Weighted graphs in Data Structures Theory - Mini Project: Build & Apply

Understanding Weighted Graphs

📖 Scenario: You are learning about weighted graphs, which are used to represent networks where connections have values like distances or costs. Imagine a map of cities connected by roads, where each road has a length.

🎯 Goal: Build a simple weighted graph using a dictionary to represent cities and the distances between them. Then, add a threshold to find roads shorter than a certain distance.

📋 What You'll Learn

Create a dictionary called graph with exact city connections and weights

Add a variable called max_distance to set a distance limit

Use a for loop with variables city and connections to iterate over graph.items()

Inside the loop, use a nested for loop with variables neighbor and distance to iterate over connections.items()

Create a list called short_roads to store tuples of roads shorter than max_distance

💡 Why This Matters

🌍 Real World

Weighted graphs are used in maps, network routing, and scheduling to represent connections with costs or distances.

💼 Career

Understanding weighted graphs is important for roles in software development, data analysis, and network engineering.

1

Create the weighted graph dictionary

Create a dictionary called graph with these exact entries: 'A': {'B': 5, 'C': 10}, 'B': {'A': 5, 'C': 3}, 'C': {'A': 10, 'B': 3}

Data Structures Theory

# Create the weighted graph dictionary
# Your code here

Need a hint?

Use a dictionary where each key is a city and each value is another dictionary of connected cities with distances.

2

Add a maximum distance threshold

Add a variable called max_distance and set it to 6 to represent the maximum road length to consider.

Data Structures Theory

graph = {
    'A': {'B': 5, 'C': 10},
    'B': {'A': 5, 'C': 3},
    'C': {'A': 10, 'B': 3}
}
# Add max_distance variable
# Your code here

Need a hint?

This variable will help filter roads by length.

3

Find roads shorter than the threshold

Create an empty list called short_roads. Use a for loop with variables city and connections to iterate over graph.items(). Inside it, use another for loop with variables neighbor and distance to iterate over connections.items(). Append a tuple (city, neighbor, distance) to short_roads if distance is less than max_distance.

Data Structures Theory

graph = {
    'A': {'B': 5, 'C': 10},
    'B': {'A': 5, 'C': 3},
    'C': {'A': 10, 'B': 3}
}
max_distance = 6
# Create short_roads list and loop to find roads shorter than max_distance
# Your code here

Need a hint?

Use nested loops to check each road's distance and add it to the list if it is less than max_distance.

4

Complete the weighted graph project

Add a final line that creates a variable called result and assigns it the value of short_roads to complete the project.

Data Structures Theory

graph = {
    'A': {'B': 5, 'C': 10},
    'B': {'A': 5, 'C': 3},
    'C': {'A': 10, 'B': 3}
}
max_distance = 6
short_roads = []
for city, connections in graph.items():
    for neighbor, distance in connections.items():
        if distance < max_distance:
            short_roads.append((city, neighbor, distance))
# Assign short_roads to result
# Your code here

Need a hint?

This final step stores the filtered roads in a variable for further use.