Graph Terminology Vertices Edges Directed Undirected Weighted in DSA C# - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to declare a graph vertex as an integer identifier.

DSA C#

int vertex = [1];

Drag options to blanks, or click blank then click option'

A1

Btrue

C"vertex"

Dnull

Attempts:

3 left

💡 Hint

Common Mistakes

Using a string or boolean instead of an integer for vertex id.

The vertex is represented as an integer identifier, so assigning 1 is correct.

2fill in blank

medium

Complete the code to add an edge between two vertices in an undirected graph.

DSA C#

graph.AddEdge([1], 2);

Drag options to blanks, or click blank then click option'

Anull

B1

Ctrue

D"vertex1"

Attempts:

3 left

💡 Hint

Common Mistakes

Using a string or null instead of an integer vertex id.

Edges connect vertices by their integer ids; 1 is a valid vertex id.

3fill in blank

hard

Fix the error in the code to correctly represent a directed edge from vertex 1 to vertex 2.

DSA C#

graph.AddEdge([1], 2, directed: true);

Drag options to blanks, or click blank then click option'

Anull

B"1"

C1

Dtrue

Attempts:

3 left

💡 Hint

Common Mistakes

Using string literals instead of integer vertex ids.

The vertex id must be an integer, so 1 is correct. Using a string causes an error.

4fill in blank

hard

Fill both blanks to create a weighted edge from vertex 3 to vertex 4 with weight 10.

DSA C#

graph.AddEdge([1], [2], weight: 10);

Drag options to blanks, or click blank then click option'

A3

B4

C5

D6

Attempts:

3 left

💡 Hint

Common Mistakes

Swapping the vertex ids or using incorrect vertex numbers.

The edge goes from vertex 3 to vertex 4 with weight 10, so use 3 and 4.

5fill in blank

hard

Fill all three blanks to create a weighted, directed edge from vertex 7 to vertex 8 with weight 15.

DSA C#

graph.AddEdge([1], [2], weight: [3], directed: true);

Drag options to blanks, or click blank then click option'

A7

B8

C15

D10

Attempts:

3 left

💡 Hint

Common Mistakes

Using wrong vertex ids or incorrect weight values.

The edge starts at vertex 7, ends at vertex 8, with weight 15 and is directed.

Practice

1. In a graph, what do we call the points or nodes where edges meet?

easy

A. Vertices

B. Edges

C. Weights

D. Paths

Solution

1. Step 1: Understand graph components

   A graph consists of points called nodes and connections called edges.

2. Step 2: Identify the term for nodes

   The points or nodes where edges meet are called vertices.

3. Final Answer:

   Vertices -> Option A

4. Quick Check:

   Nodes = Vertices [OK]

Hint: Remember: nodes = vertices, connections = edges [OK]

Common Mistakes:

• Confusing edges with vertices
• Thinking weights are nodes
• Mixing paths with vertices

2. Which of the following is the correct way to declare a directed graph using adjacency list in C#?

easy

A. int[] graph = new int[10];

B. List<int> graph = new List<int>();

C. Dictionary graph = new Dictionary();

D. Dictionary graph = new Dictionary();

Solution

1. Step 1: Understand adjacency list representation

   An adjacency list uses a dictionary mapping each vertex to a list of connected vertices.

2. Step 2: Check the correct C# syntax

   Dictionary correctly represents a graph where each int key has a list of connected nodes.

3. Final Answer:

   Dictionary<int, List<int>> graph = new Dictionary<int, List<int>>(); -> Option C

4. Quick Check:

   Adjacency list = Dictionary with List values [OK]

Hint: Adjacency list uses Dictionary with List for edges [OK]

Common Mistakes:

• Using List<int> alone
• Using array instead of dictionary
• Using Dictionary which stores single values

3. Consider the following C# code snippet for an undirected weighted graph:

var graph = new Dictionary>();
graph[1] = new List<(int, int)> { (2, 5), (3, 10) };
graph[2] = new List<(int, int)> { (1, 5), (3, 3) };
graph[3] = new List<(int, int)> { (1, 10), (2, 3) };

// What is the weight of the edge between vertex 2 and vertex 3?

medium

A. 8

B. 5

C. 10

D. 3

Solution

1. Step 1: Locate edge from vertex 2 to 3

   In graph[2], the list contains (1,5) and (3,3). The tuple (3,3) means vertex 3 with weight 3.

2. Step 2: Identify the weight value

   The weight of the edge between 2 and 3 is 3.

3. Final Answer:

   3 -> Option D

4. Quick Check:

   Edge (2,3) weight = 3 [OK]

Hint: Check the tuple with target vertex for weight [OK]

Common Mistakes:

• Confusing vertex numbers
• Picking weight from wrong tuple
• Adding weights incorrectly

4. The following C# code tries to add an edge to an undirected graph but causes a runtime error:

var graph = new Dictionary();
graph[1] = new List<int> { 2 };
// Add edge from 2 to 1
graph[2].Add(1);

What is the cause of the error?

medium

A. graph[2] is not initialized before adding

B. Cannot add edges in undirected graphs

C. List<int> cannot be used for graph edges

D. Syntax error in dictionary declaration

Solution

1. Step 1: Check initialization of graph[2]

   graph[2] is not assigned any list before calling Add, so it is null.

2. Step 2: Understand why Add causes error

   Calling Add on null causes a NullReferenceException at runtime.

3. Final Answer:

   graph[2] is not initialized before adding -> Option A

4. Quick Check:

   Null list causes error [OK]

Hint: Always initialize lists before adding elements [OK]

Common Mistakes:

• Assuming dictionary auto-initializes lists
• Thinking undirected graphs disallow adding edges
• Confusing syntax error with runtime error

5. You have a weighted directed graph represented as:

var graph = new Dictionary>
{
  {1, new List<(int, int)>{ (2, 4), (3, 1) }},
  {2, new List<(int, int)>{ (3, 2) }},
  {3, new List<(int, int)>{ (4, 7) }},
  {4, new List<(int, int)>{}}
};

// What is the total weight of the path 1 -> 3 -> 4?

hard

A. 10

B. 8

C. 7

D. 3

Solution

1. Step 1: Find weight from 1 to 3

   From graph[1], edge to 3 has weight 1.

2. Step 2: Find weight from 3 to 4

   From graph[3], edge to 4 has weight 7.

3. Step 3: Calculate total path weight

   Total weight = 1 + 7 = 8.

4. Final Answer:

   8 -> Option B

5. Quick Check:

   1->3=1 + 3->4=7 = 8 [OK]

Hint: Sum weights along the path edges [OK]

Common Mistakes:

• Adding wrong edges
• Ignoring direction of edges
• Using wrong weights from graph