Topological sorting in Data Structures Theory - Mini Project: Build & Apply

Understanding Topological Sorting

📖 Scenario: Imagine you are organizing tasks that depend on each other. For example, you must finish homework before watching TV. You want to find an order to do all tasks without breaking any rules.

🎯 Goal: You will build a simple representation of tasks and their dependencies, then find a valid order to complete all tasks using topological sorting.

📋 What You'll Learn

Create a dictionary called tasks with tasks as keys and lists of dependent tasks as values

Create a dictionary called in_degree to count how many prerequisites each task has

Use a list called order to store the sorted tasks

Implement the topological sorting logic to find a valid order of tasks

💡 Why This Matters

🌍 Real World

Topological sorting helps in scheduling tasks, organizing project steps, and resolving dependencies in software builds.

💼 Career

Understanding topological sorting is useful for roles in project management, software development, and data analysis where task ordering and dependency resolution are important.

1

Create the tasks dictionary

Create a dictionary called tasks with these exact entries: 'cook': ['eat'], 'shop': ['cook'], 'eat': [], 'clean': ['shop']

Data Structures Theory

# Create the tasks dictionary with dependencies
# Your code here

Need a hint?

Think of each task as a key and the tasks that depend on it as a list of values.

2

Create the in-degree dictionary

Create a dictionary called in_degree with all tasks as keys and initial values set to 0. Then, update in_degree by counting how many prerequisites each task has from the tasks dictionary.

Data Structures Theory

tasks = {
    'cook': ['eat'],
    'shop': ['cook'],
    'eat': [],
    'clean': ['shop']
}
# Create in_degree dictionary and update counts
# Your code here

Need a hint?

Start by setting all counts to zero, then increase the count for each dependent task.

3

Implement the topological sorting logic

Create a list called order to store the sorted tasks. Use a list called zero_in_degree to hold tasks with zero in-degree. Use a while loop to process tasks from zero_in_degree, add them to order, and decrease the in-degree of dependent tasks. Add dependent tasks to zero_in_degree when their in-degree becomes zero.

Data Structures Theory

tasks = {
    'cook': ['eat'],
    'shop': ['cook'],
    'eat': [],
    'clean': ['shop']
}
in_degree = {task: 0 for task in tasks}
for deps in tasks.values():
    for dep in deps:
        in_degree[dep] += 1
# Implement topological sorting logic
# Your code here

Need a hint?

Start with tasks that have no dependencies, then remove them and update others.

4

Complete the topological sorting project

Add a final check to verify if the length of order is equal to the number of tasks in tasks. If they are equal, it means a valid order was found. Otherwise, it means there is a cycle and no valid order exists.

Data Structures Theory

tasks = {
    'cook': ['eat'],
    'shop': ['cook'],
    'eat': [],
    'clean': ['shop']
}
in_degree = {task: 0 for task in tasks}
for deps in tasks.values():
    for dep in deps:
        in_degree[dep] += 1

order = []
zero_in_degree = [task for task, degree in in_degree.items() if degree == 0]

while zero_in_degree:
    current = zero_in_degree.pop()
    order.append(current)
    for dependent in tasks[current]:
        in_degree[dependent] -= 1
        if in_degree[dependent] == 0:
            zero_in_degree.append(dependent)
# Add final check for cycle detection
# Your code here

Need a hint?

Compare the number of tasks processed with the total number of tasks to detect cycles.