Insert at Middle Specific Position in DSA Go - 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, the time it takes depends on how far we need to go to reach that position.

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

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

func InsertAtMiddle(head *Node, data int, pos int) *Node {
    newNode := &Node{data: data}
    if pos == 0 {
        newNode.next = head
        return newNode
    }
    current := head
    for i := 0; i < pos-1; i++ {
        current = current.next
    }
    newNode.next = current.next
    current.next = newNode
    return head
}
    

This code inserts a new node with given data at a specific position in a singly linked list.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The for-loop that moves through the list to reach the position before insertion.
• How many times: It runs (pos - 1) times, which depends on the position where we insert.

How Execution Grows With Input

As the list grows, the time to reach the middle position grows roughly in proportion to the position number.

Input Size (n)	Approx. Operations
10	About 5 steps to reach middle
100	About 50 steps to reach middle
1000	About 500 steps to reach middle

Pattern observation: The steps increase linearly as the list size increases.

Final Time Complexity

Time Complexity: O(n)

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

Common Mistake

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

[OK] Correct: Because we must walk through the list to reach the middle, the time depends on the position, so it grows with the list size.

Interview Connect

Understanding how insertion time changes with list size helps you explain your code clearly and shows you know how data structures behave in real situations.

Self-Check

"What if we kept a pointer to the middle node? How would the time complexity change when inserting at the middle?"

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 only at the end of the list

C. Adding a new node exactly between two existing nodes at a given position

D. Removing a node from the middle of the list

Solution

1. Step 1: Understand linked list positions

   Positions in a linked list start from 1 at the head and increase by 1 for each node.

2. Step 2: Define middle insertion

   Inserting at a middle position means placing a new node between two existing nodes at that position.

3. Final Answer:

   Adding a new node exactly between two existing nodes at a given position -> Option C

4. Quick Check:

   Middle insertion = Insert between nodes [OK]

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

Common Mistakes:

• Confusing insertion with deletion
• Thinking insertion only happens at start or end
• Ignoring position indexing starting at 1

2. Which Go code snippet correctly inserts a new node at position 3 in a singly linked list?

easy

A. temp := head
for i := 1; i < 2; i++ {
temp = temp.next
}
newNode.next = temp.next
temp.next = newNode

B. temp := head
for i := 0; i < 3; i++ {
temp = temp.next
}
newNode.next = temp.next
temp.next = newNode

C. temp := head
for i := 1; i <= 3; i++ {
temp = temp.next
}
newNode.next = temp.next
temp.next = newNode

D. temp := head
for i := 1; i < 3; i++ {
temp = temp.next
}
newNode.next = temp.next
temp.next = newNode

Solution

1. Step 1: Loop to node before position 3

   To insert at position 3, loop until position 2 (i < 2) to get node before insertion point.

2. Step 2: Adjust pointers correctly

   Set newNode.next to temp.next, then temp.next to newNode to insert newNode at position 3.

3. Final Answer:

   Code snippet in option A correctly inserts at position 3 -> Option A

4. Quick Check:

   Loop to position-1, then insert [OK]

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

Common Mistakes:

• Looping too many times and skipping nodes
• Setting pointers in wrong order causing lost nodes
• Using wrong loop conditions (<= instead of <)

3. What will be the linked list after inserting value 99 at position 2 in the list 10 -> 20 -> 30 -> null using this Go code?

type Node struct {
  val  int
  next *Node
}

head := &Node{10, &Node{20, &Node{30, nil}}}
newNode := &Node{99, nil}
temp := head
for i := 1; i < 1; i++ {
  temp = temp.next
}
newNode.next = temp.next
temp.next = newNode

medium

A. 10 -> 99 -> 20 -> 30 -> null

B. 99 -> 10 -> 20 -> 30 -> null

C. 10 -> 20 -> 99 -> 30 -> null

D. 10 -> 20 -> 30 -> 99 -> null

Solution

1. Step 1: Loop runs zero times to position 1 node

   The loop condition i < 1 means no iteration; temp stays at head (value 10).

2. Step 2: Insert newNode after temp

   newNode.next points to temp.next (node with 20), then temp.next points to newNode, inserting 99 after 10.

3. Final Answer:

   10 -> 99 -> 20 -> 30 -> null -> Option A

4. Quick Check:

   Insert after position 1 = position 2 [OK]

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

Common Mistakes:

• Misunderstanding loop range causing wrong insertion
• Confusing head node position as 0 instead of 1
• Incorrect pointer assignments losing nodes

4. Identify the error in this Go code that tries to insert a node at position 4 in a linked list of length 3:

temp := head
for i := 1; i <= 4; i++ {
  temp = temp.next
}
newNode.next = temp.next
temp.next = newNode

medium

A. New node is not created before insertion

B. Pointers are assigned in wrong order causing lost nodes

C. Position 4 is invalid for a list of length 3

D. Loop runs too many times causing temp to be nil and panic

Solution

1. Step 1: Analyze loop iterations

   The loop runs from i=1 to i=4 inclusive, moving temp 4 times forward.

2. Step 2: Check list length and temp value

   List length is 3, so after 3 moves temp becomes nil; moving one more causes panic on temp.next.

3. Final Answer:

   Loop runs too many times causing temp to be nil and panic -> Option D

4. Quick Check:

   Loop beyond list length = nil pointer error [OK]

Hint: Loop only to position-1 within list length [OK]

Common Mistakes:

• Looping beyond list length causing runtime errors
• Not checking for nil before accessing next
• Confusing <= with < in loop condition

5. Given a singly linked list and a position k, write a Go function to insert a new node with value v at position k. If k is greater than the list length + 1, insert at the end. What will be the list after inserting 50 at position 5 in 10 -> 20 -> 30 -> 40 -> null?

hard

A. 10 -> 20 -> 50 -> 30 -> 40 -> null

B. 10 -> 20 -> 30 -> 40 -> 50 -> null

C. 50 -> 10 -> 20 -> 30 -> 40 -> null

D. 10 -> 20 -> 30 -> 50 -> 40 -> null

Solution

1. Step 1: Check position against list length

   List length is 4; position 5 is length+1, so insert at end.

2. Step 2: Insert new node at end

   Traverse to last node (40), set its next to new node with value 50, new node next is nil.

3. Final Answer:

   10 -> 20 -> 30 -> 40 -> 50 -> null -> Option B

4. Quick Check:

   Position > length = insert at end [OK]

Hint: If position too big, insert at list end [OK]

Common Mistakes:

• Trying to insert beyond list length without appending
• Misplacing new node in middle instead of end
• Not handling nil next pointer at list end