Doubly Linked List Structure and Node Design in DSA Rust - Time & Space Complexity

Time Complexity: Doubly Linked List Structure and Node Design

O(n)

Understanding Time Complexity

We want to understand how the time to create and link nodes in a doubly linked list grows as we add more nodes.

How does the work change when the list gets bigger?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

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

impl Node {
    fn new(value: i32) -> Self {
        Node { value, prev: None, next: None }
    }
}
    

This code defines a node for a doubly linked list with pointers to previous and next nodes.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Creating and linking each node with references to previous and next.
• How many times: Once per node added to the list.

How Execution Grows With Input

Each new node requires a fixed amount of work to create and link.

Input Size (n)	Approx. Operations
10	10 node creations and linkings
100	100 node creations and linkings
1000	1000 node creations and linkings

Pattern observation: The work grows directly with the number of nodes added.

Final Time Complexity

Time Complexity: O(n)

This means the time to build the list grows linearly with the number of nodes.

Common Mistake

[X] Wrong: "Linking nodes takes constant time regardless of list size."

[OK] Correct: While linking one node is constant time, building the whole list requires linking each node, so total time grows with the number of nodes.

Interview Connect

Understanding how node creation and linking scales helps you explain list operations clearly and confidently in interviews.

Self-Check

"What if we added a loop to search for a node before linking? How would the time complexity change?"

Practice

1. What is the main advantage of a doubly linked list over a singly linked list?

easy

A. It allows traversal in both forward and backward directions

B. It uses less memory per node

C. It requires fewer pointers per node

D. It can only be traversed forward

Solution

1. Step 1: Understand node pointers in doubly linked list

   A doubly linked list node has two pointers: one to the next node and one to the previous node.

2. Step 2: Compare traversal capabilities

   This allows moving forward and backward through the list, unlike singly linked lists which only allow forward traversal.

3. Final Answer:

   It allows traversal in both forward and backward directions -> Option A

4. Quick Check:

   Doubly linked list = two-way traversal [OK]

Hint: Remember: two pointers mean two directions [OK]

Common Mistakes:

• Thinking it uses less memory than singly linked list
• Assuming it only allows forward traversal
• Confusing pointer count with memory usage

2. Which of the following is the correct Rust struct definition for a doubly linked list node holding an integer value?

easy

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

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

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

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

Solution

1. Step 1: Understand ownership and pointers in Rust doubly linked list

   Rust's ownership rules prevent two owning pointers to the same data. The next pointer can own the next node using Box, but the prev pointer must be a raw pointer or weak reference to avoid ownership conflicts.

2. Step 2: Analyze options for prev pointer

   struct Node { value: i32, next: Option, prev: Option<*mut Node> } uses Option<*mut Node> (a raw mutable pointer) for prev, which is common in unsafe doubly linked list implementations. struct Node { value: i32, next: Option, prev: Option } incorrectly uses Box for prev, causing double ownership. struct Node { value: i32, next: Option, prev: Option } uses Rc which is for shared ownership but not mutable by default. struct Node { value: i32, next: Option<Node>, prev: Option<Node> } uses Option<Node> which is invalid because Node is not sized.

3. Final Answer:

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

4. Quick Check:

   Prev pointer = raw pointer to avoid ownership [OK]

Hint: Prev pointer often uses raw pointer in Rust doubly linked lists [OK]

Common Mistakes:

• Using Box for both next and prev causing ownership errors
• Using Rc without mutability for prev
• Trying to store Node directly without Box or pointer

3. Given the following Rust code snippet for a doubly linked list node insertion, what will be the printed output?

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

fn main() {
    let mut first = Box::new(Node { value: 1, next: None, prev: None });
    let mut second = Box::new(Node { value: 2, next: None, prev: None });

    second.prev = Some(&mut *first as *mut _);
    first.next = Some(second);

    println!("{} -> {}", first.value, first.next.as_ref().unwrap().value);
}

medium

A. Runtime panic due to null pointer

B. 2 -> 1

C. Compilation error due to borrowing

D. 1 -> 2

Solution

1. Step 1: Understand node creation and linking

   Two nodes are created: first with value 1, second with value 2. The second node's prev pointer is set to point to first. The first node's next pointer is set to own second.

2. Step 2: Analyze the print statement

   The print accesses first.value (1) and first.next's value (2). Since first.next is Some(second), unwrap() succeeds and prints "1 -> 2".

3. Final Answer:

   1 -> 2 -> Option D

4. Quick Check:

   First node value then next node value = 1 -> 2 [OK]

Hint: Print first node then unwrap next for correct order [OK]

Common Mistakes:

• Confusing prev pointer direction
• Expecting compilation error due to unsafe pointer
• Assuming runtime panic without dereferencing prev

4. Identify the error in this Rust doubly linked list node struct and fix it:

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

medium

A. Change next to Option for shared ownership

B. Remove prev pointer completely

C. Change prev to Option<*mut Node> to avoid double ownership

D. Use Option<Node> for both next and prev

Solution

1. Step 1: Identify ownership problem with prev pointer

   Using Box for both next and prev means both own the node, causing double ownership which Rust disallows.

2. Step 2: Fix by changing prev pointer type

   Changing prev to Option<*mut Node> uses a raw pointer, which does not own the node and avoids ownership conflicts.

3. Final Answer:

   Change prev to Option<*mut Node> to avoid double ownership -> Option C

4. Quick Check:

   Prev pointer must not own node to prevent ownership error [OK]

Hint: Prev pointer uses raw pointer to avoid ownership conflicts [OK]

Common Mistakes:

• Using Box for prev causing compile errors
• Trying to remove prev pointer losing backward traversal
• Using Option<Node> which is invalid due to size

5. You want to implement a safe doubly linked list in Rust that allows multiple owners of nodes and mutable access. Which combination of pointer types is the best design choice?

hard

A. Use raw pointers (*mut Node) for both next and prev

B. Use Rc for next and Weak for prev

C. Use Option<Node> for next and Option<Node> for prev

D. Use Box<Node> for next and Box<Node> for prev

Solution

1. Step 1: Understand ownership and mutability requirements

   Multiple owners require reference counting (Rc). Mutable access requires interior mutability (RefCell).

2. Step 2: Choose pointer types for next and prev

   Next pointer uses Rc to own and allow mutation. Prev pointer uses Weak to avoid strong reference cycles and memory leaks.

3. Final Answer:

   Use Rc for next and Weak for prev -> Option B

4. Quick Check:

   Rc + RefCell + Weak = safe mutable doubly linked list [OK]

Hint: Use Rc + RefCell for ownership and Weak for back links [OK]

Common Mistakes:

• Using Box for both pointers causing ownership errors
• Using raw pointers risking unsafe code
• Ignoring Weak to prevent reference cycles