Adjacency List vs Matrix When to Choose Which in DSA C# - Interactive Comparison Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to declare an adjacency matrix for a graph with 5 nodes.

DSA C#

int[,] adjacencyMatrix = new int[5, [1]];

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

A5

B4

C6

D1

Attempts:

3 left

💡 Hint

Common Mistakes

Using the wrong size for the matrix dimension.

Confusing number of edges with number of nodes.

An adjacency matrix for a graph with 5 nodes is a 5x5 matrix, so both dimensions are 5.

2fill in blank

medium

Complete the code to add an edge from node 2 to node 3 in an adjacency list.

DSA C#

adjacencyList[2].[1](3);

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AAdd

BRemove

CClear

DInsert

Attempts:

3 left

💡 Hint

Common Mistakes

Using Remove instead of Add.

Using Insert without specifying index.

To add an edge in an adjacency list, you use the Add method to add the connected node.

3fill in blank

hard

Fix the error in the code that initializes an adjacency list for 4 nodes.

DSA C#

List<int>[] adjacencyList = new List<int>[[1]];
for (int i = 0; i < 4; i++) {
    adjacencyList[i] = new List<int>();
}

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

A3

B5

C4

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Setting the array size smaller than the number of nodes.

Setting the array size larger than needed.

The array size must match the number of nodes, which is 4 here.

4fill in blank

hard

Fill both blanks to create a condition that checks if the graph is dense (more than half possible edges) using adjacency matrix.

DSA C#

if (edgeCount [1] (nodeCount * (nodeCount - 1) / 2)) {
    Console.WriteLine("Graph is dense");
}

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

A<

B>=

C==

D>

Attempts:

3 left

💡 Hint

Common Mistakes

Using '<' instead of '>'.

Using '==' which checks equality, not density.

A graph is dense if the number of edges is greater than half the maximum possible edges.

5fill in blank

hard

Fill all three blanks to create a dictionary comprehension that maps each node to its degree using adjacency list.

DSA C#

var degrees = new Dictionary<int, int>() {
    { [1], adjacencyList[[2]].[3] }
};

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

Anode

CCount

DLength

Attempts:

3 left

💡 Hint

Common Mistakes

Using Length instead of Count for List.

Using wrong variable names.

Each node maps to the count of its adjacency list, which is the degree.

Practice

1. Which data structure is generally better for representing a graph with many nodes but very few edges?

easy

A. Adjacency List

B. Adjacency Matrix

C. Array

D. Stack

Solution

1. Step 1: Understand graph density

   A graph with many nodes but few edges is called a sparse graph.

2. Step 2: Choose data structure for sparse graph

   Adjacency List stores only existing edges, saving space for sparse graphs.

3. Final Answer:

   Adjacency List -> Option A

4. Quick Check:

   Sparse graph = Adjacency List [OK]

Hint: Sparse graph? Use adjacency list for space efficiency [OK]

Common Mistakes:

• Choosing adjacency matrix for sparse graphs wastes space
• Confusing sparse with dense graphs
• Thinking arrays or stacks represent graphs directly

2. Which of the following is the correct way to declare an adjacency matrix for a graph with 4 nodes in C#?

easy

A. int[][] adjacencyMatrix = new int[4][]; for(int i=0; i<4; i++) adjacencyMatrix[i] = new int[4];

B. int adjacencyMatrix = new int[4];

C. List<int>[] adjacencyMatrix = new List<int>[4];

D. int[,] adjacencyMatrix = new int[4,4];

Solution

1. Step 1: Identify adjacency matrix type

   An adjacency matrix is a 2D array representing edges between nodes.

2. Step 2: Check C# syntax for 2D arrays

   In C#, 2D arrays use syntax like int[,] array = new int[rows, columns];

3. Final Answer:

   int[,] adjacencyMatrix = new int[4,4]; -> Option D

4. Quick Check:

   2D array syntax = int[,] [OK]

Hint: Adjacency matrix uses 2D array syntax int[,] [OK]

Common Mistakes:

• Using jagged arrays instead of 2D arrays for matrix
• Declaring adjacencyMatrix as a single int
• Using List<int>[] which is adjacency list, not matrix

3. Given the following adjacency list representation of a graph in C#:

var graph = new List<int>[] {
  new List<int>{1, 2},
  new List<int>{2},
  new List<int>{0}
};
Console.WriteLine(graph[0][1]);

What will be the output?

medium

A. 0

B. 1

C. 2

D. IndexOutOfRangeException

Solution

1. Step 1: Understand the adjacency list structure

   graph[0] = List<int>{1, 2}, so graph[0][1] accesses the second element which is 2.

2. Step 2: Identify the output of Console.WriteLine(graph[0][1])

   It prints the value 2 from the list at index 1 of graph[0].

3. Final Answer:

   2 -> Option C

4. Quick Check:

   graph[0][1] = 2 [OK]

Hint: Indexing starts at 0; graph[0][1] is second element in first list [OK]

Common Mistakes:

• Confusing indices and printing 1 instead of 2
• Expecting an error due to nested lists
• Thinking graph[0][1] accesses graph[1]

4. Consider this adjacency matrix code snippet in C#:

int[,] matrix = new int[3,3];
matrix[0,1] = 1;
matrix[1,2] = 1;
matrix[2,0] = 1;
Console.WriteLine(matrix[1,0]);

What is the output and why?

medium

A. 1 because matrix is symmetric

B. 0 because matrix[1,0] was never set

C. Runtime error due to invalid index

D. 1 because of default initialization

Solution

1. Step 1: Analyze matrix assignments

   Only matrix[0,1], matrix[1,2], and matrix[2,0] are set to 1; matrix[1,0] remains 0.

2. Step 2: Understand default values in int[] arrays

   Unassigned int elements default to 0 in C#.

3. Final Answer:

   0 because matrix[1,0] was never set -> Option B

4. Quick Check:

   Unset matrix elements = 0 [OK]

Hint: Unset matrix cells default to 0, not symmetric [OK]

Common Mistakes:

• Assuming adjacency matrix is symmetric by default
• Expecting runtime error for valid indices
• Confusing default values with assigned values

5. You need to represent a social network graph with 10,000 users where each user has on average 10 friends. Which representation is best and why? Choose between adjacency list and adjacency matrix.

hard

A. Adjacency list, because it uses less memory for sparse graphs

B. Adjacency matrix, because it allows quick edge checks

C. Adjacency matrix, because it is simpler to implement

D. Adjacency list, because it stores all possible edges

Solution

1. Step 1: Calculate graph density

   10,000 users with 10 friends each means about 100,000 edges, which is sparse compared to 100 million possible edges.

2. Step 2: Choose data structure for sparse graph

   Adjacency list stores only existing edges, saving huge memory compared to adjacency matrix.

3. Final Answer:

   Adjacency list, because it uses less memory for sparse graphs -> Option A

4. Quick Check:

   Sparse large graph = adjacency list [OK]

Hint: Large sparse graph? Use adjacency list for memory efficiency [OK]

Common Mistakes:

• Choosing adjacency matrix despite huge memory waste
• Thinking adjacency matrix is always simpler
• Misunderstanding adjacency list stores only existing edges