Insert at Beginning Head Insert in DSA Python - Time & Space Complexity

Time Complexity: Insert at Beginning Head Insert

O(1)

Understanding Time Complexity

We want to understand how long it takes to add a new item at the start of a linked list.

How does the time needed change as the list grows bigger?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

class Node:
    def __init__(self, data):
        self.data = data
        self.next = None

class LinkedList:
    def __init__(self):
        self.head = None

    def insert_at_beginning(self, data):
        new_node = Node(data)
        new_node.next = self.head
        self.head = new_node

This code adds a new node at the start of a linked list by adjusting pointers.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Creating a new node and updating pointers.
• How many times: This happens once per insert, no loops or traversals involved.

How Execution Grows With Input

Adding at the start always takes the same steps, no matter how big the list is.

Input Size (n)	Approx. Operations
10	3 (create node, set next, update head)
100	3 (same steps)
1000	3 (still the same steps)

Pattern observation: The number of steps stays the same regardless of list size.

Final Time Complexity

Time Complexity: O(1)

This means adding at the beginning takes a fixed amount of time no matter how big the list is.

Common Mistake

[X] Wrong: "Inserting at the start takes longer as the list grows because we have to move all nodes."

[OK] Correct: We only change a few pointers; we do not move or visit other nodes, so time stays constant.

Interview Connect

Knowing that head insertion is quick helps you choose the right method when speed matters in linked lists.

Self-Check

"What if we changed to insert at the end of the list? How would the time complexity change?"

Practice

1. What does the operation insert at beginning do in a linked list?

easy

A. Deletes the first node of the list

B. Adds a new node at the start of the list

C. Adds a new node at the end of the list

D. Deletes the last node of the list

Solution

1. Step 1: Understand the meaning of 'insert at beginning'

   Inserting at the beginning means adding a new element before the current first element.

2. Step 2: Identify the effect on the linked list

   The new node becomes the new head, pushing the old head to second position.

3. Final Answer:

   Adds a new node at the start of the list -> Option B

4. Quick Check:

   Insert at beginning = Add new head [OK]

Hint: Insert at beginning means new head node [OK]

Common Mistakes:

• Confusing insert at beginning with insert at end
• Thinking it deletes nodes instead of adding
• Assuming it changes the last node

2. Which of the following is the correct syntax to insert a new node at the beginning of a singly linked list in Python?

easy

A. new_node = head.next; head = new_node

B. head.next = new_node; new_node = head

C. head = head.next; new_node = head

D. new_node.next = head; head = new_node

Solution

1. Step 1: Understand pointer assignment for head insert

   To insert at beginning, new_node's next points to current head.

2. Step 2: Update head to new_node

   Then head is updated to new_node to make it the first node.

3. Final Answer:

   new_node.next = head; head = new_node -> Option D

4. Quick Check:

   Set new_node.next to head, then head = new_node [OK]

Hint: Link new node to head, then update head [OK]

Common Mistakes:

• Assigning head.next instead of new_node.next
• Not updating head to new_node
• Swapping assignment order incorrectly

3. What will be the linked list after executing the following code?

class Node:
    def __init__(self, data):
        self.data = data
        self.next = None

head = Node(10)
new_node = Node(20)
new_node.next = head
head = new_node

medium

A. 20 -> 10 -> null

B. 10 -> 20 -> null

C. 20 -> null

D. 10 -> null

Solution

1. Step 1: Create initial list with head node 10

   Initially, head points to node with data 10 and next is None.

2. Step 2: Insert new_node with data 20 at beginning

   new_node.next points to head (node 10), then head updated to new_node.

3. Final Answer:

   20 -> 10 -> null -> Option A

4. Quick Check:

   New node 20 becomes head, points to 10 [OK]

Hint: New node points to old head, then becomes head [OK]

Common Mistakes:

• Thinking new_node is added at end
• Not updating head to new_node
• Confusing node data order

4. Identify the error in this code snippet that tries to insert a node at the beginning of a linked list:

class Node:
    def __init__(self, data):
        self.data = data
        self.next = None

head = Node(5)
new_node = Node(15)
head = new_node
new_node.next = head

medium

A. The order of assignments is wrong; new_node.next should be set before head update

B. Node class is missing a data attribute

C. head should be None initially

D. new_node should not be created before head

Solution

1. Step 1: Analyze assignment order

   head is set to new_node first, then new_node.next is set to head (which is now new_node itself).

2. Step 2: Identify logical error

   This causes new_node.next to point to itself, losing original list starting at old head.

3. Final Answer:

   The order of assignments is wrong; new_node.next should be set before head update -> Option A

4. Quick Check:

   Set new_node.next before head = new_node [OK]

Hint: Set new_node.next before updating head [OK]

Common Mistakes:

• Updating head before linking new_node.next
• Confusing attribute initialization
• Assuming head must be None initially

5. Given a linked list with nodes containing values [30, 20, 10] (30 is head), which sequence of operations correctly inserts a new node with value 40 at the beginning and results in the list 40 -> 30 -> 20 -> 10 -> null?

hard

A. new_node = Node(40); new_node.next = None; head = new_node

B. new_node = Node(40); head.next = new_node; head = new_node

C. new_node = Node(40); new_node.next = head; head = new_node

D. new_node = Node(40); head = new_node; new_node.next = head

Solution

1. Step 1: Create new node with value 40

   new_node is created with data 40 and next initially None.

2. Step 2: Link new_node to current head

   Set new_node.next to current head (node 30) to keep existing list after new node.

3. Step 3: Update head to new_node

   Head pointer is updated to new_node, making it the first node.

4. Final Answer:

   new_node = Node(40); new_node.next = head; head = new_node -> Option C

5. Quick Check:

   Link new node to old head, then update head [OK]

Hint: Link new node to head, then update head pointer [OK]

Common Mistakes:

• Linking head.next instead of new_node.next
• Updating head before linking new_node.next
• Setting new_node.next to None losing list