Adjacency Matrix Representation in DSA Javascript - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to initialize an adjacency matrix for a graph with 4 nodes.

DSA Javascript

const size = 4;
const adjacencyMatrix = Array(size).fill(null).map(() => Array(size).fill([1]));

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

Anull

B0

C1

Dundefined

Attempts:

3 left

💡 Hint

Common Mistakes

Using 1 instead of 0 initializes all edges as connected.

Using null or undefined can cause errors when checking edges.

The adjacency matrix should start with 0s indicating no edges between nodes.

2fill in blank

medium

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

DSA Javascript

adjacencyMatrix[1][[1]] = 1;

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

A2

B3

C0

D1

Attempts:

3 left

💡 Hint

Common Mistakes

Using 3 instead of 2 (off-by-one error).

Confusing row and column indices.

Node indices start at 0, so node 3 is 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 Javascript

if (adjacencyMatrix[[1]][0] === 1) {
  console.log('Edge exists');
}

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

A0

B3

C1

D2

Attempts:

3 left

💡 Hint

Common Mistakes

Using node number directly without adjusting for zero-based index.

Mixing up row and column indices.

Node 2 corresponds to index 2 in the matrix.

4fill in blank

hard

Fill both blanks to create a function that adds an undirected edge between two nodes in the adjacency matrix.

DSA Javascript

function addEdge(matrix, node1, node2) {
  matrix[node1][[1]] = 1;
  matrix[node2][[2]] = 1;
}

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

Anode2

Bnode1

Attempts:

3 left

💡 Hint

Common Mistakes

Setting only one direction of the edge.

Mixing up node1 and node2 in assignments.

For undirected edges, set both [node1][node2] and [node2][node1] to 1.

5fill in blank

hard

Fill all three blanks to create a function that returns all neighbors of a given node from the adjacency matrix.

DSA Javascript

function getNeighbors(matrix, node) {
  const neighbors = [];
  for (let i = 0; i < matrix[[1]].length; i++) {
    if (matrix[node][i] === [2]) {
      neighbors.push([3]);
    }
  }
  return neighbors;
}

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

Anode

B1

Ci

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Looping over wrong row or column.

Checking for 0 instead of 1.

Pushing wrong value instead of neighbor index.

Loop over the row for the given node, check if edge exists (value 1), then add the column index as neighbor.

Practice

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

easy

A. A 2D array showing connections between nodes

B. A list of nodes in the graph

C. A sequence of edges in order

D. A tree structure of nodes

Solution

1. Step 1: Understand adjacency matrix structure

   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 there is a connection (edge) between two nodes.

3. Final Answer:

   A 2D array showing connections between nodes -> Option A

4. Quick Check:

   Adjacency matrix = 2D array of connections [OK]

Hint: Adjacency matrix is always a 2D array of node links [OK]

Common Mistakes:

• Confusing adjacency matrix with adjacency list
• Thinking it stores node values instead of connections
• Assuming it is a sequence or tree

2. Which of the following is the correct way to declare a 3x3 adjacency matrix in JavaScript?

easy

A. const matrix = [0,0,0];

B. const matrix = [[0,0,0],[0,0,0],[0,0,0]];

C. const matrix = new Array(3);

D. const matrix = {0:0,1:0,2:0};

Solution

1. Step 1: Understand adjacency matrix as 2D array

   It must be an array of arrays, each inner array representing a row.

2. Step 2: Check each option's structure

   const matrix = [[0,0,0],[0,0,0],[0,0,0]]; is a 3x3 array filled with zeros, correct for adjacency matrix initialization.

3. Final Answer:

   const matrix = [[0,0,0],[0,0,0],[0,0,0]]; -> Option B

4. Quick Check:

   2D array syntax = const matrix = [[0,0,0],[0,0,0],[0,0,0]]; [OK]

Hint: Adjacency matrix needs nested arrays for rows and columns [OK]

Common Mistakes:

• Using a single array instead of 2D array
• Using object instead of array
• Creating array without inner arrays

3. What is the output of the following code?

const matrix = [
  [0, 1, 0],
  [1, 0, 1],
  [0, 1, 0]
];
console.log(matrix[1][2]);

medium

A. 1

B. 0

C. undefined

D. Error

Solution

1. Step 1: Identify indices in matrix

   matrix[1] is the second row: [1, 0, 1].

2. Step 2: Access element at column 2

   matrix[1][2] is the third element in second row, which is 1.

3. Final Answer:

   1 -> Option A

4. Quick Check:

   matrix[1][2] = 1 [OK]

Hint: Remember matrix[row][column] indexing starts at 0 [OK]

Common Mistakes:

• Confusing row and column indices
• Assuming 1-based indexing
• Expecting undefined for valid indices

4. Find the error in this adjacency matrix update code:

const matrix = [
  [0, 0],
  [0, 0]
];
matrix[0][1] = 1;
matrix[1][2] = 1;

medium

A. Matrix should be 1D array

B. Cannot assign value to matrix[0][1]

C. Index 2 is out of bounds for matrix[1]

D. No error, code is correct

Solution

1. Step 1: Check matrix dimensions

   Matrix has 2 rows and 2 columns (indices 0 and 1 only).

2. Step 2: Identify invalid index access

   matrix[1][2] tries to access third element in second row, which does not exist.

3. Final Answer:

   Index 2 is out of bounds for matrix[1] -> Option C

4. Quick Check:

   Accessing invalid column index = Error [OK]

Hint: Check array length before accessing indices [OK]

Common Mistakes:

• Ignoring array size limits
• Assuming dynamic resizing on assignment
• Confusing row and column indices

5. Given a graph with 4 nodes, how would you represent an undirected edge between node 1 and node 3 in an adjacency matrix?

hard

A. Set matrix[1][1] = 1 and matrix[3][3] = 1

B. Set matrix[1][3] = 1 only

C. Set matrix[3][1] = 1 only

D. Set matrix[1][3] = 1 and matrix[3][1] = 1

Solution

1. Step 1: Understand undirected edge representation

   Undirected edges are symmetric, so both directions must be marked.

2. Step 2: Mark both connections in matrix

   Set matrix[1][3] = 1 and matrix[3][1] = 1 to show connection both ways.

3. Final Answer:

   Set matrix[1][3] = 1 and matrix[3][1] = 1 -> Option D

4. Quick Check:

   Undirected edge = symmetric matrix entries [OK]

Hint: Undirected edges need two symmetric entries set [OK]

Common Mistakes:

• Setting only one direction for undirected edge
• Setting diagonal elements instead of edge
• Confusing node indices