{x}
blog image

Serialize and Deserialize BST

Serialization is 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 search tree. There is no restriction on how your serialization/deserialization algorithm should work. You need to ensure that a binary search tree can be serialized to a string, and this string can be deserialized to the original tree structure.

The encoded string should be as compact as possible.

 

Example 1:

Input: root = [2,1,3]
Output: [2,1,3]

Example 2:

Input: root = []
Output: []

 

Constraints:

  • The number of nodes in the tree is in the range [0, 104].
  • 0 <= Node.val <= 104
  • The input tree is guaranteed to be a binary search tree.

Solution Explanation for Serialize and Deserialize BST

This problem requires designing a method to serialize (convert to a string) and deserialize (convert back from a string) a Binary Search Tree (BST). The serialization should be compact.

The solution employs Depth-First Search (DFS) for both serialization and deserialization. This approach leverages the inherent properties of a BST to reconstruct the tree efficiently.

Serialization (DFS in-order traversal):

The serialize function performs an in-order traversal of the BST. In-order traversal visits nodes in ascending order of their values (left subtree, root, right subtree). Since it's a BST, the in-order traversal yields a sorted sequence of node values. This sorted sequence is the core of our compact serialization.

The code iterates through the tree using recursion (dfs function). Each node's value is appended to a list (nums in Python, ArrayList in Java, vector in C++, a strings.Builder in Go). Finally, the list of values is converted into a space-separated string.

Deserialization (Reconstruction using Sorted Values):

The deserialize function reconstructs the BST from the space-separated string of values. It cleverly uses the sorted nature of the values and the BST properties to determine the placement of each node.

The deserialize function also uses recursion (dfs function). The input is the serialized string, and it reconstructs the tree node by node. The core idea is as follows:

  1. Base Case: If there are no more values to process or the current value falls outside the allowed range (defined by mi - minimum and mx - maximum), it returns None (or null in other languages). This handles leaf nodes and cases where a node cannot exist in a given sub-tree based on BST ordering.

  2. Recursive Step: It takes the next value from the sorted sequence. The value becomes the root node of a subtree.

  3. Subtree Construction: Recursively, it builds the left subtree using values within the range [minimum, current value) and the right subtree using values within the range (current value, maximum]. This ensures that the BST property is maintained.

The mi and mx parameters in the recursive function help constrain the search space for the left and right children, significantly improving efficiency.

Time and Space Complexity Analysis:

Serialization:

  • Time Complexity: O(N), where N is the number of nodes in the BST. This is because each node is visited exactly once during the in-order traversal.
  • Space Complexity: O(N) in the worst case (skewed tree), due to the recursive call stack. The space used to store the serialized string is also O(N).

Deserialization:

  • Time Complexity: O(N). Each node is created and processed exactly once.
  • Space Complexity: O(N) in the worst case (skewed tree), due to the recursive call stack and the space used for the tree itself.

The space complexity can be improved to O(log N) on average (balanced tree) because the recursion depth is proportional to the height of the tree, which is log N for a balanced tree. However, in the worst-case scenario of a skewed tree, the height becomes N, resulting in O(N) space complexity.

Code Examples (in Python, Java, C++, Go):

The provided code snippets demonstrate the serialization and deserialization process in several languages, implementing the explained algorithm. Each language's specific syntax is used, but the underlying logic remains the same. The comments in the code further clarify the functionality of different parts.