Insert at Beginning of Doubly Linked List in DSA Rust - Time & Space Complexity

Time Complexity: Insert at Beginning of Doubly Linked List

O(1)

Understanding Time Complexity

We want to understand how long it takes to add a new item at the start of 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>,
}

fn insert_at_beginning(head: &mut Option>, data: i32) {
    let mut new_node = Box::new(Node { data, prev: None, next: head.take() });
    if let Some(ref mut old_head) = new_node.next {
        old_head.prev = Some(&mut *new_node);
    }
    *head = Some(new_node);
}
    

This code adds a new node at the start of a doubly linked list, updating pointers accordingly.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Creating and linking one new node.
• How many times: This happens once per insertion, no loops or recursion.

How Execution Grows With Input

Adding a node at the start always takes the same steps, no matter how big the list is.

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

Pattern observation: The number of steps stays the same no matter how large the list grows.

Final Time Complexity

Time Complexity: O(1)

This means adding at the start takes a fixed amount of time, no matter the list size.

Common Mistake

[X] Wrong: "Adding at the start takes longer as the list grows because we have to move all nodes."

[OK] Correct: We only change a few pointers at the start; we do not move or touch the other nodes.

Interview Connect

Knowing this helps you explain why linked lists are good for quick insertions at the start, a common question in interviews.

Self-Check

"What if we changed to insert at the end of the doubly linked list without a tail pointer? How would the time complexity change?"

Practice

1. What is the main purpose of inserting a node at the beginning of a doubly linked list?

easy

A. To remove the first node from the list

B. To add a new node at the end of the list

C. To add a new node as the first element, updating head pointer

D. To reverse the entire list

Solution

1. Step 1: Understand the operation

   Inserting at the beginning means adding a new node before the current first node.

2. Step 2: Effect on head pointer

   The head pointer must be updated to point to this new node, making it the first element.

3. Final Answer:

   To add a new node as the first element, updating head pointer -> Option C

4. Quick Check:

   Insert at beginning = update head to new node [OK]

Hint: New node becomes head; update pointers accordingly [OK]

Common Mistakes:

• Confusing insertion at beginning with insertion at end
• Not updating the head pointer
• Not adjusting previous pointer of old head

2. Which of the following Rust code snippets correctly creates a new node and inserts it at the beginning of a doubly linked list?

easy

A. let new_node = Box::new(Node { data: val, prev: None, next: head }); head = Some(new_node);

B. let new_node = Node { data: val, prev: head, next: None }; head = Some(Box::new(new_node));

C. head = Some(Box::new(Node { data: val, prev: None, next: None }));

D. let new_node = Box::new(Node { data: val, prev: None, next: None }); tail = Some(new_node);

Solution

1. Step 1: Create new node with prev None and next as current head

   The new node's previous pointer should be None because it will be the first node. Its next pointer should point to the current head.

2. Step 2: Update head to new node

   After creating the new node, the head pointer must be updated to point to this new node.

3. Final Answer:

   let new_node = Box::new(Node { data: val, prev: None, next: head }); head = Some(new_node); -> Option A

4. Quick Check:

   New node prev None, next head, update head [OK]

Hint: Prev None, next old head, then update head [OK]

Common Mistakes:

• Setting prev to head instead of None
• Not boxing the new node
• Updating tail instead of head

3. Given the following Rust code for inserting at the beginning of a doubly linked list, what will be the printed list after insertion?

struct Node {
    data: i32,
    prev: Option,
    next: Option,
}

let mut head = Some(Box::new(Node { data: 2, prev: None, next: None }));

// Insert 1 at beginning
let new_node = Box::new(Node { data: 1, prev: None, next: head });
head = Some(new_node);

// Print list
let mut current = &head;
while let Some(node) = current {
    print!("{} -> ", node.data);
    current = &node.next;
}
print!("null");

medium

A. 1 -> 2 -> null

B. 2 -> 1 -> null

C. 1 -> null

D. 2 -> null

Solution

1. Step 1: Understand insertion

   The new node with data 1 is created with next pointing to old head (node with data 2). So list starts with 1, then 2.

2. Step 2: Trace printing loop

   Printing starts at head (1), then moves to next (2), then next is None, so ends with null.

3. Final Answer:

   1 -> 2 -> null -> Option A

4. Quick Check:

   New node at front, list prints 1 then 2 [OK]

Hint: New node points to old head; print follows next pointers [OK]

Common Mistakes:

• Confusing order of nodes after insertion
• Not updating head pointer
• Printing prev instead of next

4. Identify the error in this Rust code snippet that tries to insert a node at the beginning of a doubly linked list:

let mut head = Some(Box::new(Node { data: 3, prev: None, next: None }));
let new_node = Box::new(Node { data: 1, prev: None, next: head });
head = Some(new_node);
if let Some(ref mut old_head) = head {
    old_head.prev = Some(Box::new(Node { data: 1, prev: None, next: None }));
}

medium

A. Fails to update head pointer

B. Incorrectly creates a new node for prev instead of linking to new_node

C. Does not set new_node.next to old head

D. Uses immutable reference instead of mutable

Solution

1. Step 1: Check prev pointer update

   The code sets old_head.prev to a new node with data 1 instead of linking it to the existing new_node.

2. Step 2: Understand correct linking

   Prev pointer should point to the new_node itself, not a new separate node.

3. Final Answer:

   Incorrectly creates a new node for prev instead of linking to new_node -> Option B

4. Quick Check:

   Prev must link to new_node, not new node copy [OK]

Hint: Prev pointer links to existing node, not a new duplicate [OK]

Common Mistakes:

• Creating duplicate nodes instead of linking
• Not using mutable references for modification
• Not updating prev pointer at all

5. You have a doubly linked list with nodes containing values 3 <-> 5 <-> 7. You want to insert 1 at the beginning. Which sequence of pointer updates is correct to maintain list integrity?

hard

A. Create new node with prev old head, next old head; update head to new node

B. Create new node with prev old head, next None; set old head next to new node; update head to new node

C. Create new node with prev None, next None; update head to new node only

D. Create new node with prev None, next old head; set old head prev to new node; update head to new node

Solution

1. Step 1: Create new node with prev None and next pointing to old head

   The new node is first, so prev is None. Next points to old head (node with 3).

2. Step 2: Update old head's prev pointer to new node and head pointer to new node

   Old head's prev must point back to new node. Head pointer must be updated to new node.

3. Final Answer:

   Create new node with prev None, next old head; set old head prev to new node; update head to new node -> Option D

4. Quick Check:

   New node prev None, next old head; old head prev new node; update head [OK]

Hint: New node prev None, next old head; old head prev new node; update head [OK]

Common Mistakes:

• Setting new node prev to old head
• Not updating old head prev pointer
• Not updating head pointer