BST property and invariant in Data Structures Theory - Mini Project: Build & Apply

Understanding BST Property and Invariant

📖 Scenario: Imagine you are organizing books on a shelf so that you can find any book quickly. You decide to arrange them so that all books with titles alphabetically before a certain book are on the left, and all books with titles alphabetically after are on the right. This is similar to how a Binary Search Tree (BST) organizes data.

🎯 Goal: You will build a simple representation of a BST property and invariant using a dictionary to understand how data is organized and checked in a BST.

📋 What You'll Learn

Create a dictionary representing nodes with their values

Add a variable to represent the root node value

Write a condition to check the BST property for left and right children

Add a final statement confirming the BST invariant holds

💡 Why This Matters

🌍 Real World

BSTs are used in databases and file systems to organize data for quick search, insertion, and deletion.

💼 Career

Understanding BST properties is essential for software developers working with data structures, algorithms, and performance optimization.

1

Create the BST nodes dictionary

Create a dictionary called nodes with these exact entries: 'root': 10, 'left_child': 5, 'right_child': 15.

Data Structures Theory

# Create the nodes dictionary with root, left_child, and right_child
# Your code here

Need a hint?

Use a dictionary with keys 'root', 'left_child', and 'right_child' and assign the values 10, 5, and 15 respectively.

2

Set the root value variable

Create a variable called root_value and set it to the value of the root node from the nodes dictionary.

Data Structures Theory

nodes = {'root': 10, 'left_child': 5, 'right_child': 15}
# Set root_value to nodes['root']
# Your code here

Need a hint?

Access the root value from the dictionary using the key 'root' and assign it to root_value.

3

Check the BST property for children

Write a condition using if that checks if the left child's value is less than root_value and the right child's value is greater than root_value. Use nodes['left_child'] and nodes['right_child'] to get the children values.

Data Structures Theory

nodes = {'root': 10, 'left_child': 5, 'right_child': 15}
root_value = nodes['root']
# Check if left_child < root_value < right_child
# Your code here

Need a hint?

Use a chained comparison to check the BST property and assign True or False to bst_property_holds.

4

Confirm the BST invariant

Add a final variable called bst_invariant and set it to the value of bst_property_holds to confirm the BST property is maintained.

Data Structures Theory

nodes = {'root': 10, 'left_child': 5, 'right_child': 15}
root_value = nodes['root']
if nodes['left_child'] < root_value < nodes['right_child']:
    bst_property_holds = True
else:
    bst_property_holds = False
# Set bst_invariant to bst_property_holds
# Your code here

Need a hint?

Assign the result of the BST property check to bst_invariant to confirm the invariant.