Reorder Linked List in DSA Python - 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, how the steps grow when we rearrange nodes from start and end alternately.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

class ListNode:
    def __init__(self, val=0, next=None):
        self.val = val
        self.next = next

def reorderList(head):
    if not head or not head.next:
        return
    slow, fast = head, head
    while fast and fast.next:
        slow = slow.next
        fast = fast.next.next
    prev, curr = None, slow.next
    slow.next = None
    while curr:
        next_temp = curr.next
        curr.next = prev
        prev = curr
        curr = next_temp
    first, second = head, prev
    while second:
        tmp1, tmp2 = first.next, second.next
        first.next = second
        second.next = tmp1
        first, second = tmp1, tmp2

This code reorders a linked list by first finding the middle, reversing the second half, then merging both halves alternately.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

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

How Execution Grows With Input

Each loop goes through about half or all of the list nodes, so the total steps grow roughly in a straight line with the number of nodes.

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

Pattern observation: The operations increase linearly as the list size 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: "Reversing the second half or merging halves takes extra nested loops, so complexity is O(n²)."

[OK] Correct: Each loop runs separately over parts of the list without nesting inside each other, so total steps add up linearly, not multiply.

Interview Connect

Understanding this helps you explain how to efficiently reorder linked lists, a common task in coding challenges and real-world data handling.

Self-Check

"What if we used recursion to reverse the second half instead of a loop? How would the time complexity change?"

Practice

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

easy

A. Remove duplicate nodes from the linked list

B. Sort the linked list in ascending order

C. Reverse the entire linked list

D. Rearrange the list so nodes alternate from start and end towards the center

Solution

1. Step 1: Understand the problem statement

   The problem asks to reorder the list so that nodes come alternately from the start and end, like L0 -> Ln -> L1 -> Ln-1 -> L2 -> Ln-2 ...

2. Step 2: Differentiate from other operations

   This is not sorting or reversing the entire list, but a specific pattern of rearrangement.

3. Final Answer:

   Rearrange the list so nodes alternate from start and end towards the center -> Option D

4. Quick Check:

   Reorder means alternate start/end nodes = A [OK]

Hint: Remember: reorder means alternate front and back nodes [OK]

Common Mistakes:

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

2. Which of the following Python code snippets correctly splits a linked list into two halves for reordering?

easy

A. slow, fast = head, head.next
while fast and fast.next:
slow = slow.next
fast = fast.next.next
second = slow.next
slow.next = null

B. slow, fast = head, head
while fast and fast.next:
slow = slow.next
fast = fast.next.next
second = slow.next
slow.next = null

C. slow, fast = head.next, head
while fast and fast.next:
slow = slow.next
fast = fast.next.next
second = slow.next
slow.next = null

D. slow, fast = head, head
while fast.next and fast.next.next:
slow = slow.next
fast = fast.next.next
second = slow.next
slow.next = null

Solution

1. Step 1: Understand slow and fast pointer technique

   Using slow and fast pointers starting at head, fast moves twice as fast to find middle.

2. Step 2: Check code correctness

   slow, fast = head, head while fast and fast.next: slow = slow.next fast = fast.next.next second = slow.next slow.next = null correctly initializes both at head and uses while fast and fast.next to move pointers safely.

3. Final Answer:

   Option B code snippet correctly splits the list into two halves -> Option B

4. Quick Check:

   Slow and fast start at head, fast moves twice = B [OK]

Hint: Start slow and fast at head; fast moves twice as fast [OK]

Common Mistakes:

• Starting fast at head.next causes off-by-one errors
• Incorrect while loop conditions causing crashes
• Not breaking the list by setting slow.next = null

3. What is the output linked list after reordering the list 1 -> 2 -> 3 -> 4 -> 5 -> null?

medium

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

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

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

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

Solution

1. Step 1: Identify the reorder pattern

   Reorder means first node, last node, second node, second last node, and so on.

2. Step 2: Apply pattern to given list

   For 1->2->3->4->5, reordered is 1->5->2->4->3.

3. Final Answer:

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

4. Quick Check:

   Alternate front and back nodes = C [OK]

Hint: Pick nodes alternately from front and back [OK]

Common Mistakes:

• Reversing entire list instead of reordering
• Keeping original order unchanged
• Skipping nodes or mixing order

4. Given the following code snippet for reordering a linked list, what is the bug?

def reorderList(head):
    if not head or not head.next:
        return
    slow, fast = head, head
    while fast and fast.next:
        slow = slow.next
        fast = fast.next.next
    second = slow.next
    slow.next = null
    prev = null
    while second:
        temp = second.next
        second.next = prev
        prev = second
        second = temp
    first, second = head, prev
    while second:
        temp1 = first.next
        temp2 = second.next
        first.next = second
        second.next = temp1
        first = temp1
        second = temp2

medium

A. The function does not return the head after reordering

B. The slow pointer should start at head.next to find middle correctly

C. The while loop merging two halves should check first and second, not just second

D. The code does not handle the case when the list has only one node

Solution

1. Step 1: Analyze function return behavior

   The function modifies the list in place but does not return anything, which is acceptable if list nodes are modified directly.

2. Step 2: Check if returning head is necessary

   Since the list is modified in place, returning head is optional; however, if used in some contexts, returning head is safer.

3. Step 3: Identify actual bug

   All other parts correctly find middle, reverse second half, and merge. The main issue is no return statement if function expected to return head.

4. Final Answer:

   The function does not return the head after reordering -> Option A

5. Quick Check:

   Missing return statement = A [OK]

Hint: Check if function returns the modified list head [OK]

Common Mistakes:

• Starting slow pointer at head.next causing wrong middle
• Merging loop condition incorrect causing infinite loop
• Ignoring single node edge case

5. You have a linked list 1 -> 2 -> 3 -> 4 -> 5 -> 6 -> null. After applying the reorder linked list algorithm, what will be the final list? Also, explain why the middle node is chosen as it is.

hard

A. 1 -> 6 -> 2 -> 5 -> 3 -> 4 -> null; middle chosen to split list evenly

B. 1 -> 2 -> 3 -> 4 -> 5 -> 6 -> null; no reordering done for even length

C. 1 -> 6 -> 2 -> 5 -> 3 -> 4 -> null; middle chosen as the first of the two middle nodes

D. 1 -> 5 -> 2 -> 4 -> 3 -> 6 -> null; middle chosen as the last node

Solution

1. Step 1: Apply reorder pattern to even length list

   For 1->2->3->4->5->6, reordered list is 1->6->2->5->3->4.

2. Step 2: Explain middle node choice

   Using slow and fast pointers, slow stops at the first middle node (3), splitting list into two halves evenly.

3. Final Answer:

   1 -> 6 -> 2 -> 5 -> 3 -> 4 -> null; middle chosen as the first of the two middle nodes -> Option C

4. Quick Check:

   Even length split uses first middle node = D [OK]

Hint: For even length, slow stops at first middle node [OK]

Common Mistakes:

• Choosing second middle node as split point
• Not reordering even length lists
• Mixing node order in final list