Closure of attributes in DBMS Theory - Mini Project: Build & Apply

Closure of Attributes in Database Management

📖 Scenario: You are working with a database design team. They want to find all the attributes that can be functionally determined by a given set of attributes in a table. This helps in understanding keys and dependencies.

🎯 Goal: Build a step-by-step solution to find the closure of a set of attributes given a list of functional dependencies.

📋 What You'll Learn

Create a dictionary called functional_dependencies where keys are tuples of attributes and values are sets of attributes they determine

Create a set called attributes representing the initial attribute set whose closure is to be found

Write a loop that repeatedly adds attributes to the closure set if they can be functionally determined by the current closure

Complete the closure calculation by returning or storing the final closure set

💡 Why This Matters

🌍 Real World

Finding attribute closures is essential in database design to identify candidate keys and ensure normalization.

💼 Career

Database administrators and designers use attribute closure calculations to optimize database schemas and maintain data integrity.

1

Setup Functional Dependencies

Create a dictionary called functional_dependencies with these exact entries: {('A',): {'B', 'C'}, ('B',): {'D'}, ('C',): {'E'}}

DBMS Theory

# Create the functional_dependencies dictionary
# Your code here

Need a hint?

Use a dictionary where keys are tuples of attributes and values are sets of attributes.

2

Define Initial Attribute Set

Create a set called attributes with the exact elements {'A'} to represent the starting attributes.

DBMS Theory

functional_dependencies = {('A',): {'B', 'C'}, ('B',): {'D'}, ('C',): {'E'}}
# Create the attributes set
# Your code here

Need a hint?

Use a set literal with the attribute 'A'.

3

Calculate Closure Core Logic

Create a set called closure initialized with attributes. Then write a while loop that continues as long as new attributes are added. Inside the loop, use a for loop with variables lhs and rhs to iterate over functional_dependencies.items(). Add attributes from rhs to closure if lhs is a subset of closure.

DBMS Theory

functional_dependencies = {('A',): {'B', 'C'}, ('B',): {'D'}, ('C',): {'E'}}
attributes = {'A'}
# Calculate the closure of attributes
# Your code here

Need a hint?

Use a loop that repeats until no new attributes are added to the closure.

4

Complete Closure Calculation

Add a final line that assigns the variable final_closure to the value of closure to store the result.

DBMS Theory

functional_dependencies = {('A',): {'B', 'C'}, ('B',): {'D'}, ('C',): {'E'}}
attributes = {'A'}
closure = set(attributes)
changed = True
while changed:
    changed = False
    for lhs, rhs in functional_dependencies.items():
        if set(lhs).issubset(closure) and not rhs.issubset(closure):
            closure.update(rhs)
            changed = True
# Store the final closure
# Your code here

Need a hint?

Assign the closure set to a new variable to keep the result.