Insert at Middle Specific Position in DSA Java - 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, we want to know how the time it takes 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.

public void insertAtPosition(int[] arr, int n, int pos, int val) {
    for (int i = n - 1; i >= pos; i--) {
        arr[i + 1] = arr[i];
    }
    arr[pos] = val;
}

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.
• How many times: It runs from the end of the list down to the insertion position, so roughly n - pos times.

How Execution Grows With Input

As the list gets bigger, the number of shifts depends on where we insert.

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

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

Final Time Complexity

Time Complexity: O(n)

This means the time to insert grows linearly with the list size because shifting elements takes more steps as the list grows.

Common Mistake

[X] Wrong: "Inserting at any position always takes the same time as adding at the end."

[OK] Correct: Inserting in the middle or start requires moving many elements, which takes more time than just adding at the end.

Interview Connect

Understanding how insertion time changes with list size helps you explain and improve data handling in real projects.

Self-Check

"What if we used a linked list instead of an array? How would the time complexity of insertion at a middle position change?"

Practice

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

easy

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

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

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 position-based insertion

   Inserting at a specific position means placing the new node exactly at that index, shifting others if needed.

2. Step 2: Differentiate from other insertions

   Start or end insertions are special cases, but middle insertion targets a specific index inside the list.

3. Final Answer:

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

4. Quick Check:

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

Hint: Middle insert means place node exactly at given index [OK]

Common Mistakes:

• Confusing insertion with replacement
• Thinking insertion only happens at start or end
• Ignoring zero-based or one-based indexing

2. Which of the following Java code snippets correctly inserts a new node with value 10 at position 3 in a singly linked list?

easy

A. Node newNode = new Node(10); newNode.next = head.next.next.next; head.next.next.next = newNode;

B. Node newNode = new Node(10); newNode.next = head.next; head.next = newNode;

C. Node newNode = new Node(10); newNode.next = head.next.next; head.next.next = newNode;

D. Node newNode = new Node(10); newNode.next = head; head = newNode;

Solution

1. Step 1: Identify position 3 in zero-based indexing

   Position 3 means after two nodes: head -> next -> next, so newNode.next should point to head.next.next.

2. Step 2: Link newNode correctly

   Set newNode.next to head.next.next, then update head.next.next to newNode to insert at position 3.

3. Final Answer:

   Node newNode = new Node(10); newNode.next = head.next.next; head.next.next = newNode; -> Option C

4. Quick Check:

   Insert at position 3 = link newNode after second node [OK]

Hint: Link new node's next to current node at position, then update previous node [OK]

Common Mistakes:

• Incorrectly setting newNode.next to wrong node
• Not updating previous node's next pointer
• Confusing position indexing

3. What will be the linked list after inserting a node with value 25 at position 2 in the list: 10 -> 20 -> 30 -> 40 -> null?

Node head = new Node(10);
head.next = new Node(20);
head.next.next = new Node(30);
head.next.next.next = new Node(40);

// Insert 25 at position 2
Node newNode = new Node(25);
Node temp = head;
for (int i = 1; i < 2; i++) {
    temp = temp.next;
}
newNode.next = temp.next;
temp.next = newNode;

medium

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

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

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

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

Solution

1. Step 1: Traverse to node at position 1

   The loop runs once (i=1), so temp points to node with value 20.

2. Step 2: Insert newNode after temp

   newNode.next points to temp.next (node 30), then temp.next points to newNode, inserting 25 after 20.

3. Final Answer:

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

4. Quick Check:

   Insert at position 2 places 25 after 20 [OK]

Hint: Loop to node before position, link new node next, update previous next [OK]

Common Mistakes:

• Looping one extra time causing wrong insertion
• Not updating newNode.next correctly
• Confusing position indexing

4. Identify the error in the following code that tries to insert a node with value 15 at position 1 in a linked list:

Node newNode = new Node(15);
Node temp = head;
for (int i = 0; i < 1; i++) {
    temp = temp.next;
}
newNode.next = temp.next;
temp.next = newNode;

medium

A. Loop moves temp too far, skipping the head node

B. newNode.next is assigned incorrectly

C. temp.next is not updated after insertion

D. No error, code works fine

Solution

1. Step 1: Analyze loop movement

   The loop runs once, moving temp from head to head.next, so temp points to node at position 1, not before it.

2. Step 2: Understand insertion point

   To insert at position 1, temp should point to node before position 1 (head), but here it points to position 1 node, causing incorrect insertion.

3. Final Answer:

   Loop moves temp too far, skipping the head node -> Option A

4. Quick Check:

   Loop should stop before position to insert [OK]

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

Common Mistakes:

• Looping one time too many
• Confusing position indexing
• Not handling insertion at position 0 separately

5. Given a singly linked list with nodes: 5 -> 10 -> 15 -> 20 -> null, write the output after inserting a node with value 12 at position 3 using the following code:

Node newNode = new Node(12);
Node temp = head;
int position = 3;
for (int i = 1; i < position - 1; i++) {
    temp = temp.next;
}
newNode.next = temp.next;
temp.next = newNode;

// Print list
Node current = head;
while (current != null) {
    System.out.print(current.data + " -> ");
    current = current.next;
}
System.out.print("null");

hard

A. 5 -> 10 -> 15 -> 12 -> 20 -> null

B. 12 -> 5 -> 10 -> 15 -> 20 -> null

C. 5 -> 12 -> 10 -> 15 -> 20 -> null

D. 5 -> 10 -> 12 -> 15 -> 20 -> null

Solution

1. Step 1: Loop to node before position 3

   The loop runs with i=1 only, so temp moves from head (5) to next (10), which is node before position 3.

2. Step 2: Insert newNode after temp

   newNode.next points to temp.next (15), then temp.next points to newNode, inserting 12 between 10 and 15.

3. Final Answer:

   5 -> 10 -> 12 -> 15 -> 20 -> null -> Option D

4. Quick Check:

   Insert at position 3 places 12 after 10 [OK]

Hint: Loop to node before position, link new node, update next pointers [OK]

Common Mistakes:

• Looping too many times causing wrong insertion
• Not updating newNode.next correctly
• Confusing position indexing