Adjacency Matrix Representation in DSA Typescript - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to initialize an adjacency matrix for a graph with n vertices.

DSA Typescript

const adjacencyMatrix: number[][] = Array.from({ length: n }, () => Array(n).fill([1]));

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

A0

B1

C-1

Dnull

Attempts:

3 left

💡 Hint

Common Mistakes

Using 1 instead of 0 will incorrectly show edges where there are none.

Using null or -1 is not standard for adjacency matrices.

The adjacency matrix is initialized with 0s to indicate no edges between vertices initially.

2fill in blank

medium

Complete the code to add an edge from vertex u to vertex v in the adjacency matrix.

DSA Typescript

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

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

Av

Bu

C0

Dn

Attempts:

3 left

💡 Hint

Common Mistakes

Swapping u and v will add the edge in the wrong direction.

Using 0 or n as index will cause errors.

To add an edge from u to v, set the matrix at row u and column v to 1.

3fill in blank

hard

Fix the error in the code that checks if there is an edge from u to v.

DSA Typescript

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

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

Av

Bu

C0

Dn

Attempts:

3 left

💡 Hint

Common Mistakes

Using u for both indices checks a self-loop incorrectly.

Using 0 or n as index causes out-of-bounds errors.

The second index should be v to check the edge from u to v.

4fill in blank

hard

Fill both blanks to create a function that returns true if there is an edge from source to target.

DSA Typescript

function hasEdge(adjacencyMatrix: number[][], source: number, target: number): boolean {
  return adjacencyMatrix[[1]][[2]] === 1;
}

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

Asource

Btarget

Attempts:

3 left

💡 Hint

Common Mistakes

Swapping source and target indices will check the wrong edge.

Using incorrect variable names causes errors.

The function checks adjacencyMatrix[source][target] to see if the edge exists.

5fill in blank

hard

Fill all three blanks to create a function that builds an adjacency matrix from a list of edges.

DSA Typescript

function buildAdjacencyMatrix(n: number, edges: [number, number][]): number[][] {
  const matrix = Array.from({ length: n }, () => Array(n).fill(0));
  for (const [[1], [2]] of edges) {
    matrix[[3]][[2]] = 1;
  }
  return matrix;
}

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

Au

Bv

Attempts:

3 left

💡 Hint

Common Mistakes

Using v as the row index and u as the column index swaps edge direction.

Not destructuring edges properly causes errors.

The function loops over edges, destructuring each edge into u and v, then sets matrix[u][v] = 1.

Practice

1. What does an adjacency matrix represent in a graph?
Adjacency matrix is a way to show connections between nodes. What does a 1 in the matrix mean?

easy

A. There is no edge between two nodes

B. The graph is weighted

C. The nodes are the same

D. There is a direct edge between two nodes

Solution

1. Step 1: Understand adjacency matrix basics

   An adjacency matrix uses rows and columns to represent nodes. Each cell shows if two nodes connect.

2. Step 2: Interpret the value 1 in the matrix

   A value of 1 means there is a direct edge between the nodes represented by that row and column.

3. Final Answer:

   There is a direct edge between two nodes -> Option D

4. Quick Check:

   1 means edge exists [OK]

Hint: 1 means connected, 0 means no connection [OK]

Common Mistakes:

• Thinking 1 means no edge
• Confusing node identity with connection
• Assuming matrix shows weights always

2. Which of the following is the correct TypeScript syntax to declare a 3x3 adjacency matrix initialized with zeros without shared row references?

easy

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

B. const matrix: number[3][3] = new Array(3).fill(new Array(3).fill(0));

C. const matrix = Array(3).map(Array(3).fill(0));

D. const matrix: number[][] = new Array(3).fill(new Array(3).fill(0));

Solution

1. Step 1: Check TypeScript array declaration syntax

   const matrix: number[][] = [[0,0,0],[0,0,0],[0,0,0]]; uses explicit 2D array with nested arrays and zeros, which is valid syntax and creates independent rows.

2. Step 2: Identify issues in other options

   const matrix: number[3][3] = new Array(3).fill(new Array(3).fill(0)); uses invalid TypeScript syntax for fixed-size arrays. const matrix = Array(3).map(Array(3).fill(0)); passes an array to map() instead of a function, causing a runtime error. const matrix: number[][] = new Array(3).fill(new Array(3).fill(0)); uses fill with the same inner array reference, causing shared rows.

3. Final Answer:

   const matrix: number[][] = [[0,0,0],[0,0,0],[0,0,0]]; -> Option A

4. Quick Check:

   Explicit nested arrays with zeros [OK]

Hint: Use explicit nested arrays to avoid shared references [OK]

Common Mistakes:

• Using fill with same inner array causing shared rows
• Passing non-function to map()
• Wrong type annotations

3. Given the following adjacency matrix for a directed graph:

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

What will be the output?

medium

A. 1

B. Error

C. undefined

D. 0

Solution

1. Step 1: Locate matrix[2][0]

   Row 2 is [1, 0, 0], so element at index 0 is 1.

2. Step 2: Confirm output of console.log

   console.log prints the value 1 found at matrix[2][0].

3. Final Answer:

   1 -> Option A

4. Quick Check:

   matrix[2][0] = 1 [OK]

Hint: Remember matrix[row][column] indexing [OK]

Common Mistakes:

• Confusing row and column indices
• Expecting zero instead of one
• Thinking index out of range

4. Consider this TypeScript code snippet to create an adjacency matrix for 3 nodes:

const size = 3;
const matrix = new Array(size).fill(new Array(size).fill(0));
matrix[0][1] = 1;
console.log(matrix);

What is the problem with this code?

medium

A. It creates a matrix with all zeros correctly

B. The matrix is not initialized at all

C. All rows point to the same inner array, so all rows change when one changes

D. It throws a runtime error

Solution

1. Step 1: Understand fill with reference types

   Using fill with new Array(size).fill(0) creates one inner array shared by all rows.

2. Step 2: Effect of modifying matrix[0][1]

   Changing matrix[0][1] changes the shared inner array, so all rows show the change.

3. Final Answer:

   All rows point to the same inner array, so all rows change when one changes -> Option C

4. Quick Check:

   Shared inner array causes unexpected updates [OK]

Hint: Avoid fill with objects/arrays; use map for unique rows [OK]

Common Mistakes:

• Assuming fill creates independent arrays
• Ignoring shared reference behavior
• Expecting only one row to change

5. You have an undirected graph with 4 nodes. You want to represent it using an adjacency matrix in TypeScript. Which of the following code snippets correctly initializes the matrix and sets an edge between node 1 and node 3?

hard

A. const size = 4;
const matrix = new Array(size).fill(new Array(size).fill(0));
matrix[1][3] = 1;
matrix[3][1] = 1;

B. const size = 4;
const matrix = Array.from({ length: size }, () => Array(size).fill(0));
matrix[1][3] = 1;
matrix[3][1] = 1;

C. const size = 4;
const matrix = Array(size).fill(Array(size).fill(0));
matrix[1][3] = 1;

D. const size = 4;
const matrix = Array(size).map(() => Array(size).fill(0));
matrix[1][3] = 1;

Solution

1. Step 1: Check matrix initialization for unique rows

   const size = 4; const matrix = Array.from({ length: size }, () => Array(size).fill(0)); matrix[1][3] = 1; matrix[3][1] = 1; uses Array.from with a function to create unique inner arrays, avoiding shared references.

2. Step 2: Verify setting edges for undirected graph

   Setting matrix[1][3] and matrix[3][1] to 1 correctly represents an undirected edge.

3. Step 3: Identify issues in other options

   Options B and C use fill causing shared inner arrays. const size = 4; const matrix = Array(size).map(() => Array(size).fill(0)); matrix[1][3] = 1; initializes correctly but only sets matrix[1][3] = 1, missing matrix[3][1] = 1 for undirected graph.

4. Final Answer:

   const size = 4; const matrix = Array.from({ length: size }, () => Array(size).fill(0)); matrix[1][3] = 1; matrix[3][1] = 1; -> Option B

5. Quick Check:

   Use Array.from with function for unique rows [OK]

Hint: Use Array.from with function to avoid shared rows [OK]

Common Mistakes:

• Using fill causing shared inner arrays
• Using map on empty array without initialization
• Setting only one direction for undirected edge