Reorder Linked List in DSA C - 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 grows.

Specifically, how the steps increase when we rearrange nodes in a special order.

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->...
void reorderList(ListNode* head) {
    if (!head || !head->next) return;

    // Find middle
    ListNode *slow = head, *fast = head;
    while (fast && fast->next) {
        slow = slow->next;
        fast = fast->next->next;
    }

    // Reverse second half
    ListNode* prev = NULL;
    ListNode* curr = slow;
    while (curr) {
        ListNode* nextTemp = curr->next;
        curr->next = prev;
        prev = curr;
        curr = nextTemp;
    }

    // Merge two halves
    ListNode* first = head;
    ListNode* second = prev;
    while (second && second->next) {
        ListNode* tmp1 = first->next;
        ListNode* tmp2 = second->next;
        first->next = second;
        second->next = tmp1;
        first = tmp1;
        second = tmp2;
    }
}
    

This code reorders a linked list by first finding the middle, reversing the second half, then merging the two halves in alternating order.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Traversing the list multiple times: once to find middle, once to reverse, once to merge.
• How many times: Each traversal goes through about n/2 to n nodes, where n is list length.

How Execution Grows With Input

As the list size grows, each step takes longer roughly proportional to 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 total steps grow roughly in a straight line with input size.

Final Time Complexity

Time Complexity: O(n)

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

Common Mistake

[X] Wrong: "Reversing the second half or merging halves takes more than linear time because it looks complicated."

[OK] Correct: Each step only visits each node once or twice, so total work is still proportional to n, not more.

Interview Connect

Understanding this helps you explain how to handle linked lists efficiently, a common skill interviewers look for.

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 operation?

easy

A. To rearrange the list so nodes alternate from start and end

B. To sort the linked list in ascending order

C. To reverse the entire linked list

D. To remove duplicate nodes from the list

Solution

1. Step 1: Understand the reorder pattern

   The reorder linked list operation rearranges nodes so that 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 start and end alternatively.

3. Final Answer:

   To rearrange the list so nodes alternate from start and end -> Option A

4. Quick Check:

   Reorder = alternate start and end nodes [OK]

Hint: Reorder means alternate nodes from front and back [OK]

Common Mistakes:

• Confusing reorder with sorting
• Thinking reorder means reversing the list
• Assuming reorder removes duplicates

2. Which of the following C code snippets correctly finds the middle node of a singly linked list for reordering?

easy

A. while (fast && fast->next) { fast = fast->next; slow = slow->next; }

B. while (slow && slow->next) { fast = fast->next; slow = slow->next->next; }

C. while (fast && fast->next) { slow = slow->next; fast = fast->next->next; }

D. while (fast && slow) { slow = slow->next->next; fast = fast->next->next; }

Solution

1. Step 1: Identify the fast and slow pointer technique

   To find the middle node, fast pointer moves two steps, slow pointer moves one step until fast reaches end.

2. Step 2: Check each option for correct pointer movement

   while (fast && fast->next) { slow = slow->next; fast = fast->next->next; } correctly moves fast by two and slow by one. Others have incorrect pointer movements causing errors or wrong middle.

3. Final Answer:

   while (fast && fast->next) { slow = slow->next; fast = fast->next->next; } -> Option C

4. Quick Check:

   Fast moves 2 steps, slow moves 1 step [OK]

Hint: Fast pointer moves twice as fast as slow pointer [OK]

Common Mistakes:

• Swapping fast and slow pointer movements
• Not checking fast->next before fast->next->next
• Using slow pointer to move two steps

3. Given the linked list: 1 -> 2 -> 3 -> 4 -> 5 -> NULL, what is the reordered list after applying the reorder operation?

medium

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

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

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

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

Solution

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

   The reorder pattern takes first node, last node, second node, second last node, and so on.

2. Step 2: Apply pattern to given list

   Start with 1, then 5, then 2, then 4, then 3. So reordered list is 1 -> 5 -> 2 -> 4 -> 3 -> NULL.

3. Final Answer:

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

4. Quick Check:

   Alternate front and back nodes [OK]

Hint: Alternate nodes from start and end [OK]

Common Mistakes:

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

4. Consider this buggy C code snippet for reordering a linked list. What is the main error?

void reorderList(Node* head) {
  Node *slow = head, *fast = head;
  while (fast && fast->next) {
    slow = slow->next;
    fast = fast->next;
  }
  // further code omitted
}

medium

A. Fast pointer moves only one step instead of two

B. Slow pointer moves two steps instead of one

C. Missing check for head being NULL

D. Using wrong variable names for pointers

Solution

1. Step 1: Analyze pointer movements in the loop

   Fast pointer should move two steps to find middle, but here it moves only one step.

2. Step 2: Identify impact of incorrect fast pointer movement

   This causes slow pointer to not reach the true middle, breaking reorder logic.

3. Final Answer:

   Fast pointer moves only one step instead of two -> Option A

4. Quick Check:

   Fast must move 2 steps, not 1 [OK]

Hint: Fast pointer moves twice as fast as slow [OK]

Common Mistakes:

• Not moving fast pointer two steps
• Ignoring NULL checks
• Confusing slow and fast pointer roles

5. You have a linked list: 10 -> 20 -> 30 -> 40 -> 50 -> 60 -> NULL. After reordering, what will be the list? Also, explain why the middle node is chosen as it is.

hard

A. 10 -> 60 -> 20 -> 50 -> 30 -> 40 -> NULL; middle is 40 because it's the node after center

B. 10 -> 60 -> 20 -> 50 -> 30 -> 40 -> NULL; middle is 30 because it's the exact center for even length

C. 10 -> 50 -> 20 -> 40 -> 30 -> 60 -> NULL; middle is 30 because it's the exact center

D. 10 -> 60 -> 20 -> 50 -> 30 -> 40 -> NULL; middle is 20 because it's the first half's end

Solution

1. Step 1: Find the middle node for even length list

   For 6 nodes, middle is node 3 (value 30) because slow pointer stops at exact center when fast moves two steps.

2. Step 2: Apply reorder pattern

   Reorder alternates nodes from start and end: 10, 60, 20, 50, 30, 40.

3. Final Answer:

   10 -> 60 -> 20 -> 50 -> 30 -> 40 -> NULL; middle is 30 because it's the exact center for even length -> Option B

4. Quick Check:

   Middle at center, reorder alternates front and back [OK]

Hint: Middle is center node; reorder alternates front and back [OK]

Common Mistakes:

• Choosing wrong middle for even length
• Mixing reorder order
• Confusing node positions