Delete from End of Doubly Linked List in DSA Rust - Time & Space Complexity

Time Complexity: Delete from End of Doubly Linked List

O(n)

Understanding Time Complexity

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

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

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

struct Node {
    data: i32,
    prev: Option<*mut Node>,
    next: Option<Box<Node>>,
}

fn delete_from_end(head: &mut Option<Box<Node>>) {
    if head.is_none() { return; }
    if head.as_ref().unwrap().next.is_none() {
        *head = None;
        return;
    }
    let mut current = head.as_mut();
    while let Some(node) = current {
        if node.next.is_none() {
            // Remove last node
            if let Some(prev) = node.prev {
                unsafe {
                    (*prev).next = None;
                }
            }
            break;
        }
        current = node.next.as_mut();
    }
}
    

This code removes the last node from a doubly linked list by walking to the end and unlinking it.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Loop that moves through nodes from head to end.
• How many times: Once for each node until the last one (depends on list size).

How Execution Grows With Input

As the list gets longer, the code checks more nodes one by one until it reaches the end.

Input Size (n)	Approx. Operations
10	About 10 steps to reach the end
100	About 100 steps to reach the end
1000	About 1000 steps to reach the end

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

Final Time Complexity

Time Complexity: O(n)

This means the time to delete the last node grows in a straight line with the number of nodes.

Common Mistake

[X] Wrong: "Deleting the last node is always quick and takes constant time."

[OK] Correct: Without a direct pointer to the last node, we must walk through the list, so time depends on list length.

Interview Connect

Understanding this helps you explain how linked lists work and why having a tail pointer can speed up some operations.

Self-Check

"What if we kept a pointer to the last node? How would the time complexity change?"

Practice

1. What happens when you delete the last node from a doubly linked list that has multiple nodes?

easy

A. The second last node becomes the new tail and its next pointer is set to null

B. The head pointer is set to null

C. The list becomes circular

D. The first node is deleted instead

Solution

1. Step 1: Understand the tail node removal

   When deleting the last node, the node before it becomes the new tail.

2. Step 2: Update pointers

   The new tail's next pointer must be set to null to mark the end of the list.

3. Final Answer:

   The second last node becomes the new tail and its next pointer is set to null -> Option A

4. Quick Check:

   Tail update = new tail with next = null [OK]

Hint: Last node removal means update tail and set next to null [OK]

Common Mistakes:

• Not updating the tail pointer
• Forgetting to set next pointer of new tail to null
• Deleting the head instead of the tail

2. Which Rust code snippet correctly deletes the last node from a doubly linked list?

easy

A. if let Some(tail) = self.tail.take() { if let Some(prev) = tail.prev.take() { prev.next = null; self.tail = Some(prev); } else { self.head = null; } }

B. self.head = null; self.tail = null;

C. self.tail = self.tail.unwrap().prev;

D. self.tail = null; self.head = null;

Solution

1. Step 1: Check tail existence and update pointers

   The code safely takes the tail node, then updates the previous node's next pointer to null.

2. Step 2: Update tail or head accordingly

   If previous node exists, tail is updated to it; else, list becomes empty by setting head to null.

3. Final Answer:

   Code snippet that safely updates tail and head pointers -> Option A

4. Quick Check:

   Safe pointer update with if let Some(tail) = self.tail.take() { if let Some(prev) = tail.prev.take() { prev.next = null; self.tail = Some(prev); } else { self.head = null; } } [OK]

Hint: Use take() and update prev.next and tail safely [OK]

Common Mistakes:

• Directly assigning tail without checking Option
• Not updating previous node's next pointer
• Setting head to null without checking list length

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

let mut list = DoublyLinkedList::new();
list.push_back(1);
list.push_back(2);
list.push_back(3);
list.delete_from_end();
list.print();

medium

A. 1 -> 2 -> 3 -> null

B. 1 -> 2 -> null

C. 2 -> 3 -> null

D. null

Solution

1. Step 1: Initial list state

   The list contains nodes 1, 2, 3 in order.

2. Step 2: Delete last node

   Deleting from end removes node 3, so list becomes 1 -> 2.

3. Final Answer:

   1 -> 2 -> null -> Option B

4. Quick Check:

   After deletion, last node removed = 1 -> 2 [OK]

Hint: Deleting end removes last node only [OK]

Common Mistakes:

• Assuming head node is deleted
• Not updating tail pointer
• Printing old list without deletion

4. Identify the bug in this Rust function that deletes the last node from a doubly linked list:

fn delete_from_end(&mut self) {
    if self.tail.is_none() {
        return;
    }
    let tail = self.tail.unwrap();
    if let Some(prev) = tail.prev {
        prev.next = null;
        self.tail = Some(prev);
    } else {
        self.head = null;
        self.tail = null;
    }
}

medium

A. prev.next is not set to null

B. Not updating head pointer when list has multiple nodes

C. Using unwrap() on Option without safe handling causes panic

D. Function does not check if list is empty

Solution

1. Step 1: Analyze unwrap() usage

   Calling unwrap() on tail without checking can panic if tail is null.

2. Step 2: Suggest safe handling

   Use if let or take() to safely handle Option values without panic.

3. Final Answer:

   Using unwrap() on Option without safe handling causes panic -> Option C

4. Quick Check:

   Unsafe unwrap() = panic risk [OK]

Hint: Avoid unwrap() on Option; use safe pattern matching [OK]

Common Mistakes:

• Ignoring Option safety and causing runtime panic
• Not updating tail pointer after deletion
• Forgetting to set prev.next to null

5. You have a doubly linked list with nodes containing values [10, 20, 30]. After deleting the last node twice, what will be the state of the list?

hard

A. 10 -> 20 -> null

B. null

C. 20 -> 30 -> null

D. 10 -> null

Solution

1. Step 1: Initial list nodes

   The list starts as 10 -> 20 -> 30.

2. Step 2: Delete last node once

   Removing last node 30 results in 10 -> 20.

3. Step 3: Delete last node again

   Removing last node 20 results in 10.

4. Final Answer:

   10 -> null -> Option D

5. Quick Check:

   Two deletions remove last two nodes [OK]

Hint: Each delete removes last node, update tail and next [OK]

Common Mistakes:

• Deleting head instead of tail
• Not updating tail after each deletion
• Assuming list becomes empty too early