Computer Science
Grade 10
20 min
Graph Algorithms
Graph Algorithms
What you'll learn
- Identify at least three different types of information (like words, numbers, or symbols) that can be printed using a print statement.
- Explain in your own words what a print statement does in a computer program, focusing on how it shows information to the user.
- Apply the use of print statements to write a short program (3-5 lines) that displays a personalized greeting message on the screen, including the user's name.
- Solve simple debugging tasks by identifying and correcting errors in print statements, like missing quotation marks or incorrect spelling, in at least two provided code snippets.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Define a graph and its core components: vertices, edges, and weights.
Differentiate between directed and undirected graphs.
Represent a simple graph using an Adjacency Matrix.
Represent a simple graph using an Adjacency List.
Manually trace a Breadth-First Search (BFS) traversal on a small graph.
Manually trace a Depth-First Search (DFS) traversal on a small graph.
Identify real-world scenarios that can be modeled using graphs.
How does Google Maps find the fastest route from your home to school, navigating through hundreds of streets and intersections? 🗺️ It uses the power of graph algorithms!
In this lesson, you'll learn about graphs, a powerful data structure used to model networks and relationships. We will explore how to build and represent g...
2
Key Concepts & Vocabulary
TermDefinitionExample
GraphA data structure consisting of a set of vertices (or nodes) and a set of edges that connect these vertices.A map of cities is a graph, where each city is a vertex and the roads connecting them are edges.
Vertex (Node)A fundamental part of a graph that represents an object or a point. It's like a dot in a drawing of a network.In a social network graph, each person's profile is a vertex.
Edge (Link)A connection between two vertices in a graph.In a social network graph, the 'friendship' connection between two people is an edge.
Undirected GraphA graph where edges have no direction. The connection between two vertices is a two-way street.A Facebook friendship is undirected. If you are friends with someone, they are also friends with you.
Directed...
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Core Syntax & Patterns
Adjacency Matrix Representation
Create a 2D array (matrix) `M` of size V x V, where V is the number of vertices. `M[i][j] = 1` if there is an edge from vertex `i` to vertex `j`, and `0` otherwise.
Use this when the graph is dense (has many edges) or when you need to quickly check if an edge exists between two specific vertices. It can use a lot of memory for sparse graphs.
Adjacency List Representation
Create an array or dictionary where each index `i` corresponds to a vertex. The value at `i` is a list of all vertices that `i` has an edge to.
This is the most common way to represent graphs. It is memory-efficient for sparse graphs (graphs with few edges) and makes it easy to find all neighbors of a vertex.
4 more steps in this tutorial
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Challenging
Consider the social network example. A new person, Eve (4), becomes friends with only David (3). How does this change the BFS traversal from the original worked example, which started at Alice (0)?
A.The traversal order will be completely different.
B.The traversal order will be 0, 1, 2, 3, 4.
C.Eve (4) will be visited before David (3).
D.The traversal will not be able to reach Eve (4).
Challenging
A student implements DFS on a graph that contains a cycle (e.g., A -> B -> C -> A) but forgets to include a 'visited' set. What is the most likely outcome when the program is run?
A.stack overflow error due to infinite recursion.
B.The program will run correctly but will be very slow.
C.The program will produce an incorrect traversal order but will terminate.
D.The program will crash with an index out of bounds error.
Challenging
You are modeling a large city map with 10,000 intersections (vertices) where each intersection connects to an average of 3 other intersections. Which representation is more memory-efficient and why?
A.Adjacency Matrix, because it's a V x V structure that is easy to index.
B.Neither, both would require roughly the same amount of memory.
C.Adjacency Matrix, because the graph is very large.
D.Adjacency List, because the graph is sparse (few edges per vertex).
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Frequently asked questions
What grade level is "Graph Algorithms"?
Graph Algorithms is a Grade 10 Computer Science lesson on ExcelOS.
What will I learn in Graph Algorithms?
You'll be able to: Identify at least three different types of information (like words, numbers, or symbols) that can be printed using a print statement; Explain in your own words what a print statement does in a computer program, focusing on how….
Is "Graph Algorithms" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with Graph Algorithms?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.