Flatten Multilevel List in O(n) Time Using C++

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 preserved as specified.

Multilevel linked lists are commonly used in scenarios where hierarchical data structures need to be represented, such as file systems or organizational charts.

Potential pitfalls include missing nodes due to incorrect handling of child pointers or creating cycles in the list.

Approach

To solve this problem, we can use a recursive approach to traverse the list and flatten it. Here’s a step-by-step breakdown:

Naive Solution

A naive solution would involve iterating through the list and appending child nodes to the end of the list. However, this approach is not optimal as it can lead to excessive time complexity due to repeated traversals.

Optimized Solution

An optimized solution involves using recursion to flatten the list in a single pass. The idea is to recursively flatten each child list and then merge it with the main list.

Algorithm

1. Start from the head of the list.
2. For each node, if it has a child, recursively flatten the child list.
3. Merge the flattened child list with the main list.
4. Continue to the next node and repeat the process.

Code Implementation

// Definition for a Node.
class Node {
public:
    int val;
    Node* prev;
    Node* next;
    Node* child;
};

class Solution {
public:
    Node* flatten(Node* head) {
        if (!head) return head;
        
        Node* curr = head;
        while (curr) {
            if (curr->child) {
                Node* next = curr->next;
                Node* child = flatten(curr->child);
                
                curr->next = child;
                child->prev = curr;
                curr->child = nullptr;
                
                while (curr->next) {
                    curr = curr->next;
                }
                
                curr->next = next;
                if (next) next->prev = curr;
            }
            curr = curr->next;
        }
        return head;
    }
};

Complexity Analysis

The time complexity of this approach 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) if we ignore the recursion stack. Otherwise, it is O(d), where d is the maximum depth of the multilevel linked list.

Edge Cases

Consider the following edge cases:

• An empty list (head = []). The output should be an empty list.
• A list with no child pointers. The output should be the same as the input list.
• A list where all nodes have child pointers. The algorithm should correctly flatten all levels.

Testing

To test the solution comprehensively, consider the following test cases:

• Simple lists with no child pointers.
• Lists with varying depths of child pointers.
• Edge cases such as empty lists and single-node lists.

Use a testing framework like Google Test for C++ to automate the testing process.

Thinking and Problem-Solving Tips

When approaching such problems, it is essential to:

• Understand the data structure and its properties.
• Break down the problem into smaller, manageable parts.
• Consider edge cases and how to handle them.
• Write clean, modular code with comments to explain the logic.

Practice solving similar problems to improve problem-solving skills and gain familiarity with different data structures and algorithms.

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, you can efficiently flatten the list in O(n) time.

Understanding and solving such problems is crucial for developing strong 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
• C++ Classes and Objects