Serialize and Deserialize N-ary Tree

Refer editorial.

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class Codec:
    # Encodes a tree to a single string.
    def serialize(self, root: 'Node') -> str:
        def serializeHelper(root, lst):
            if root is None:
                return
            else:
                lst.append(str(root.val))
                lst.append(str(len(root.children)))
                for child in root.children:
                    serializeHelper(child, lst)

        lst = []
        serializeHelper(root, lst)
        return ",".join(lst)

    # Decodes your encoded data to tree.
    def deserialize(self, data: str) -> 'Node':
        if not data:
            return None

        ss = data.split(",")
        q = deque(ss)
        return self.deserializeHelper(q)

    def deserializeHelper(self, q):
        root = Node()
        root.val = int(q.popleft())
        size = int(q.popleft())
        root.children = []
        for _ in range(size):
            root.children.append(self.deserializeHelper(q))
        return root

Identifying Problem Isomorphism

“Serialize and Deserialize N-ary Tree” can be mapped to “Serialize and Deserialize Binary Tree”.

The reason for this isomorphism is that both problems share the same core objective: to serialize (or convert) a tree data structure into a string format that can be reconstructed back into the original tree, and then to deserialize (or convert back) the string into the original tree structure.

The difference is that one deals with an N-ary tree (a tree where each node can have any number of children), while the other deals with a binary tree (a tree where each node has at most two children). The concepts used to solve both problems are similar - you will need to perform tree traversal to read the nodes of the tree and encode this information in some manner.

“Serialize and Deserialize Binary Tree” is simpler because binary trees are a special case of N-ary trees where N is equal to 2. The rules for binary trees are a bit more constrained, which might make the problem slightly easier to tackle.

10 Prerequisite LeetCode Problems

“Serialize and Deserialize N-ary Tree” is a problem that requires an understanding of tree traversal and the concepts of serialization and deserialization. Here are 10 problems that could help you prepare for it:

Maximum Depth of Binary Tree: This problem is a good starting point to understand tree traversal.
Symmetric Tree: This problem helps you understand the structure of trees and how to traverse them.
Binary Tree Level Order Traversal: This problem introduces the concept of level order traversal which is crucial for serialization and deserialization.
Populating Next Right Pointers in Each Node: This problem deals with connecting nodes at the same level which can help in understanding the N-ary tree structure.
Serialize and Deserialize Binary Tree: This problem is directly related and provides the basis for the N-ary tree version.
Construct Binary Tree from Preorder and Inorder Traversal: This problem requires you to reconstruct a tree from given traversals.
Flatten Nested List Iterator: This problem can help understand the concept of flattening a complex structure, similar to serializing a tree.
Encode N-ary Tree to Binary Tree: Understanding this problem will help with understanding the structure of N-ary trees.
Clone N-ary Tree: This problem will help understand how to build an N-ary tree, which is necessary for the deserialization part.
N-ary Tree Preorder Traversal: This problem will help understand how to traverse an N-ary tree, which is necessary for the serialization part.

Problem Classification

Problem Statement:Serialization is the process of converting a data structure or object into a sequence of bits so that it can be stored in a file or memory buffer, or transmitted across a network connection link to be reconstructed later in the same or another computer environment.

Design an algorithm to serialize and deserialize an N-ary tree. An N-ary tree is a rooted tree in which each node has no more than N children. There is no restriction on how your serialization/deserialization algorithm should work. You just need to ensure that an N-ary tree can be serialized to a string and this string can be deserialized to the original tree structure.

For example, you may serialize the following 3-ary tree

as [1 [3[5 6] 2 4]]. Note that this is just an example, you do not necessarily need to follow this format.

Or you can follow LeetCode’s level order traversal serialization format, where each group of children is separated by the null value.

For example, the above tree may be serialized as [1,null,2,3,4,5,null,null,6,7,null,8,null,9,10,null,null,11,null,12,null,13,null,null,14].

You do not necessarily need to follow the above-suggested formats, there are many more different formats that work so please be creative and come up with different approaches yourself.

Example 1:

Input: root = [1,null,2,3,4,5,null,null,6,7,null,8,null,9,10,null,null,11,null,12,null,13,null,null,14] Output: [1,null,2,3,4,5,null,null,6,7,null,8,null,9,10,null,null,11,null,12,null,13,null,null,14] Example 2:

Input: root = [1,null,3,2,4,null,5,6] Output: [1,null,3,2,4,null,5,6] Example 3:

Input: root = [] Output: []

Constraints:

The number of nodes in the tree is in the range [0, 104]. 0 <= Node.val <= 104 The height of the n-ary tree is less than or equal to 1000 Do not use class member/global/static variables to store states. Your encode and decode algorithms should be stateless.

Analyze the provided problem statement. Categorize it based on its domain, ignoring ‘How’ it might be solved. Identify and list out the ‘What’ components. Based on these, further classify the problem. Explain your categorizations.

Visual Model of the Problem

How to visualize the problem statement for this problem?

Problem Restatement

Could you start by paraphrasing the problem statement in your own words? Try to distill the problem into its essential elements and make sure to clarify the requirements and constraints. This exercise should aid in understanding the problem better and aligning our thought process before jumping into solving it.

Abstract Representation of the Problem

Could you help me formulate an abstract representation of this problem?

Given this problem, how can we describe it in an abstract way that emphasizes the structure and key elements, without the specific real-world details?

Terminology

Are there any specialized terms, jargon, or technical concepts that are crucial to understanding this problem or solution? Could you define them and explain their role within the context of this problem?

Problem Simplification and Explanation

Could you please break down this problem into simpler terms? What are the key concepts involved and how do they interact? Can you also provide a metaphor or analogy to help me understand the problem better?

Constraints

Given the problem statement and the constraints provided, identify specific characteristics or conditions that can be exploited to our advantage in finding an efficient solution. Look for patterns or specific numerical ranges that could be useful in manipulating or interpreting the data.

What are the key insights from analyzing the constraints?

Case Analysis

Could you please provide additional examples or test cases that cover a wider range of the input space, including edge and boundary conditions? In doing so, could you also analyze each example to highlight different aspects of the problem, key constraints and potential pitfalls, as well as the reasoning behind the expected output for each case? This should help in generating key insights about the problem and ensuring the solution is robust and handles all possible scenarios.

Identification of Applicable Theoretical Concepts

Can you identify any mathematical or algorithmic concepts or properties that can be applied to simplify the problem or make it more manageable? Think about the nature of the operations or manipulations required by the problem statement. Are there existing theories, metrics, or methodologies in mathematics, computer science, or related fields that can be applied to calculate, measure, or perform these operations more effectively or efficiently?

Problem Breakdown and Solution Methodology

Given the problem statement, can you explain in detail how you would approach solving it? Please break down the process into smaller steps, illustrating how each step contributes to the overall solution. If applicable, consider using metaphors, analogies, or visual representations to make your explanation more intuitive. After explaining the process, can you also discuss how specific operations or changes in the problem’s parameters would affect the solution? Lastly, demonstrate the workings of your approach using one or more example cases.

Inference of Problem-Solving Approach from the Problem Statement

How did you infer from the problem statement that this problem can be solved using ?

Could you please provide a stepwise refinement of our approach to solving this problem?
How can we take the high-level solution approach and distill it into more granular, actionable steps?
Could you identify any parts of the problem that can be solved independently?
Are there any repeatable patterns within our solution?

Solution Approach and Analysis

Thought Process

Explain the thought process by thinking step by step to solve this problem from the problem statement and code the final solution. Write code in Python3. What are the cues in the problem statement? What direction does it suggest in the approach to the problem? Generate insights about the problem statement.

From Brute Force to Optimal Solution

Could you please begin by illustrating a brute force solution for this problem? After detailing and discussing the inefficiencies of the brute force approach, could you then guide us through the process of optimizing this solution? Please explain each step towards optimization, discussing the reasoning behind each decision made, and how it improves upon the previous solution. Also, could you show how these optimizations impact the time and space complexity of our solution?

Coding Constructs

Consider the following piece of complex software code.

What are the high-level problem-solving strategies or techniques being used by this code?
If you had to explain the purpose of this code to a non-programmer, what would you say?
Can you identify the logical elements or constructs used in this code, independent of any programming language?
Could you describe the algorithmic approach used by this code in plain English?
What are the key steps or operations this code is performing on the input data, and why?
Can you identify the algorithmic patterns or strategies used by this code, irrespective of the specific programming language syntax?

Language Agnostic Coding Drills

Your mission is to deconstruct this code into the smallest possible learning units, each corresponding to a separate coding concept. Consider these concepts as unique coding drills that can be individually implemented and later assembled into the final solution.

Dissect the code and identify each distinct concept it contains. Remember, this process should be language-agnostic and generally applicable to most modern programming languages.
Once you’ve identified these coding concepts or drills, list them out in order of increasing difficulty. Provide a brief description of each concept and why it is classified at its particular difficulty level.
Next, describe the problem-solving approach that would lead from the problem statement to the final solution. Think about how each of these coding drills contributes to the overall solution. Elucidate the step-by-step process involved in using these drills to solve the problem. Please refrain from writing any actual code; we’re focusing on understanding the process and strategy.

Targeted Drills in Python

Now that you’ve identified and ordered the coding concepts from a complex software code in the previous exercise, let’s focus on creating Python-based coding drills for each of those concepts.

Begin by writing a separate piece of Python code that encapsulates each identified concept. These individual drills should illustrate how to implement each concept in Python. Please ensure that these are suitable even for those with a basic understanding of Python.
In addition to the general concepts, identify and write coding drills for any problem-specific concepts that might be needed to create a solution. Describe why these drills are essential for our problem.
Once all drills have been coded, describe how these pieces can be integrated together in the right order to solve the initial problem. Each drill should contribute to building up to the final solution.

Remember, the goal is to not only to write these drills but also to ensure that they can be cohesively assembled into one comprehensive solution.