Flatten Multilevel List in O(n) Time Using Python

Input: head = [1,2,3,4,5,6,null,null,null,7,8,9,10,null,null,11,12]
Output: [1,2,3,7,8,11,12,9,10,4,5,6]
Explanation:

The multilevel linked list in the input is as follows:



After flattening the multilevel linked list it becomes:

Input: head = [1,2,null,3]
Output: [1,3,2]
Explanation:

The input multilevel linked list is as follows:

  1---2---NULL
  |
  3---NULL

Input: head = []
Output: []

 1---2---3---4---5---6--NULL
         |
         7---8---9---10--NULL
             |
             11--12--NULL

[1,2,3,4,5,6,null]
[7,8,9,10,null]
[11,12,null]

[1,2,3,4,5,6,null]
[null,null,7,8,9,10,null]
[null,11,12,null]

[1,2,3,4,5,6,null,null,null,7,8,9,10,null,null,11,12]

Your algorithm should be recursive and run in O(n) time.

Understanding the Problem

The core challenge of this problem is to traverse a multilevel doubly linked list and flatten it into a single-level doubly linked list. This involves handling the child pointers and ensuring that the order of nodes is maintained as specified.

Common applications of this problem include data structures that need to be linearized for easier processing or storage.

Potential pitfalls include not correctly handling the child pointers or losing track of the next pointers during the flattening process.

Approach

To solve this problem, we can use a recursive approach. The idea is to traverse the list and whenever we encounter a node with a child, we recursively flatten the child list and then merge it with the main list.

Here is a step-by-step approach:

1. Start from the head of the list.
2. Traverse the list node by node.
3. If a node has a child, recursively flatten the child list.
4. Merge the flattened child list with the main list.
5. Continue until all nodes are processed.

Algorithm

Let's break down the algorithm step-by-step:

1. Define a helper function that takes a node and returns the tail of the flattened list starting from that node.
2. In the helper function, traverse the list starting from the given node.
3. If a node has a child, recursively flatten the child list and merge it with the main list.
4. Update the next and previous pointers accordingly.
5. Return the tail of the flattened list.

Code Implementation

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

def flatten(head):
    if not head:
        return head

    # Helper function to flatten the list and return the tail
    def flatten_dfs(node):
        current = node
        last = node

        while current:
            next_node = current.next
            # If the current node has a child, we need to flatten the child list
            if current.child:
                # Recursively flatten the child list
                child_tail = flatten_dfs(current.child)

                # Connect current node to the child
                current.next = current.child
                current.child.prev = current

                # If next_node is not None, connect the tail of the child list to next_node
                if next_node:
                    child_tail.next = next_node
                    next_node.prev = child_tail

                # Clear the child pointer
                current.child = None

                # Update the last node to the tail of the child list
                last = child_tail
            else:
                last = current

            # Move to the next node
            current = next_node

        return last

    flatten_dfs(head)
    return head

Complexity Analysis

The time complexity of this algorithm is O(n), where n is the total number of nodes in the multilevel linked list. This is because each node is visited exactly once.

The space complexity is O(1) in terms of additional space used, but the recursion stack can go as deep as the maximum depth of the multilevel linked list, which makes the space complexity O(d), where d is the maximum depth.

Edge Cases

Some potential edge cases include:

• An empty list (head is None).
• A list with only one node.
• A list where all nodes have children.

Each of these cases should be handled correctly by the algorithm.

Testing

To test the solution comprehensively, we should include a variety of test cases:

• Simple cases with no children.
• Cases with multiple levels of children.
• Edge cases like an empty list or a single node list.

We can use Python's unittest framework to write and run these tests.

Thinking and Problem-Solving Tips

When approaching such problems, it's important to:

• Break down the problem into smaller, manageable parts.
• Think recursively if the problem involves hierarchical data structures.
• Draw diagrams to visualize the problem and the solution.
• Write pseudocode before jumping into the actual implementation.

Conclusion

Flattening a multilevel linked list is a common problem that tests your understanding of linked lists and recursion. By breaking down the problem and using a recursive approach, we can solve it efficiently in O(n) time.

Understanding and solving such problems is crucial for improving your problem-solving skills and preparing for technical interviews.

Additional Resources

For further reading and practice, consider the following resources:

• LeetCode: Flatten a Multilevel Doubly Linked List
• GeeksforGeeks: Flatten a Linked List with Next and Child Pointers
• Coursera: Data Structures