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

Time Complexity: Insert at Middle Specific Position

O(n)

Understanding Time Complexity

When inserting an element at a specific middle position in a list, we want to know how the time needed changes as the list grows.

How does the number of steps grow when the list gets bigger?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

public void InsertAtPosition(List<int> list, int position, int value)
{
    list.Insert(position, value);
}
    

This code inserts a value at a given position in a list.

Identify Repeating Operations

• Primary operation: Shifting elements after the insertion point to the right.
• How many times: Number of elements after the position, which depends on list size and position.

How Execution Grows With Input

When the list is small, few elements need to move. As the list grows, more elements may need shifting.

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

Pattern observation: The number of steps grows roughly in direct proportion to the list size.

Final Time Complexity

Time Complexity: O(n)

This means the time to insert grows linearly with the list size because elements after the position must move.

Common Mistake

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

[OK] Correct: Because elements after the insertion point must shift, the time depends on how many elements move, not just the position.

Interview Connect

Understanding how insertion time grows helps you explain trade-offs in data structures and shows you can reason about performance clearly.

Self-Check

"What if we changed the list to a linked list? How would the time complexity change for insertion at a middle position?"

Practice

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

easy

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

B. Adding a new element exactly between two existing nodes at a given position

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

D. Removing an element from the middle of the list

Solution

1. Step 1: Understand linked list insertion

   Inserting at a specific position means placing a new node between existing nodes, not just at start or end.

2. Step 2: Define middle position insertion

   Middle insertion targets a position inside the list, not at boundaries.

3. Final Answer:

   Adding a new element exactly between two existing nodes at a given position -> Option B

4. Quick Check:

   Middle insertion = between nodes [OK]

Hint: Middle insertion means placing node between two nodes [OK]

Common Mistakes:

• Confusing middle insertion with adding at start
• Thinking middle insertion removes nodes
• Assuming insertion only happens at end

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

easy

A. Node current = head; for(int i=1; i<2; i++) current = current.next; newNode.next = current.next; current.next = newNode;

B. Node current = head; for(int i=1; i<3; i++) current = current.next; newNode.next = current.next; current.next = newNode;

C. Node current = head; for(int i=0; i<3; i++) current = current.next; newNode.next = current.next; current.next = newNode;

D. Node current = head; for(int i=1; i<=3; i++) current = current.next; newNode.next = current.next; current.next = newNode;

Solution

1. Step 1: Understand zero-based vs one-based indexing

   Position 3 means after 2 nodes, so loop runs i from 1 to 2 to reach node before position 3.

2. Step 2: Check loop and insertion logic

   Node current = head; for(int i=1; i<2; i++) current = current.next; newNode.next = current.next; current.next = newNode; loops correctly to node 2, then inserts newNode after it.

3. Final Answer:

   Node current = head; for(int i=1; i<2; i++) current = current.next; newNode.next = current.next; current.next = newNode; -> Option A

4. Quick Check:

   Loop to node before position = i < position-1 [OK]

Hint: Loop to node before position: i < position - 1 [OK]

Common Mistakes:

• Looping too many times and skipping target node
• Using wrong loop bounds causing null reference
• Not updating next pointers correctly

3. Given the linked list: 10 -> 20 -> 30 -> 40 -> null, what is the list after inserting 25 at position 3 using this code?

Node newNode = new Node(25);
Node current = head;
for(int i = 1; i < 2; i++) current = current.next;
newNode.next = current.next;
current.next = newNode;

medium

A. 10 -> 25 -> 20 -> 30 -> 40 -> null

B. 25 -> 10 -> 20 -> 30 -> 40 -> null

C. 10 -> 20 -> 30 -> 25 -> 40 -> null

D. 10 -> 20 -> 25 -> 30 -> 40 -> null

Solution

1. Step 1: Trace loop to position before insertion

   Loop runs i=1; i<2, so current moves from 10 to 20 (node at position 2).

2. Step 2: Insert newNode after current

   newNode.next points to current.next (30), current.next points to newNode (25).

3. Final Answer:

   10 -> 20 -> 25 -> 30 -> 40 -> null -> Option D

4. Quick Check:

   Inserted 25 at position 3 correctly [OK]

Hint: Insert after node at position-1 to place at position [OK]

Common Mistakes:

• Inserting at wrong position due to loop bounds
• Not updating newNode.next correctly
• Confusing node values and positions

4. What is the error in this code snippet that tries to insert a node at position 4 in a linked list?

Node current = head;
for(int i = 1; i <= 4; i++)
  current = current.next;
newNode.next = current.next;
current.next = newNode;

medium

A. Loop runs too many times causing current to be null before insertion

B. newNode.next is not assigned before insertion

C. The loop should start from i = 0 instead of 1

D. The newNode is not created before insertion

Solution

1. Step 1: Analyze loop bounds

   Loop runs i=1 to 4 inclusive, moving current 4 times ahead, which may make current null if list length is less than 5.

2. Step 2: Identify null reference risk

   Accessing current.next after current is null causes runtime error.

3. Final Answer:

   Loop runs too many times causing current to be null before insertion -> Option A

4. Quick Check:

   Loop bounds must stop at position-1 [OK]

Hint: Loop to position-1, not position, to avoid null [OK]

Common Mistakes:

• Using <= instead of < in loop condition
• Not checking for null before accessing next
• Incorrect loop start index

5. You have a singly linked list: 5 -> 15 -> 25 -> 35 -> 45 -> null. Write the steps to insert a new node with value 30 at position 4, and what will be the final list?

hard

A. Traverse to node at position 2, link new node's next to current's next, then set current's next to new node. Result: 5 -> 15 -> 30 -> 25 -> 35 -> 45 -> null

B. Traverse to node at position 4, link new node's next to current's next, then set current's next to new node. Result: 5 -> 15 -> 25 -> 35 -> 30 -> 45 -> null

C. Traverse to node at position 3, link new node's next to current's next, then set current's next to new node. Result: 5 -> 15 -> 25 -> 30 -> 35 -> 45 -> null

D. Insert new node at head and shift all nodes. Result: 30 -> 5 -> 15 -> 25 -> 35 -> 45 -> null

Solution

1. Step 1: Traverse to node before position 4

   Move current pointer to node at position 3 (value 25).

2. Step 2: Insert new node after current

   Set newNode.next to current.next (35), then current.next to newNode (30).

3. Final Answer:

   5 -> 15 -> 25 -> 30 -> 35 -> 45 -> null -> Option C

4. Quick Check:

   Insert at position 4 means after node 3 [OK]

Hint: Insert after node at position-1 for correct placement [OK]

Common Mistakes:

• Inserting at wrong position by off-by-one error
• Not updating next pointers correctly
• Confusing position with node value