428. Serialize and Deserialize N-ary Tree - Detailed Explanation

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Problem Statement

Description:
You are given the root of an N-ary tree (a tree where each node can have 0 or more children). Your task is to design algorithms to:

Serialize: Convert the N-ary tree into a string representation.
Deserialize: Reconstruct the original tree from the serialized string.

The key challenge is to design a serialization format that can uniquely represent the tree structure—including the value of each node and the relationship (i.e. which nodes are the children of which node)—so that the tree can be perfectly reconstructed later.

Node Definition (Typically):

Each tree node is defined as:

val: An integer representing the node’s value.
children: A list (or array) of child nodes.

Example:

Consider the following N-ary tree:

One way to serialize this tree is to record each node’s value along with the number of its children. For example, a possible serialization (using space or comma delimiters) is:

"1 3 2 0 3 2 5 0 6 0 4 0"

This can be interpreted as:

1 3 → Node 1 has value 1 and 3 children.
Next, for Node 1’s children:
- 2 0 → Node 2 with value 2 has 0 children.
- 3 2 → Node 3 with value 3 has 2 children.
  - 5 0 → Node 5 with value 5 has 0 children.
  - 6 0 → Node 6 with value 6 has 0 children.
- 4 0 → Node 4 with value 4 has 0 children.

Hints

Recursion/DFS Traversal:
Use a depth-first (preorder) traversal to serialize the tree. For each node, output its value and the number of children, then recursively serialize each child.
Include Child Count:
Storing the number of children is essential because it allows you to know where the current node’s children end during deserialization.
Token Delimiters:
Use a delimiter (e.g., a space or comma) between tokens (node values and counts) so that the string can be split into a list of tokens for easy parsing.
Handling an Empty Tree:
Decide on a representation for an empty tree (for example, an empty string or a special marker) and handle it appropriately.

Approaches

Approach 1: Preorder Traversal with Child Count

Serialization:

Traverse the tree in preorder.
For each node:
- Append its value.
- Append the number of its children.
- Recursively serialize each child.

Deserialization:

Split the serialized string into tokens.
Use a helper function with a pointer (or index) to read tokens in order.
For each call:
- Read a token for the node’s value.
- Read the next token for the number of children.
- Recursively create each child node according to the child count.
Return the constructed node.

Approach 2: Bracket Notation (Alternative)

Serialization:
Represent the tree using delimiters (for example, using square brackets) to group children.
E.g., "1 [ 2, 3 [ 5, 6 ], 4 ]".
Deserialization:
Parse the string recursively using the brackets as delimiters.

Note: The first approach is typically simpler and more direct for this problem.

Code Implementations

Python Implementation

Python3

. . . .

Java Implementation

Java

. . . .

Step-by-Step Walkthrough (Using Approach 1)

Let’s walk through the serialization and deserialization for the tree in our example:

Serialization Steps:

Start at Root (Node 1):
- Node value: 1
- Number of children: 3
- Serialized so far: "1 3"
Serialize Children of Node 1:
- First Child (Node 2):
  - Value: 2
  - Number of children: 0
  - Serialized token: "2 0"
- Second Child (Node 3):
  - Value: 3
  - Number of children: 2
  - Serialized token: "3 2"
- Third Child (Node 4):
  - Value: 4
  - Number of children: 0
  - Serialized token: "4 0"
Serialize Children of Node 3:
- For Node 3, process its children:
  - First Child (Node 5):
    - Value: 5
    - Number of children: 0
    - Serialized token: "5 0"
  - Second Child (Node 6):
    - Value: 6
    - Number of children: 0
    - Serialized token: "6 0"
Final Serialized String:
Combining all tokens in order (using spaces or commas), we get:
```
"1 3 2 0 3 2 5 0 6 0 4 0"
```

Deserialization Steps:

Tokenize:
Split the string into tokens:
[ "1", "3", "2", "0", "3", "2", "5", "0", "6", "0", "4", "0" ].
Reconstruct the Tree Recursively:
- Read the first token: 1 → Create root node with value 1.
- Read the next token: 3 → Root has 3 children.
- For each of the 3 children:
  - First Child:
    - Read token: 2 → Create node with value 2.
    - Next token: 0 → Node 2 has 0 children.
  - Second Child:
    - Read token: 3 → Create node with value 3.
    - Next token: 2 → Node 3 has 2 children.
    - For Node 3’s children:
      - Read token: 5 → Create node with value 5.
        
        Next token: 0 → No children.
      - Read token: 6 → Create node with value 6.
        
        Next token: 0 → No children.
  - Third Child:
    - Read token: 4 → Create node with value 4.
    - Next token: 0 → No children.
- The tree is fully reconstructed.

Complexity Analysis

Time Complexity:
- Serialization: (O(n)), where (n) is the number of nodes (each node is visited once).
- Deserialization: (O(n)), as each token is processed once.
Space Complexity:
- (O(n)) for storing the serialized string and the recursion stack during deserialization.

Common Mistakes

Missing the Child Count:
Failing to record the number of children for each node leads to ambiguous serialization.
Improper Token Parsing:
Ensure tokens are correctly split and processed in order during deserialization.
Edge Case Handling:
Handle the case of an empty tree (often represented by an empty string or a specific marker).

Edge Cases

Empty Tree:
If the input tree is empty (root is null), the serialization could be an empty string and deserialization should return null.
Single Node:
A tree with one node (with no children) should serialize as something like "nodeVal 0".
Deep Trees:
Ensure that the recursion does not cause stack overflow if the tree is very deep (within problem constraints this is typically not an issue).

Relevant Problems

If you enjoyed this problem, you might also like:

Serialize and Deserialize Binary Tree (LeetCode 297):
A similar problem for binary trees where each node has at most two children.
N-ary Tree Level Order Traversal:
Explore different ways of traversing N-ary trees.
Find Duplicate Subtrees:
A problem that involves serializing subtrees to detect duplicates.
Construct N-ary Tree from Preorder and Postorder Traversal:
A tree construction problem that uses traversal orders.