Flatten a Multilevel Doubly Linked List

To flatten this multilevel doubly linked list, I would first analyze the structure to understand the depth of nesting. The core challenge is preserving the doubly linked properties—specifically ensuring that both 'next' and 'prev' pointers remain consistent after restructuring. I propose using a recursive depth-first search approach because it naturally handles arbitrary nesting depths. My algorithm starts at the head. If a node has a child, I temporarily store its original 'next' pointer. Then, I set the child as the new 'next' node and update the child's 'prev' pointer to the current node. Next, I recursively call the function on this new child node to flatten the entire sub-list. Once the recursion returns, the current node's 'next' will point to the tail of the flattened child list. At this point, I reconnect the stored original 'next' pointer to the end of the child list and update its 'prev' pointer accordingly. If there is no child, I simply move to the next node. This ensures every node is visited exactly once, resulting in O(N) time complexity where N is the total number of nodes, and O(D) space complexity for the recursion stack where D is the maximum depth. This approach aligns well with Google's emphasis on clean, efficient algorithms that handle edge cases robustly.