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

Time Complexity: Insert at Middle Specific Position

O(n)

Understanding Time Complexity

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

We ask: How much work does the computer do when the list gets bigger?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

function insertAtMiddle(arr: number[], value: number, position: number): number[] {
  for (let i = arr.length; i > position; i--) {
    arr[i] = arr[i - 1];
  }
  arr[position] = value;
  return arr;
}
    

This code inserts a value at a given position by shifting elements to the right to make space.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The for-loop that shifts elements one by one to the right.
• How many times: It runs from the end of the array down to the insertion position, so roughly n - position times.

How Execution Grows With Input

As the list grows, the number of shifts depends on how far the insertion point is from the end.

Input Size (n)	Approx. Operations (shifts)
10	About 5 if inserted in middle
100	About 50 if inserted in middle
1000	About 500 if inserted in middle

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

Final Time Complexity

Time Complexity: O(n)

This means the time to insert grows linearly as the list gets bigger.

Common Mistake

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

[OK] Correct: Because elements after the insertion point must move, the time depends on how many elements shift, which grows with list size.

Interview Connect

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

Self-Check

"What if we changed the data structure to a linked list? How would the time complexity of inserting at a middle position change?"

Practice

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

easy

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

B. Removing a node from the middle of the list

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

D. Adding a new node exactly at the given position counting from the start

Solution

1. Step 1: Understand insertion position

   Inserting at a specific middle position means placing the new node exactly at that position counting from the start of the list.

2. Step 2: Differentiate from other insertions

   Insertion at beginning or end is different; here we insert inside the list at a given index.

3. Final Answer:

   Adding a new node exactly at the given position counting from the start -> Option D

4. Quick Check:

   Insert at position = Add node at that index [OK]

Hint: Insert means add node exactly at given index [OK]

Common Mistakes:

• Confusing insertion with deletion
• Thinking insertion only happens at start or end
• Ignoring the position index

2. Which of the following TypeScript code snippets correctly inserts a node with value 10 at position 2 in a singly linked list?

easy

A. function insertAtPosition(head, val, pos) { let newNode = {value: val, next: null}; let current = head; for(let i=1; i

B. function insertAtPosition(head, val, pos) { let newNode = {value: val, next: null}; let current = head; for(let i=0; i

C. function insertAtPosition(head, val, pos) { let newNode = {value: val, next: null}; newNode.next = head; head = newNode; return head; }

D. function insertAtPosition(head, val, pos) { let newNode = {value: val, next: null}; head.next = newNode; return head; }

Solution

1. Step 1: Analyze loop for position

   The loop runs from 1 to pos-2 to reach node before insertion point (pos-1).

2. Step 2: Insert new node correctly

   New node's next points to current.next, then current.next updated to new node.

3. Final Answer:

   Code in option A correctly inserts at position 2 -> Option A

4. Quick Check:

   Loop to pos-1, link new node [OK]

Hint: Loop to node before position, then insert [OK]

Common Mistakes:

• Looping too far or too short
• Not updating newNode.next correctly
• Inserting at wrong position index

3. What will be the linked list after inserting value 99 at position 3 in the list 1 -> 2 -> 3 -> 4 -> null using the following TypeScript code?

function insertAtPosition(head, val, pos) {
  let newNode = {value: val, next: null};
  if (pos === 1) {
    newNode.next = head;
    return newNode;
  }
  let current = head;
  for (let i = 1; i < pos - 1; i++) {
    current = current.next;
  }
  newNode.next = current.next;
  current.next = newNode;
  return head;
}

// Initial list: 1 -> 2 -> 3 -> 4 -> null
// Insert 99 at position 3
let head = {value:1, next:{value:2, next:{value:3, next:{value:4, next:null}}}};
head = insertAtPosition(head, 99, 3);

medium

A. 1 -> 2 -> 3 -> 4 -> 99 -> null

B. 1 -> 2 -> 99 -> 3 -> 4 -> null

C. 99 -> 1 -> 2 -> 3 -> 4 -> null

D. 1 -> 99 -> 2 -> 3 -> 4 -> null

Solution

1. Step 1: Traverse to node before position 3

   Loop runs i=1 to pos-2=1, so current moves to node with value 2.

2. Step 2: Insert new node after current

   New node 99 points to current.next (node 3), current.next updated to new node.

3. Final Answer:

   1 -> 2 -> 99 -> 3 -> 4 -> null -> Option B

4. Quick Check:

   Insert at pos 3 places 99 after 2 [OK]

Hint: Insert after node at pos-1 [OK]

Common Mistakes:

• Inserting at wrong position
• Not updating links correctly
• Confusing position indexing

4. Identify the error in the following TypeScript function that tries to insert a node at position 2 in a linked list.

function insertAtPosition(head, val, pos) {
  let newNode = {value: val, next: null};
  let current = head;
  for(let i = 0; i < pos - 1; i++) {
    current = current.next;
  }
  newNode.next = current.next;
  current.next = newNode;
  return head;
}

medium

A. The loop runs one step too many, causing current to be null before insertion

B. The newNode.next is not assigned correctly

C. The function does not handle insertion at position 1

D. The function returns newNode instead of head

Solution

1. Step 1: Analyze loop range

   The loop runs from i=0 to pos-2, moving current pos-1 times, which moves current too far.

2. Step 2: Consequence of loop

   Current becomes the node at position pos, so current.next is undefined, causing error on insertion.

3. Final Answer:

   The loop runs one step too many, causing current to be null before insertion -> Option A

4. Quick Check:

   Loop overshoot breaks insertion [OK]

Hint: Loop to node before position, not at position [OK]

Common Mistakes:

• Looping to position instead of position-1
• Not checking for position 1 insertion
• Incorrectly updating links

5. Given a singly linked list and a position that may be greater than the list length, how should you modify the insertAtPosition function to insert the new node at the end if the position is beyond the list length? Choose the correct approach.

hard

A. Insert the new node at the head regardless of position

B. Throw an error if position is greater than list length

C. Traverse until current.next is null or position reached, then insert new node at current.next

D. Ignore the insertion if position is invalid

Solution

1. Step 1: Traverse safely

   Move current node forward until either position-1 steps or current.next is null (end of list).

2. Step 2: Insert at end if position too large

   If position is beyond length, current.next will be null, so insert new node at end by setting current.next to new node.

3. Final Answer:

   Traverse until current.next is null or position reached, then insert new node at current.next -> Option C

4. Quick Check:

   Insert at end if position too large [OK]

Hint: Stop at end or position, then insert [OK]

Common Mistakes:

• Not handling position beyond length
• Throwing error unnecessarily
• Inserting at wrong place when position invalid