A binary search tree, or BST for short, is a tree whose nodes each store a key greater than all their left child nodes and less than all of their right child
A binary search tree, or BST for short, is a tree whose nodes each store a key greater than all their left child nodes and less than all of their right child nodes. Binary trees are useful for storing data in an organized way, which allows for it to be fetched, inserted, updated, and deleted quickly. The greater-than and less-than ordering of nodes mean that each comparison skips about half of the remaining tree, so the whole lookup takes time proportional to the number of nodes in the tree.
To be precise, binary search trees provide an average Big-O complexity of
O(log(n)) for retrieval, insertion, update, and delete operations. Log(n) is much faster than the linear
O(n) time required to find items in an unsorted array. Many popular production databases such as PostgreSQL and MySQL use binary trees under the hood to speed up CRUD operations.
Our implementation won’t use a
Tree class, but instead just a
Node class. Binary trees are really just a pointer to a root node that in turn connects to each child node, so we’ll run with that idea.
First, we create a constructor:
class BSTNode: def __init__(self, val=None): self.left = None self.right = None self.val = val
We’ll allow a value (key) to be provided, but if one isn’t provided we’ll just set it to
None. We’ll also initialize both children of the new node to
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