Adjacency Matrix Representation in DSA C# - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to declare a 2D adjacency matrix for 4 nodes.

DSA C#

int[,] adjacencyMatrix = new int[4, [1]];

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

A3

B5

C2

D4

Attempts:

3 left

💡 Hint

Common Mistakes

Using a different size for the second dimension causes errors or incorrect representation.

The adjacency matrix for 4 nodes is a 4x4 matrix, so both dimensions must be 4.

2fill in blank

medium

Complete the code to set an edge from node 1 to node 3 in the adjacency matrix.

DSA C#

adjacencyMatrix[1, [1]] = 1;

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

A1

B3

C2

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Using node numbers directly without adjusting for zero-based indexing.

Node indices start at 0, so node 3 corresponds to index 2.

3fill in blank

hard

Fix the error in the code to correctly check if there is an edge from node 2 to node 0.

DSA C#

if (adjacencyMatrix[[1], 0] == 1) {
    Console.WriteLine("Edge exists");
}

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

A1

B2

C0

D3

Attempts:

3 left

💡 Hint

Common Mistakes

Using node numbers directly without subtracting 1 for zero-based indexing.

Node 2 corresponds to index 1 because indexing starts at 0.

4fill in blank

hard

Fill both blanks to correctly initialize a 3x3 adjacency matrix with no edges.

DSA C#

int[,] matrix = new int[[1], [2]];

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

A3

B4

C2

D5

Attempts:

3 left

💡 Hint

Common Mistakes

Using different sizes for rows and columns.

For 3 nodes, the adjacency matrix must be 3x3, so both dimensions are 3.

5fill in blank

hard

Fill all three blanks to set an edge from node 0 to node 2 and print if it exists.

DSA C#

matrix[[1], [2]] = 1;
if (matrix[[3], 2] == 1) {
    Console.WriteLine("Edge exists");
}

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

A0

B1

C2

D3

Attempts:

3 left

💡 Hint

Common Mistakes

Mixing up node indices or using wrong indices.

Set edge from node 0 (index 0) to node 2 (index 2). Then check if edge from node 0 to node 2 exists.

Practice

1. What does an adjacency matrix represent in graph theory?

easy

A. A queue of nodes to visit

B. A list of nodes in the graph

C. A 2D array showing edges between nodes

D. A stack of visited nodes

Solution

1. Step 1: Understand adjacency matrix concept

   An adjacency matrix is a 2D array where rows and columns represent nodes.

2. Step 2: Identify what the matrix stores

   Each cell shows if an edge exists between two nodes (1 for edge, 0 for no edge).

3. Final Answer:

   A 2D array showing edges between nodes -> Option C

4. Quick Check:

   Adjacency matrix = 2D array of edges [OK]

Hint: Adjacency matrix is always a 2D array showing connections [OK]

Common Mistakes:

• Confusing adjacency matrix with adjacency list
• Thinking it stores node values instead of edges
• Mixing up matrix with traversal order

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

easy

A. int[] matrix = new int[4];

B. int[,] matrix = new int[4,4];

C. int[][] matrix = new int[4];

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

Solution

1. Step 1: Identify correct 2D array syntax in C#

   In C#, a 2D array is declared as int[,] with size [rows, columns].

2. Step 2: Check each option

   int[,] matrix = new int[4,4]; uses int[,] with size [4,4], correct for adjacency matrix of 4 nodes.

3. Final Answer:

   int[,] matrix = new int[4,4]; -> Option B

4. Quick Check:

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

Hint: Use int[,] for 2D arrays in C# [OK]

Common Mistakes:

• Using jagged array syntax instead of 2D array
• Declaring 1D array for adjacency matrix
• Missing comma in array declaration

3. Given the following adjacency matrix for a graph with 3 nodes:

int[,] matrix = new int[,] {
  {0, 1, 0},
  {1, 0, 1},
  {0, 1, 0}
};

What is the output of Console.WriteLine(matrix[1,2]);?

medium

A. 1

B. 0

C. 2

D. Error

Solution

1. Step 1: Locate matrix element at row 1, column 2

   Matrix rows and columns start at 0, so matrix[1,2] is second row, third column.

2. Step 2: Check value at matrix[1,2]

   From the matrix, second row is {1, 0, 1}, third element is 1.

3. Final Answer:

   1 -> Option A

4. Quick Check:

   matrix[1,2] = 1 [OK]

Hint: Remember zero-based indexing for matrix rows and columns [OK]

Common Mistakes:

• Confusing row and column indices
• Assuming 1-based indexing
• Misreading matrix values

4. Identify the error in this C# code snippet for creating an adjacency matrix of 3 nodes:

int[] matrix = new int[3];
matrix[0,1] = 1;

medium

A. Incorrect array declaration syntax

B. No error, code is correct

C. Index out of range error

D. Cannot assign value to matrix[0,1]

Solution

1. Step 1: Analyze array declaration

   int[] matrix = new int[3]; declares a 1D array of 3 integers.

2. Step 2: Examine the assignment

   matrix[0,1] = 1; attempts to use 2D indexing on a 1D array, which is invalid in C#.

3. Final Answer:

   Cannot assign value to matrix[0,1] -> Option D

4. Quick Check:

   1D array indexing mismatch [OK]

Hint: 1D arrays cannot use [row,col] indexing [OK]

Common Mistakes:

• Using 2D indexing on 1D array
• Assuming jagged array syntax for 2D array
• Ignoring compiler error messages

5. You have a directed graph with 4 nodes. Which adjacency matrix correctly represents edges from node 0 to 1 and 2, and from node 3 to 0?

hard

A. int[,] matrix = new int[,] {
{0, 1, 1, 0},
{0, 0, 0, 0},
{0, 0, 0, 0},
{1, 0, 0, 0}
};

B. int[,] matrix = new int[,] {
{0, 1, 0, 0},
{1, 0, 0, 0},
{1, 0, 0, 0},
{0, 0, 0, 1}
};

C. int[,] matrix = new int[,] {
{0, 0, 0, 1},
{1, 0, 0, 0},
{1, 0, 0, 0},
{0, 1, 1, 0}
};

D. int[,] matrix = new int[,] {
{0, 1, 1, 0},
{0, 0, 0, 1},
{0, 0, 0, 0},
{0, 0, 0, 0}
};

Solution

1. Step 1: Understand directed edges in adjacency matrix

   For directed graph, matrix[i,j] = 1 means edge from node i to node j.

2. Step 2: Check edges from node 0 to 1 and 2

   Row 0 should have 1s at columns 1 and 2.

3. Step 3: Check edge from node 3 to 0

   Row 3 should have 1 at column 0.

4. Step 4: Verify options

   int[,] matrix = new int[,] { {0, 1, 1, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {1, 0, 0, 0} }; matches all conditions exactly.

5. Final Answer:

   {{0, 1, 1, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {1, 0, 0, 0}} -> Option A

6. Quick Check:

   Directed edges = matrix[i,j] = 1 [OK]

Hint: Row = from node, column = to node in adjacency matrix [OK]

Common Mistakes:

• Confusing rows and columns for direction
• Using symmetric matrix for directed graph
• Missing edges or adding extra edges