serialization on Binary Tree

Question

Implement a function to serialize a binary tree into a string representation and a function to deserialize a string back into the original binary tree structure. The serialization should produce a compact format that can be easily reconstructed, and the output should handle edge cases such as empty trees. Your solution should efficiently manage both operations with a time complexity of O(n), where n is the number of nodes in the tree.

Codemia · Accepted Answer

The problem requires us to serialize and deserialize a binary tree. The serialization should produce a compact format that can be easily reconstructed. The two key operations (serialization and deserialization) suggest that we can utilize a **preorder traversal** approach, which is particularly well-suited for this task. Preorder traversal visits nodes in the order: root, left, right, which allows us to easily reconstruct the tree's structure during deserialization. This traversal ensures that we capture every node and the order in which they appear, maintaining the necessary information to rebuild the tree.

1. **Serialization**: We will implement a recursive function that traverses the tree in preorder. For each node, we will append its value to a list and use a special marker (e.g., 'null') for null children. For example, for a tree with root value 1, left child 2, and right child 3, the serialized string would look like '1,2,null,null,3,null,null'.

2. **Deserialization**: We will split the serialized string back into a list of values and use a recursive function to build the tree. We will utilize an index to track our position in the list. Whenever we encounter a value, we will create a node; if we hit 'null', we return None. For instance, given the input '1,2,null,null,3,null,null', we can reconstruct the tree by following the same order as our serialization.

```python
class TreeNode:
    def __init__(self, val=0, left=None, right=None):
        self.val = val
        self.left = left
        self.right = right

class Codec:
    def serialize(self, root: TreeNode) -> str:
        def preorder(node):
            if not node:
                return ['null']
            return [str(node.val)] + preorder(node.left) + preorder(node.right)
        return ','.join(preorder(root))

def deserialize(self, data: str) -> TreeNode:
        values = data.split(',')
        self.index = 0

def build_tree():
            if values[self.index] == 'null':
                self.index += 1
                return None
            node = TreeNode(int(values[self.index]))
            self.index += 1
            node.left = build_tree()
            node.right = build_tree()
            return node

return build_tree()
```

The time complexity for both serialization and deserialization is O(n), where n is the number of nodes in the tree. This is because we visit each node exactly once during traversal. The space complexity is also O(n) for the serialized string storage and the recursive call stack during deserialization. The constraints allow for efficient management of this space usage since we are directly mapping the tree structure into a linear format.

1. **Empty Tree**: If the tree is empty (i.e., root is None), the serialized output should be 'null'. The deserialize function should handle this correctly and return a None node. 
2. **Single Node Tree**: For a tree with only one node, e.g., root value 5, the serialization would yield '5,null,null'. This should also reconstruct correctly back to the single node. 
3. **Tree with Only Left or Right Children**: These scenarios should be handled gracefully, ensuring that our null markers accurately represent the absence of children.

serialization on Binary Tree

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