Flatten a Multilevel Doubly Linked List

Flatten a Multilevel Doubly Linked List

1. What is this problem about?

The Flatten a Multilevel Doubly Linked List interview question involves a complex data structure where each node in a doubly linked list has a child pointer. This child pointer can point to another separate doubly linked list, which can also have children, creating a multi-level structure. Your goal is to "flatten" this into a single-level doubly linked list where the child nodes appear immediately after their parent.

2. Why is this asked in interviews?

Companies like Microsoft and Bloomberg use the Flatten a Multilevel Linked List coding problem to test a candidate's ability to manipulate pointers in a non-linear way. It evaluations your knowledge of Depth-First Search (DFS) and your ability to preserve the "doubly linked" property (both next and prev pointers) during a structural reorganization.

3. Algorithmic pattern used

This problem is solved using the DFS (Recursion or Stack) pattern.

1. Traversal: Iterate through the list. When a node has a child:
   • Find the tail of the flattened child list.
   • Connect the current node's next to the child.
   • Connect the child's prev to the current node.
   • Connect the tail of the child list back to the original next node.
   • Set child pointer to null.
2. Recursive Step: Repeat the flattening for every node in the original and child lists.

4. Example explanation

List: 1 <-> 2 <-> 3. Node 2 has child A <-> B.

1. Start at 1. Move to 2.
2. 2 has child A.
3. Store 2's next (3).
4. Link 2 <-> A.
5. Link B (tail of child list) <-> 3.
6. List is now: 1 <-> 2 <-> A <-> B <-> 3.

5. Common mistakes candidates make

• Losing Pointers: Forgetting to store the original next node before re-linking the child list.
• Broken Back-links: Updating next but forgetting to update the corresponding prev pointers, breaking the doubly-linked property.
• Child cleanup: Forgetting to set the child pointer to null after flattening.

6. Interview preparation tip

Think of this as a "Depth-First" traversal. If you were to traverse this as a tree (where next and child are branches), the flattened order is exactly the same as a Pre-order DFS. Use this analogy to explain your logic clearly to the interviewer.