Why Binary Search Trees Are Great for Finding Things

Binary Search Trees, or BSTs, are created to make searching for information easier and faster.

Here’s how they work:

In a BST, each part, called a node, follows a special rule.

• The left side has values that are smaller than the main value.
• The right side has values that are bigger.

This setup helps us find what we need quickly. With every comparison we make while searching, we can cut the number of options in half!

Here are the main reasons why BSTs are efficient:

1. Tree Height: In a balanced BST, the height (how tall it is) is about $O(\log n)$. For example, if there are a lot of nodes, the tree stays pretty short. So, searching for a value usually takes only about $O(\log n)$ comparisons.

2. Simple Comparisons: When we begin at the top (the root), we only need to compare one value at a time. Depending on whether our value is larger or smaller, we can easily decide to go left or right.

Let’s look at a simple example. Imagine we want to find the number 25 in this BST:

      30
     /  \
    20   40
   / \   
  10  25  

1. First, we compare 25 with 30. Since 25 is smaller, we go left.
2. Next, we compare with 20. This time, since 25 is larger, we go to the right.
3. Finally, we find 25.

We only needed to do three comparisons, which is pretty quick!

In short, BSTs make it fast and easy to find things. That’s why they are popular in computer science for searching.