Doubly linked list in Data Structures Theory - Step-by-Step Execution

Concept Flow - Doubly linked list

Create new node

↓

Set new_node.prev to current tail

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Set current tail.next to new_node

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Update tail pointer to new_node

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If list empty, set head to new_node

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Done - node added at end

This flow shows how a new node is added at the end of a doubly linked list by updating pointers forward and backward.

Execution Sample

Data Structures Theory

1. Create node A (value=10)
2. Create node B (value=20)
3. Link A <-> B
4. Add node C (value=30) at end
5. Link B <-> C

This example adds three nodes to a doubly linked list, linking them forward and backward.

Analysis Table

Step	Operation	Nodes in List	Pointer Changes	Visual State
1	Create node A	A	head = A, tail = A	A(prev=None, next=None)
2	Create node B	A, B	B.prev = None, B.next = None	A(prev=None, next=None), B(prev=None, next=None)
3	Link A <-> B	A <-> B	A.next = B, B.prev = A, tail = B	A(prev=None, next=B) <-> B(prev=A, next=None)
4	Create node C	A <-> B, C	C.prev = None, C.next = None	A(prev=None, next=B) <-> B(prev=A, next=None), C(prev=None, next=None)
5	Add C at end	A <-> B <-> C	B.next = C, C.prev = B, tail = C	A(prev=None, next=B) <-> B(prev=A, next=C) <-> C(prev=B, next=None)
6	End	A <-> B <-> C	No changes	Final list with head=A and tail=C

💡 All nodes linked correctly; tail points to last node; list is doubly linked.

State Tracker

Variable	Start	After Step 1	After Step 3	After Step 5	Final
head	None	A	A	A	A
tail	None	A	B	C	C
A.prev	None	None	None	None	None
A.next	None	None	B	B	B
B.prev	None	None	A	A	A
B.next	None	None	None	C	C
C.prev	None	None	None	B	B
C.next	None	None	None	None	None

Key Insights - 3 Insights

Why do we need both prev and next pointers in a doubly linked list?

Because each node must link to both its previous and next nodes to allow traversal in both directions, as shown in steps 3 and 5 where both pointers are set.

What happens if the list is empty when adding the first node?

The head and tail both point to the new node, and its prev and next pointers are None, as shown in step 1.

Why do we update the tail pointer when adding a node at the end?

Because the tail must always point to the last node to allow efficient additions at the end, as updated in step 5.

Visual Quiz - 3 Questions

Look at the execution table at step 3. What is the value of A.next?

A B

B None

C A

D C

💡 Hint

Check the 'Pointer Changes' and 'Visual State' columns at step 3.

At which step does the tail pointer change to node C?

A Step 1

B Step 3

C Step 5

D Step 6

💡 Hint

Look at the 'Pointer Changes' column for tail updates.

If we forget to set B.prev = A at step 3, what would happen?

A Tail pointer would be incorrect

B Traversal backward from B would fail

C Traversal forward from A would fail

D Head pointer would be None

💡 Hint

Consider the importance of the prev pointer for backward traversal.

Concept Snapshot

Doubly linked list nodes have two pointers: prev and next.
Each node links to its previous and next nodes.
Head points to first node; tail points to last node.
Adding at end updates tail and links both ways.
Allows traversal forward and backward efficiently.

Full Transcript

A doubly linked list is a chain of nodes where each node points to both its previous and next nodes. This allows moving forward and backward through the list. When adding a new node at the end, we create the node, link its prev pointer to the current tail, update the current tail's next pointer to the new node, and then update the tail pointer to the new node. If the list is empty, the new node becomes both head and tail. This structure supports efficient insertion and traversal in both directions.