(node) = current {
        if node.data == value {
            // Remove node by adjusting pointers
            // ... (pointer updates omitted for brevity)
            break;
        }
        current = node.next.as_mut();
    }
}

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

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 search may need to 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 operations 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 list size.

Common Mistake

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

[OK] Correct: We must first find the node, which can take time proportional to the list length.

Interview Connect

Understanding this helps you explain how linked lists work and how searching affects performance.

Self-Check

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

Practice

1. What is the main purpose of the delete_by_value function in a doubly linked list?

easy

A. To remove the first node that contains the given value

B. To add a new node with the given value at the end

C. To reverse the entire doubly linked list

D. To count how many nodes have the given value

Solution

1. Step 1: Understand the function's goal

   The delete_by_value function searches for a node with the specified value.

2. Step 2: Identify the action performed

   Once found, it removes that node from the doubly linked list, adjusting pointers accordingly.

3. Final Answer:

   To remove the first node that contains the given value -> Option A

4. Quick Check:

   Delete by value means remove matching node [OK]

Hint: Delete by value removes first matching node [OK]

Common Mistakes:

• Confusing delete with insert
• Thinking it reverses the list
• Assuming it counts nodes

2. Which Rust syntax correctly declares a mutable doubly linked list node struct with prev and next pointers?

easy

A. struct Node { value: i32, prev: Option>, next: Option> }

B. struct Node { value: i32, prev: Option<*mut Node>, next: Option<*mut Node> }

C. struct Node { value: i32, prev: Option, next: Option }

D. struct Node { value: i32, prev: Option<Node>, next: Option<Node> }

Solution

1. Step 1: Understand Rust pointer types for doubly linked lists

   Rust needs shared ownership and mutability for prev and next pointers, so Rc is used.

2. Step 2: Check options for correct pointer usage

   struct Node { value: i32, prev: Option>, next: Option> } uses Option> which allows multiple owners and interior mutability, suitable for doubly linked lists.

3. Final Answer:

   struct Node { value: i32, prev: Option>, next: Option> } -> Option A

4. Quick Check:

   Use Rc and RefCell for mutable shared nodes [OK]

Hint: Use Rc for mutable shared pointers [OK]

Common Mistakes:

• Using Box for both prev and next causes ownership issues
• Using raw pointers without unsafe code
• Using direct Node type causing infinite size

3. Given the following Rust code snippet for deleting a value from a doubly linked list, what will be the printed list after deleting value 3?

let mut list = DoublyLinkedList::new();
list.push_back(1);
list.push_back(3);
list.push_back(5);
list.delete_by_value(3);
list.print();

medium

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

B. 1 -> 5 -> null

C. 3 -> 5 -> null

D. 1 -> null

Solution

1. Step 1: Understand initial list state

   After pushing 1, 3, 5, the list is 1 -> 3 -> 5 -> null.

2. Step 2: Delete node with value 3

   The delete_by_value(3) removes the node containing 3, linking 1 directly to 5.

3. Final Answer:

   1 -> 5 -> null -> Option B

4. Quick Check:

   Deleted 3, list is 1 -> 5 [OK]

Hint: Deleting value removes that node, links neighbors [OK]

Common Mistakes:

• Not updating prev and next pointers correctly
• Deleting wrong node or none
• Printing old list without deletion

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

fn delete_by_value(&mut self, val: i32) {
    let mut current = self.head.clone();
    while let Some(node) = current {
        if node.borrow().value == val {
            // deletion logic here
            break;
        }
        current = node.borrow().next.clone();
    }
}

What is a common bug if the deletion logic forgets to update the prev pointer of the next node?

medium

A. The list will reverse automatically

B. The head pointer will always point to null

C. The deleted node will remain in memory forever

D. The list may become corrupted with dangling backward links

Solution

1. Step 1: Identify pointer updates needed on deletion

   When deleting a node, the previous node's next and the next node's prev pointers must be updated to bypass the deleted node.

2. Step 2: Consequence of missing prev update

   If the next node's prev pointer is not updated, it still points to the deleted node, causing backward links to be incorrect and list corruption.

3. Final Answer:

   The list may become corrupted with dangling backward links -> Option D

4. Quick Check:

   Missing prev update breaks backward links [OK]

Hint: Always update both prev and next pointers when deleting [OK]

Common Mistakes:

• Updating only next pointer
• Not breaking loop after deletion
• Forgetting to handle head or tail cases

5. You have a doubly linked list with nodes: 2 -> 4 -> 6 -> 4 -> 8 -> null. You want to delete all nodes with value 4 using a delete_by_value function that removes only the first matching node per call. How many times must you call delete_by_value(4) to remove all 4s, and what will the final list look like?

hard

A. Call once; final list: 2 -> 4 -> 6 -> 8 -> null

B. Call once; final list: 2 -> 6 -> 4 -> 8 -> null

C. Call twice; final list: 2 -> 6 -> 8 -> null

D. Call twice; final list: 2 -> 4 -> 6 -> 8 -> null

Solution

1. Step 1: Understand deletion per call

   Each call to delete_by_value(4) removes only the first node with value 4.

2. Step 2: Count how many 4s and calls needed

   There are two nodes with value 4. So, two calls are needed to remove both.

3. Step 3: Final list after deletions

   After two deletions, the list becomes 2 -> 6 -> 8 -> null.

4. Final Answer:

   Call twice; final list: 2 -> 6 -> 8 -> null -> Option C

5. Quick Check:

   Two 4s, two deletes, final list without 4s [OK]

Hint: Delete one node per call; repeat to remove all matches [OK]

Common Mistakes:

• Assuming one call removes all matching nodes
• Not updating pointers after each deletion
• Confusing node values or order