Doubly Linked List Structure and Node Design in DSA Python - Time & Space Complexity

Time Complexity: Doubly Linked List Structure and Node Design

O(n)

Understanding Time Complexity

We want to understand how the time to create and link nodes in a doubly linked list grows as we add more nodes.

How does the work change when the list gets bigger?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

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

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

    def append(self, data):
        new_node = Node(data)
        if not self.head:
            self.head = new_node
            return
        current = self.head
        while current.next:
            current = current.next
        current.next = new_node
        new_node.prev = current

This code creates nodes and adds them to the end of a doubly linked list.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The while loop that moves through the list to find the last node.
• How many times: It runs once for each node already in the list before adding the new one.

How Execution Grows With Input

As the list grows, the time to add a new node grows because we must walk through all existing nodes to reach the end.

Input Size (n)	Approx. Operations
10	About 10 steps to find the end
100	About 100 steps to find the end
1000	About 1000 steps to find the end

Pattern observation: The work grows directly with the number of nodes already in the list.

Final Time Complexity

Time Complexity: O(n)

This means adding a node takes longer as the list gets bigger, because we must walk through all nodes to find the end.

Common Mistake

[X] Wrong: "Adding a node is always fast and takes the same time no matter how big the list is."

[OK] Correct: Because without keeping track of the last node, we must walk through the whole list each time, so it takes longer as the list grows.

Interview Connect

Understanding how linked list operations scale helps you explain your code choices clearly and shows you know how data structures behave in real situations.

Self-Check

"What if we kept a pointer to the last node in the list? How would the time complexity of adding a node change?"

Practice

1. What is the main difference between a doubly linked list node and a singly linked list node?

easy

A. A doubly linked list node does not store any data.

B. A doubly linked list node has pointers to both the previous and next nodes.

C. A doubly linked list node can only point to the next node.

D. A doubly linked list node stores data in a different format.

Solution

1. Step 1: Understand node pointers in singly linked list

   A singly linked list node has only one pointer to the next node.

2. Step 2: Understand node pointers in doubly linked list

   A doubly linked list node has two pointers: one to the previous node and one to the next node.

3. Final Answer:

   A doubly linked list node has pointers to both the previous and next nodes. -> Option B

4. Quick Check:

   Doubly linked list nodes have two pointers = D [OK]

Hint: Remember: doubly means two pointers, singly means one [OK]

Common Mistakes:

• Thinking doubly linked list nodes store data differently
• Confusing pointer count between singly and doubly linked lists
• Assuming doubly linked list nodes have only one pointer

2. Which of the following is the correct way to define a doubly linked list node class in Python?

easy

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

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

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

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

Solution

1. Step 1: Check for data storage and pointers

   A doubly linked list node must store data and have both prev and next pointers.

2. Step 2: Verify class definitions

   class Node: def __init__(self, data): self.data = data self.prev = None self.next = None correctly defines data, prev, and next attributes in __init__.

3. Final Answer:

   class Node:\n def __init__(self, data):\n self.data = data\n self.prev = None\n self.next = None -> Option D

4. Quick Check:

   Node class with data, prev, next = B [OK]

Hint: Doubly linked nodes need both prev and next pointers [OK]

Common Mistakes:

• Omitting the prev pointer
• Not initializing data attribute
• Defining only next pointer like singly linked list

3. What will be the output of the following code snippet?

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

head = Node(1)
second = Node(2)
third = Node(3)

head.next = second
second.prev = head
second.next = third
third.prev = second

current = third
result = []
while current:
    result.append(current.data)
    current = current.prev
print(result)

medium

A. [3, 2, 1]

B. [1, 2, 3]

C. [1, 3, 2]

D. [3, 1, 2]

Solution

1. Step 1: Understand the linked list connections

   Nodes are linked as 1 <-> 2 <-> 3 with prev and next pointers set correctly.

2. Step 2: Trace the while loop starting from third node

   Starting at node with data 3, append 3, move to prev (2), append 2, move to prev (1), append 1, then prev is None, loop ends.

3. Final Answer:

   [3, 2, 1] -> Option A

4. Quick Check:

   Traverse backward from third node = [3, 2, 1] [OK]

Hint: Backward traversal collects nodes in reverse order [OK]

Common Mistakes:

• Confusing next and prev pointers during traversal
• Starting traversal from head instead of third
• Appending data in wrong order

4. Identify the error in the following doubly linked list node insertion code and select the correct fix.

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

head = Node(1)
new_node = Node(2)

# Insert new_node after head
new_node.next = head.next
head.next.prev = new_node
head.next = new_node
new_node.prev = head

medium

A. No error; code inserts node correctly.

B. new_node.prev should be assigned before head.next.

C. head.next.prev causes AttributeError; fix by checking if head.next is not None before accessing prev.

D. new_node.next should be assigned after head.next.

Solution

1. Step 1: Analyze head.next before insertion

   Initially, head.next is None, so head.next.prev causes AttributeError.

2. Step 2: Fix by checking if head.next exists before accessing prev

   Adding a condition to check if head.next is not None before setting head.next.prev avoids error.

3. Final Answer:

   head.next.prev causes AttributeError; fix by checking if head.next is not None before accessing prev. -> Option C

4. Quick Check:

   Check for None before accessing prev pointer [OK]

Hint: Always check if next node exists before accessing its prev [OK]

Common Mistakes:

• Ignoring None check causing runtime error
• Assigning pointers in wrong order
• Assuming head.next is always valid

5. You want to insert a new node with value 4 between nodes with values 2 and 3 in a doubly linked list. Given the nodes are connected as 1 <-> 2 <-> 3, which sequence of pointer updates correctly inserts the new node?

hard

A. new_node.prev = node2; new_node.next = node3; node2.next = new_node; node3.prev = new_node

B. new_node.next = node2; new_node.prev = node3; node3.next = new_node; node2.prev = new_node

C. node2.next = new_node; new_node.next = node3; node3.next = new_node; new_node.prev = node2

D. node3.prev = new_node; new_node.prev = node2; node2.next = new_node; new_node.next = node2

Solution

1. Step 1: Set new_node pointers to neighbors

   new_node.prev should point to node2 and new_node.next to node3 to link correctly.

2. Step 2: Update neighbors to point to new_node

   node2.next must point to new_node and node3.prev must point to new_node to complete insertion.

3. Final Answer:

   new_node.prev = node2; new_node.next = node3; node2.next = new_node; node3.prev = new_node -> Option A

4. Quick Check:

   Set new_node pointers then update neighbors [OK]

Hint: Link new node to neighbors, then neighbors back to new node [OK]

Common Mistakes:

• Swapping prev and next pointers
• Updating neighbors before setting new_node pointers
• Forgetting to update one neighbor pointer