Reorder Linked List in DSA Rust - Time & Space Complexity

Time Complexity: Reorder Linked List

O(n)

Understanding Time Complexity

We want to understand how the time needed to reorder a linked list changes as the list gets bigger.

Specifically, we ask: how does the work grow when we rearrange nodes in this way?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

// Reorder linked list: L0->L1->…->Ln-1->Ln
// to L0->Ln->L1->Ln-1->L2->Ln-2->…
fn reorder_list(head: &mut Option>) {
    if head.is_none() || head.as_ref().unwrap().next.is_none() {
        return;
    }
    // 1. Find middle
    let mut slow = head.as_ref();
    let mut fast = head.as_ref();
    while fast.is_some() && fast.unwrap().next.is_some() {
        slow = slow.unwrap().next.as_ref();
        fast = fast.unwrap().next.as_ref().unwrap().next.as_ref();
    }
    // 2. Reverse second half
    // 3. Merge two halves
}
    

This code finds the middle of the list, reverses the second half, then merges the two halves to reorder the list.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Traversing the linked list multiple times.
• How many times: Three main passes: one to find the middle, one to reverse the second half, and one to merge.

How Execution Grows With Input

Each pass goes through about half or all of the list, so the total work grows roughly in a straight line with the list size.

Input Size (n)	Approx. Operations
10	~30 (3 passes x 10 nodes)
100	~300 (3 passes x 100 nodes)
1000	~3000 (3 passes x 1000 nodes)

Pattern observation: The operations increase linearly as the list grows.

Final Time Complexity

Time Complexity: O(n)

This means the time to reorder grows directly in proportion to the number of nodes in the list.

Common Mistake

[X] Wrong: "Reordering the list takes more than linear time because of multiple steps."

[OK] Correct: Each step only passes through the list once or half once, so combined they still add up to a linear amount of work.

Interview Connect

Understanding this helps you explain how to efficiently manipulate linked lists, a common skill in coding interviews and real projects.

Self-Check

"What if we used recursion to reorder the list instead of iteration? How would the time complexity change?"

Practice

1. What is the main goal of the Reorder Linked List problem?

easy

A. Sort the linked list in ascending order

B. Reverse the entire linked list

C. Rearrange the list so nodes alternate from start and end

D. Remove duplicate nodes from the list

Solution

1. Step 1: Understand the reorder pattern

   The reorder linked list problem requires rearranging nodes so the first node is followed by the last node, then the second node, then the second last node, and so on.

2. Step 2: Differentiate from other operations

   This is different from sorting, reversing, or removing duplicates because it mixes nodes from both ends alternatively.

3. Final Answer:

   Rearrange the list so nodes alternate from start and end -> Option C

4. Quick Check:

   Reorder = alternate start and end nodes [OK]

Hint: Remember: reorder mixes front and back nodes alternately [OK]

Common Mistakes:

• Confusing reorder with sorting
• Thinking reorder means full reversal
• Assuming duplicates are removed

2. Which Rust syntax correctly defines a singly linked list node struct for Reorder Linked List?

easy

A. struct Node { val: i32, next: Option }

B. struct Node { val: i32, next: &Node }

C. struct Node { val: i32, next: Box<Node> }

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

Solution

1. Step 1: Understand Rust ownership for linked lists

   Rust requires using Option for the next pointer to allow nullable and heap allocation.

2. Step 2: Check each option

   struct Node { val: i32, next: Option } uses Option which is correct. struct Node { val: i32, next: &Node } uses a reference which is invalid for ownership. struct Node { val: i32, next: Box<Node> } misses Option so no null. struct Node { val: i32, next: Option<Node> } uses Option<Node> which is invalid because Node is not sized.

3. Final Answer:

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

4. Quick Check:

   Rust linked list node = Option [OK]

Hint: Use Option for nullable next pointer in Rust [OK]

Common Mistakes:

• Using references instead of Box for next
• Omitting Option causing compile errors
• Using non-boxed Node causing size errors

3. Given the linked list 1 -> 2 -> 3 -> 4 -> null, what is the reordered list after applying the reorder algorithm?

medium

A. 1 -> 4 -> 2 -> 3 -> null

B. 4 -> 3 -> 2 -> 1 -> null

C. 1 -> 3 -> 2 -> 4 -> null

D. 1 -> 2 -> 3 -> 4 -> null

Solution

1. Step 1: Identify the reorder pattern on the list

   Start with first node (1), then last node (4), then second node (2), then second last node (3).

2. Step 2: Write the reordered list

   The reordered list is 1 -> 4 -> 2 -> 3 -> null.

3. Final Answer:

   1 -> 4 -> 2 -> 3 -> null -> Option A

4. Quick Check:

   Reorder 1-2-3-4 = 1-4-2-3 [OK]

Hint: Alternate nodes from front and back to reorder [OK]

Common Mistakes:

• Reversing entire list instead of alternating
• Keeping original order unchanged
• Swapping adjacent nodes incorrectly

4. Consider this Rust function snippet for reordering a linked list:

fn reorder_list(head: &mut Option) {
    let mut slow = head.as_ref();
    let mut fast = head.as_ref();
    while fast.is_some() && fast.unwrap().next.is_some() {
        slow = slow.unwrap().next.as_ref();
        fast = fast.unwrap().next.as_ref().unwrap().next.as_ref();
    }
}

What is the main issue in this code?

medium

A. The loop condition is incorrect and causes infinite loop

B. Using as_ref() causes immutable borrow, preventing mutation later

C. The unwrap calls will panic if list is empty

D. The slow pointer moves too fast skipping nodes

Solution

1. Step 1: Analyze use of as_ref()

   Using as_ref() creates an immutable reference, so slow and fast cannot be used to mutate the list later.

2. Step 2: Understand mutation needs in reorder

   Reordering requires mutable access to split and merge nodes, so immutable borrows block this.

3. Final Answer:

   Using as_ref() causes immutable borrow, preventing mutation later -> Option B

4. Quick Check:

   Immutable borrow blocks mutation in reorder [OK]

Hint: Use mutable references, not as_ref(), to modify list [OK]

Common Mistakes:

• Ignoring borrow rules causing compile errors
• Assuming unwrap always safe without checks
• Misunderstanding pointer movement speed

5. You have a linked list 1 -> 2 -> 3 -> 4 -> 5 -> null. After splitting the list into two halves, reversing the second half, and merging alternately, what is the final reordered list?

hard

A. 1 -> 2 -> 3 -> 4 -> 5 -> null

B. 5 -> 4 -> 3 -> 2 -> 1 -> null

C. 1 -> 3 -> 5 -> 2 -> 4 -> null

D. 1 -> 5 -> 2 -> 4 -> 3 -> null

Solution

1. Step 1: Split the list into two halves

   For 1->2->3->4->5, the middle is at 3, so first half: 1->2->3, second half: 4->5.

2. Step 2: Reverse the second half

   Reverse 4->5 to get 5->4.

3. Step 3: Merge alternately

   Merge nodes from first and reversed second half: 1->5->2->4->3->null.

4. Final Answer:

   1 -> 5 -> 2 -> 4 -> 3 -> null -> Option D

5. Quick Check:

   Split, reverse second half, merge = 1-5-2-4-3 [OK]

Hint: Split, reverse second half, then merge alternately [OK]

Common Mistakes:

• Not reversing second half before merge
• Merging without alternating nodes
• Incorrect middle node calculation