# Deserialize a binary search tree from an inorder sequence

21 Nov 2009A friend of mine asked me about the ways a binary search tree (BST henceforth) could be transferred over the network. There are many ways to do so but I found one approach worth discussing here. BST can be serialized by storing the BST in pre-order or in-order sequence and then wired over the network and then reconstructed by deserializing the sequence. Deserialization from a pre-order sequence is pretty straight forward but deserializing a in-order sequence in to BST is worth a blog post, so I decided to post it here. I have been spending some time with Python for sometime so decided to give a try (The fact is that I find Python to be really cool).

DISCLAIMER: I am not a Python expert, so please do not expect perfect pythonic code here :)

It is being assumed that an in-order sequence will be given as input to be de-serialized.

Defined a class TreeNode to capture a properties of tree node.

`def __init__(self, val): self.val = val self.left = None self.right = None`

We can use famous Divide and Conquer philosophy to solve this problem by building first the left sub-tree, then right-subtree and then combining the two to create the complete tree. Here is the recursive function.

`def build_tree(sequence, low, high): if low > high: return None if low == high: return TreeNode(sequence[low]) mid = (low + high)/2 node = TreeNode(sequence[mid]) node.left = build_tree(sequence, low, mid -1) node.right = build_tree(sequence, mid + 1, high) return node`

Recursive function to print the content of the tree in in-order sequence.

`def traverse(node): if not node: return traverse(node.left) print node.val, traverse(node.right)`

Finally lets test out the code with following inorder sequence. Currently, we do not check if the input sequence if indeed a sorted sequence or not.

`if __name__ == "__main__": sequence = [8, 10, 11, 12, 14, 18, 20] tree = build_tree(sequence, 0, len(sequence) -1) traverse(tree)`

Do share your views about it.

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