Writing a Binary Search Tree in Python with Examples

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Lane Wagner
Lane Wagner Boot.dev co-founder and backend engineer

Last published October 1, 2022

What is a binary search tree?

A binary search tree, or BST for short, is a tree where each node is a value greater than all of its left child nodes and less than all of its right child nodes. Read on for an implementation of a binary search tree in Python from scratch!

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Why would I use a binary search tree?

Binary trees are useful for storing data in an organized manner so that it can be quickly retrieved, inserted, updated, and deleted. This arrangement of nodes allows each comparison to skip about half of the rest of the tree, so each operation as a whole is lightning fast.

To be precise, binary search trees provide an average Big-O complexity of O(log(n)) for search, insert, update, and delete operations. log(n) is much faster than the linear O(n) time required to find elements in an unsorted array. Many popular production databases such as PostgreSQL and MySQL use binary trees under the hood to speed up CRUD operations.

Binary Search Tree

Pros of a BST

  • When balanced, a BST provides lightning-fast O(log(n)) insertions, deletions, and lookups.
  • Binary search trees are simple to implement. An ordinary BST, unlike a balanced red-black tree, requires very little code to get running.

Cons of a BST

  • Slow for a brute-force search. If you need to iterate over each node, you might have more success with an array.
  • When the tree becomes unbalanced, all fast O(log(n)) operations quickly degrade to O(n).
  • Since pointers to whole objects are typically involved, a BST can require quite a bit more memory than an array, although this depends on the implementation.

Implementing a B-tree in Python

Step 1 - BSTNode Class

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, which will also act as the key, to be provided. If one isn’t provided we’ll just set it to None. We’ll also initialize both children of the new node to None.

Step 2 - Insert

insert binary search

We need a way to insert new data into the tree. Inserting a new node should append it as a leaf node in the proper spot.

  10                                10
 /   \        Insert 5            /    \
 2    60    --------->           2     60
/  \                            /  \
1   3                           1   3
                                     \
                                      5

The insert method is as follows:

def insert(self, val):
    if not self.val:
        self.val = val
        return

    if self.val == val:
        return

    if val < self.val:
        if self.left:
            self.left.insert(val)
            return
        self.left = BSTNode(val)
        return

    if self.right:
        self.right.insert(val)
        return
    self.right = BSTNode(val)

If the node doesn’t yet have a value, we can just set the given value and return. If we ever try to insert a value that also exists, we can also simply return as this can be considered a “no-op”. If the given value is less than our node’s value and we already have a left child then we recursively call insert on our left child. If we don’t have a left child yet then we just make the given value our new left child. We can do the same (but inverted) for our right side.

Step 3 - Get Min and Get Max

def get_min(self):
    current = self
    while current.left is not None:
        current = current.left
    return current.val

def get_max(self):
    current = self
    while current.right is not None:
        current = current.right
    return current.val

getMin and getMax are useful helper functions, and they’re easy to write! They are simple recursive functions that traverse the edges of the tree to find the smallest or largest values stored therein.

Step 4 - Delete

def delete(self, val):
    if self == None:
        return self
    if val < self.val:
        self.left = self.left.delete(val)
        return self
    if val > self.val:
        self.right = self.right.delete(val)
        return self
    if self.right == None:
        return self.left
    if self.left == None:
        return self.right
    min_larger_node = self.right
    while min_larger_node.left:
        min_larger_node = min_larger_node.left
    self.val = min_larger_node.val
    self.right = self.right.delete(min_larger_node.val)
    return self

The delete operation is one of the more complex ones. It is a recursive function as well, but it also returns the new state of the given node after performing the delete operation. This allows a parent whose child has been deleted to properly set it’s left or right data member to None.

Step 5 - Exists

The exists function is another simple recursive function that returns True or False depending on whether a given value already exists in the tree.

def exists(self, val):
    if val == self.val:
        return True

    if val < self.val:
        if self.left == None:
            return False
        return self.left.exists(val)

    if self.right == None:
        return False
    return self.right.exists(val)

Step 6 - Inorder

It’s useful to be able to print out the tree in a readable format. The inorder method print’s the values in the tree in the order of their keys.

def inorder(self, vals):
    if self.left is not None:
        self.left.inorder(vals)
    if self.val is not None:
        vals.append(self.val)
    if self.right is not None:
        self.right.inorder(vals)
    return vals

Step 7 - Preorder

def preorder(self, vals):
    if self.val is not None:
        vals.append(self.val)
    if self.left is not None:
        self.left.preorder(vals)
    if self.right is not None:
        self.right.preorder(vals)
    return vals

Step 8 - Postorder

def postorder(self, vals):
    if self.left is not None:
        self.left.postorder(vals)
    if self.right is not None:
        self.right.postorder(vals)
    if self.val is not None:
        vals.append(self.val)
    return vals

Using the BST

def main():
    nums = [12, 6, 18, 19, 21, 11, 3, 5, 4, 24, 18]
    bst = BSTNode()
    for num in nums:
        bst.insert(num)
    print("preorder:")
    print(bst.preorder([]))
    print("#")

    print("postorder:")
    print(bst.postorder([]))
    print("#")

    print("inorder:")
    print(bst.inorder([]))
    print("#")

    nums = [2, 6, 20]
    print("deleting " + str(nums))
    for num in nums:
        bst.delete(num)
    print("#")

    print("4 exists:")
    print(bst.exists(4))
    print("2 exists:")
    print(bst.exists(2))
    print("12 exists:")
    print(bst.exists(12))
    print("18 exists:")
    print(bst.exists(18))

Full Binary Search Tree in Python

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

    def insert(self, val):
        if not self.val:
            self.val = val
            return

        if self.val == val:
            return

        if val < self.val:
            if self.left:
                self.left.insert(val)
                return
            self.left = BSTNode(val)
            return

        if self.right:
            self.right.insert(val)
            return
        self.right = BSTNode(val)

    def get_min(self):
        current = self
        while current.left is not None:
            current = current.left
        return current.val

    def get_max(self):
        current = self
        while current.right is not None:
            current = current.right
        return current.val

    def delete(self, val):
        if self == None:
            return self
        if self.right == None:
            return self.left
        if self.left == None:
            return self.right
        if val < self.val:
            if self.left:
                self.left = self.left.delete(val)
            return self
        if val > self.val:
            if self.right:
                self.right = self.right.delete(val)
            return self
        min_larger_node = self.right
        while min_larger_node.left:
            min_larger_node = min_larger_node.left
        self.val = min_larger_node.val
        self.right = self.right.delete(min_larger_node.val)
        return self

    def exists(self, val):
        if val == self.val:
            return True

        if val < self.val:
            if self.left == None:
                return False
            return self.left.exists(val)

        if self.right == None:
            return False
        return self.right.exists(val)

    def preorder(self, vals):
        if self.val is not None:
            vals.append(self.val)
        if self.left is not None:
            self.left.preorder(vals)
        if self.right is not None:
            self.right.preorder(vals)
        return vals

    def inorder(self, vals):
        if self.left is not None:
            self.left.inorder(vals)
        if self.val is not None:
            vals.append(self.val)
        if self.right is not None:
            self.right.inorder(vals)
        return vals

    def postorder(self, vals):
        if self.left is not None:
            self.left.postorder(vals)
        if self.right is not None:
            self.right.postorder(vals)
        if self.val is not None:
            vals.append(self.val)
        return vals

Where would you use a binary search tree in real life?

There are many applications of binary search trees in real life, and one of the most common use cases is in storing indexes and keys in a database.

For example, in MySQL or PostgreSQL when you create a primary key column, what you’re really doing is creating a binary tree where the keys are the values of the column, and those nodes point to database rows. This lets the application easily search database rows by providing a key. For example, getting a user record by the email primary key.

There are many applications of binary search trees in real life, and one of the most common use cases is storing indexes and keys in a database.

For example, when you create a primary key column in MySQL or PostgreSQL, you create a binary tree where the keys are the values of the column and the nodes point to database rows. This allows the application to easily search for database rows by specifying a key, for example, to find a user record using the email primary key.

Other common uses include:

  • Pathfinding algorithms in video games (A*) use BSTs
  • File compression using a Huffman encoding scheme uses a binary search tree
  • Rendering calculations - Doom (1993) was famously the first game to use a BST
  • Compilers for low-level coding languages parse syntax using a BST
  • Almost every database in existence uses BSTs for key lookups

What’s the difference between a Binary Tree and a Linked List?

While binary trees and linked lists both use pointers to keep track of nodes, binary trees are more efficient for searching. In fact, linked lists are O(n) when used to search for a specific element - that’s pretty bad! Linked lists excel at removing and inserting elements quickly in the middle of the list.

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