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Serialize and Deserialize Binary Tree

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 a binary tree. 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 structure.

Clarification: The input/output format is the same as how LeetCode serializes a binary tree. You do not necessarily need to follow this format, so please be creative and come up with different approaches yourself.

 

Example 1:

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

Example 2:

Input: root = []
Output: []

 

Constraints:

  • The number of nodes in the tree is in the range [0, 104].
  • -1000 <= Node.val <= 1000

Solution Explanation: Serializing and Deserializing a Binary Tree

This problem involves designing an algorithm to serialize (convert to a string) and deserialize (convert back from a string) a binary tree. The solution presented uses Level Order Traversal (Breadth-First Search).

Approach:

  1. Serialization:

    • We perform a level-order traversal of the binary tree.
    • For each node encountered:
      • If the node is not null, we append its value (converted to a string) to a list.
      • If the node is null, we append a special marker, such as "#".
    • Finally, we join the elements of the list using a delimiter (e.g., ",") to create the serialized string.

  2. Deserialization:

    • We split the serialized string using the delimiter to get a list of strings.
    • We create a queue to store nodes that need to have their children processed. We start by creating the root node from the first element of the list.
    • We iterate through the list:
      • If the current element is not "#", we create a new node with the value from the element and add it to the queue. We then assign this new node as the left or right child of the node currently at the head of the queue.
      • If the element is "#", it represents a null node, and we don't create a new node.
    • The process continues until the queue is empty.

Time Complexity:

Both serialization and deserialization involve visiting each node in the tree exactly once. Therefore, the time complexity for both operations is O(N), where N is the number of nodes in the binary tree.

Space Complexity:

  • Serialization: The space complexity is O(N) because we use a queue to store nodes during traversal. In the worst case (a complete binary tree), the queue will hold up to N/2 nodes. The resulting string also has length proportional to N.
  • Deserialization: The space complexity is also O(N) because of the queue used for processing nodes and the intermediate string representation.

Code Examples (Python, Java, C++, Go, Javascript, C#):

The code examples provided demonstrate the level order traversal approach in multiple languages. Each implementation follows the same basic logic but uses the language-specific data structures (queues, lists/arrays, string manipulation). Key points:

  • Queue: A queue is crucial for level-order traversal; it ensures nodes are processed level by level.
  • Null Handling: The "#" or null marker is essential to represent missing nodes in the serialized string. Without it, we wouldn't be able to reconstruct the tree correctly during deserialization.
  • String Manipulation: The code uses string methods (join, split) to convert between string and list representations.

Remember to handle edge cases like an empty tree or a tree with only a root node. The provided code examples include these checks.