297. Serialize and Deserialize Binary Tree - Detailed Explanation

Problem Statement

You are asked to design an algorithm to serialize and deserialize a binary tree. Serialization is the process of converting a tree into a string, and deserialization is the process of converting the string back to the original tree structure. There is no restriction on how your serialization/deserialization algorithm should work. You just need to ensure that a binary tree can be serialized to a string and this string can be deserialized to the original tree.

Example

Consider the following binary tree:

      1
     / \
    2   3
       / \
      4   5

A possible serialization using preorder traversal might be:
"1,2,null,null,3,4,null,null,5,null,null"

• Serialization:
  The tree is converted to a string by performing a preorder traversal (node, left, right) and using a special marker (for example, "null") for null pointers.

• Deserialization:
  The string is split (e.g., by commas) and then used to reconstruct the tree by reading values in the same order that they were serialized.

Constraints

• The number of nodes in the tree can be large.
• Node values can be any integer.
• The algorithm should be able to correctly reconstruct the tree even if it is unbalanced or contains duplicate values.

Hints and Intuition

• Hint 1:
  Think about using a traversal (preorder, inorder, or level-order) that uniquely represents the tree structure when combined with markers for null nodes.

• Hint 2:
  When deserializing, maintain an index or pointer to track your position in the serialized string/array so that you can reconstruct the tree recursively or iteratively.

• Hint 3:
  A recursive approach using preorder traversal is intuitive. Serialize the root, then serialize the left subtree, and finally serialize the right subtree. Use a marker (like "null") for empty nodes.

Detailed Approaches

Approach A: Recursive Preorder Traversal (DFS)

Serialization:

1. Base Case:
   If the current node is null, append a marker (e.g., "null") to the serialized string.
2. Recursive Case:
   Append the node's value, then recursively serialize the left subtree and the right subtree.
3. Combine:
   Use a delimiter (such as a comma) to separate the values.

Deserialization:

1. Tokenization:
   Split the serialized string by the delimiter to form a list of tokens.
2. Recursive Reconstruction:
   Use a helper function that reads tokens one by one. If a token is "null", return null; otherwise, create a new node with the token’s value and recursively build its left and right children.

Approach B: Level-Order Traversal (BFS)

Serialization:

1. BFS Traversal:
   Use a queue to perform level-order traversal.
2. Record Nodes:
   Append the value of each node; if a node is null, append a marker.
3. Optimization:
   You can remove trailing "null" markers from the resulting string.

Deserialization:

1. Queue and List:
   Split the string into tokens.
2. Reconstruct Tree:
   Use a queue to iteratively build the tree level by level. Read tokens for the left and right children of each node.

Note: While both approaches work correctly, the recursive preorder method is typically more straightforward to implement and understand.

Step-by-Step Walkthrough (Using Recursive Preorder)

Consider the binary tree:

      1
     / \
    2   3
       / \
      4   5

Serialization Process:

1. Start at root (1).
   Serialized string becomes: "1"

2. Process left subtree (2):

   • Node 2 → "2"
   • Left child is null → "null"
   • Right child is null → "null"
     So subtree serialized as: "2,null,null"

3. Process right subtree (3):

   • Node 3 → "3"
   • Process left subtree (4): "4,null,null"
   • Process right subtree (5): "5,null,null"
     So subtree serialized as: "3,4,null,null,5,null,null"

4. Combine:
   Final serialized string:
   "1,2,null,null,3,4,null,null,5,null,null"

Deserialization Process:

1. Split the string into tokens:
   ["1", "2", "null", "null", "3", "4", "null", "null", "5", "null", "null"]

2. Read first token "1" → Create root node with value 1.

3. Recursively construct the left subtree:

   • Next token "2" → Create node with value 2.

   • Next token "null" → Left child of node 2 is null.

   • Next token "null" → Right child of node 2 is null.

4. Recursively construct the right subtree:

   • Next token "3" → Create node with value 3.
   • For node 3, left child is constructed from token "4" → and its children are built from subsequent "null" tokens.
   • For node 3, right child is constructed from token "5" → and its children are built from subsequent "null" tokens.

5. The tree is fully reconstructed matching the original.

Code Implementation

Python Implementation