Insert at Middle Specific Position in DSA C - Time & Space Complexity

Time Complexity: Insert at Middle Specific Position

O(n)

Understanding Time Complexity

When we insert a new item at a specific middle position in a list, it takes some steps to find the right spot and then add the item.

We want to know how the time needed grows as the list gets bigger.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

void insertAtPosition(Node** head, int data, int position) {
    Node* newNode = malloc(sizeof(Node));
    newNode->data = data;
    newNode->next = NULL;

    if (position == 1) {
        newNode->next = *head;
        *head = newNode;
        return;
    }

    Node* temp = *head;
    for (int i = 1; i < position - 1 && temp != NULL; i++) {
        temp = temp->next;
    }

    if (temp == NULL) return; // position out of bounds

    newNode->next = temp->next;
    temp->next = newNode;
}
    

This code inserts a new node at a given position in a singly linked list by first moving to the node before that position.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The for-loop that moves through the list to reach the node before the insertion point.
• How many times: Up to (position - 2) times, which depends on the input position.

How Execution Grows With Input

As the list gets longer, the number of steps to reach the insertion point grows roughly in proportion to the position.

Input Size (n)	Approx. Operations
10	Up to 9 steps to reach position
100	Up to 99 steps to reach position
1000	Up to 999 steps to reach position

Pattern observation: The time grows linearly as the position increases within the list.

Final Time Complexity

Time Complexity: O(n)

This means the time to insert grows in a straight line with the size of the list or the position where we insert.

Common Mistake

[X] Wrong: "Inserting at the middle is always very fast and takes constant time."

[OK] Correct: Because we must first walk through the list to find the right spot, which takes time proportional to the position.

Interview Connect

Understanding how insertion time depends on position helps you explain and reason about linked list operations clearly in interviews.

Self-Check

"What if we had a pointer directly to the middle node? How would the time complexity change?"

Practice

1. What does inserting a node at a specific middle position in a linked list mean?

easy

A. Adding a new node only at the start of the list

B. Adding a new node exactly at the given position counting from the head

C. Adding a new node only at the end of the list

D. Replacing the node at the given position with a new node

Solution

1. Step 1: Understand the position concept

   Inserting at a specific position means counting nodes from the head and placing the new node exactly there.

2. Step 2: Differentiate from other insertions

   Insertion at start or end is special cases; here we insert in the middle without removing nodes.

3. Final Answer:

   Adding a new node exactly at the given position counting from the head -> Option B

4. Quick Check:

   Insert at position = Insert node at that place [OK]

Hint: Insert at position means count nodes and place new node there [OK]

Common Mistakes:

• Confusing insertion with replacement
• Thinking insertion only happens at start or end
• Ignoring the position count from head

2. Which of the following C code snippets correctly inserts a new node at position 3 in a singly linked list?

easy

A. Traverse to node 2, set newNode->next = current->next; current->next = newNode;

B. Set newNode->next = head; head = newNode;

C. Traverse to node 3, set current->next = newNode; newNode->next = NULL;

D. Set newNode->next = NULL; current->next = newNode;

Solution

1. Step 1: Identify correct traversal

   To insert at position 3, we must reach node 2 (one before position 3).

2. Step 2: Link new node correctly

   Set newNode->next to current->next, then current->next to newNode to insert properly.

3. Final Answer:

   Traverse to node 2, set newNode->next = current->next; current->next = newNode; -> Option A

4. Quick Check:

   Insert at pos 3 = link after node 2 [OK]

Hint: Insert after (position-1)th node by adjusting pointers [OK]

Common Mistakes:

• Inserting at wrong node position
• Not updating newNode->next before linking
• Setting newNode->next to NULL incorrectly

3. What will be the linked list after inserting a node with value 99 at position 3 in the list 10 -> 20 -> 30 -> 40 -> NULL?

medium

A. 99 -> 10 -> 20 -> 30 -> 40 -> NULL

B. 10 -> 20 -> 30 -> 99 -> 40 -> NULL

C. 10 -> 20 -> 30 -> 40 -> 99 -> NULL

D. 10 -> 20 -> 99 -> 30 -> 40 -> NULL

Solution

1. Step 1: Identify position 3 in the list

   Positions: 1=10, 2=20, 3=30, so new node goes before 30.

2. Step 2: Insert new node at position 3

   New node with 99 points to 30, node 20 points to new node.

3. Final Answer:

   10 -> 20 -> 99 -> 30 -> 40 -> NULL -> Option D

4. Quick Check:

   Insert at pos 3 places 99 before 30 [OK]

Hint: Insert at pos 3 means new node is third in list [OK]

Common Mistakes:

• Inserting after instead of at position
• Appending at end instead of middle
• Confusing node values and positions

4. Given the following code snippet to insert at position 2, what is the error?

void insertAtPos(Node** head, int data, int pos) {
  Node* newNode = malloc(sizeof(Node));
  newNode->data = data;
  newNode->next = NULL;
  Node* temp = *head;
  for(int i = 1; i < pos - 1; i++) {
    temp = temp->next;
  }
  newNode->next = temp->next;
  temp->next = newNode;
}

medium

A. Memory for newNode is not allocated

B. newNode->next is not set before linking

C. Loop runs one time too many causing temp to be NULL

D. Head pointer is not updated after insertion

Solution

1. Step 1: Analyze loop for position 2

   Loop should run from i=1 to i < pos-1 to stop at node before insertion point.

2. Step 2: Check temp usage after loop

   Original loop runs one time too many, moving temp to node 2 instead of node 1, causing incorrect insertion or NULL access.

3. Final Answer:

   Loop runs one time too many causing temp to be NULL -> Option C

4. Quick Check:

   Loop overshoots node before position [OK]

Hint: Loop should stop at position-1 to avoid NULL [OK]

Common Mistakes:

• Loop runs to pos instead of pos-1
• Not checking for NULL before accessing temp->next
• Forgetting to allocate memory for new node

5. You have a singly linked list with 5 nodes: 1 -> 2 -> 3 -> 4 -> 5 -> NULL. You want to insert a node with value 99 at position 6. What should happen and what will be the final list?

hard

A. Node 99 is appended at the end; list becomes 1 -> 2 -> 3 -> 4 -> 5 -> 99 -> NULL

B. Node 99 is inserted at position 5; list becomes 1 -> 2 -> 3 -> 4 -> 99 -> 5 -> NULL

C. Node 99 replaces node 5; list becomes 1 -> 2 -> 3 -> 4 -> 99 -> NULL

D. Insertion fails because position 6 is invalid; list remains unchanged

Solution

1. Step 1: Check list length and position

   List has 5 nodes; position 6 means insert after last node (append).

2. Step 2: Insert node at end

   Since position is one more than length, node 99 is added after node 5.

3. Final Answer:

   Node 99 is appended at the end; list becomes 1 -> 2 -> 3 -> 4 -> 5 -> 99 -> NULL -> Option A

4. Quick Check:

   Insert at pos > length means append [OK]

Hint: Position beyond length means append at end [OK]

Common Mistakes:

• Rejecting valid append position
• Replacing last node instead of appending
• Inserting at wrong position due to off-by-one