Adjacency List vs Matrix When to Choose Which in DSA Typescript - Compare & Choose

Challenge - 5 Problems

🧠 Conceptual

intermediate

When is an adjacency list better than an adjacency matrix?

Choose the best scenario where using an adjacency list is more efficient than an adjacency matrix.

A When the graph is dense with many edges close to the maximum possible.

B When you need to quickly check if an edge exists between any two nodes.

C When the graph is sparse with relatively few edges compared to the number of nodes.

D When the graph has a fixed small number of nodes and many edges.

💡 Hint

Think about memory usage and how many edges are stored.

An adjacency list stores only existing edges, so it uses less memory for sparse graphs. An adjacency matrix always uses space for all possible edges, which is inefficient for sparse graphs.

❓ Predict Output

intermediate

Output of adjacency matrix edge check

What is the output of the following TypeScript code that uses an adjacency matrix to check for an edge?

DSA Typescript

const graph = [
  [0, 1, 0],
  [1, 0, 1],
  [0, 1, 0]
];

console.log(graph[0][2]);

A 1

B TypeError

C undefined

D 0

💡 Hint

Look at the value stored at row 0, column 2.

The adjacency matrix uses 0 to represent no edge and 1 to represent an edge. graph[0][2] is 0, meaning no edge between node 0 and node 2.

❓ Predict Output

advanced

Output of adjacency list traversal

What will be printed by this TypeScript code that uses an adjacency list to print neighbors of node 1?

DSA Typescript

const graph: number[][] = [
  [1],       // neighbors of node 0
  [0, 2],    // neighbors of node 1
  [1]        // neighbors of node 2
];

for (const neighbor of graph[1]) {
  console.log(neighbor);
}

A 0\n2

B 1\n2

C 1

D 0

💡 Hint

Look at the neighbors stored for node 1.

Node 1 has neighbors 0 and 2, so the loop prints 0 and then 2 on separate lines.

🧠 Conceptual

advanced

Why is adjacency matrix better for dense graphs?

Select the main reason adjacency matrix is preferred over adjacency list for dense graphs.

A Because adjacency matrix is easier to implement for sparse graphs.

B Because adjacency matrix allows faster edge existence checks between any two nodes.

C Because adjacency matrix uses less memory for dense graphs.

D Because adjacency matrix stores neighbors as lists.

💡 Hint

Think about how quickly you can check if an edge exists.

Adjacency matrix allows O(1) time to check if an edge exists between any two nodes, which is useful in dense graphs where many edges exist.

🚀 Application

expert

Choosing data structure for a social network graph

You are designing a social network with millions of users but each user has only a few friends on average. Which data structure is best to represent the friendship connections and why?

A Use an adjacency list because it saves memory by storing only existing friendships.

B Use a 2D array with all zeros because most users have no friends.

C Use an adjacency matrix because it allows quick checks if two users are friends.

D Use a linked list for each user storing all users in the network.

💡 Hint

Consider memory usage and average number of connections per user.

Since each user has few friends compared to total users, adjacency list saves memory by storing only actual friendships instead of all possible pairs.

Practice

1. Which data structure is generally more space-efficient for representing a graph with very few edges compared to the number of vertices?

easy

A. Adjacency List

B. Adjacency Matrix

C. Edge List

D. Incidence Matrix

Solution

1. Step 1: Understand graph density

   Sparse graphs have few edges compared to vertices, so storing all possible edges wastes space.

2. Step 2: Compare space usage of adjacency list and matrix

   Adjacency list stores only existing edges, using less space for sparse graphs. Adjacency matrix always uses space for all possible edges.

3. Final Answer:

   Adjacency List -> Option A

4. Quick Check:

   Sparse graph = Adjacency List [OK]

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

Common Mistakes:

• Choosing adjacency matrix for sparse graphs
• Confusing edge count with vertex count
• Ignoring space complexity differences

2. Which of the following is the correct TypeScript syntax to declare an adjacency matrix for a graph with 3 vertices initialized with zeros?

easy

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

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

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

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

Solution

1. Step 1: Understand adjacency matrix type

   An adjacency matrix is a 2D array (array of arrays) of numbers representing edges.

2. Step 2: Check initialization correctness

   const matrix: number[][] = [[0,0,0],[0,0,0],[0,0,0]]; explicitly creates a 3x3 matrix with zeros. const matrix: number[][] = new Array(3).fill(new Array(3).fill(0)); uses fill with the same inner array reference, causing bugs. const matrix: number[][] = Array(3).map(() => Array(3).fill(0)); uses map on empty array, which won't work as expected. const matrix: number[] = [0,0,0]; is 1D array, not matrix.

3. Final Answer:

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

4. Quick Check:

   Explicit 2D array with zeros = const matrix: number[][] = [[0,0,0],[0,0,0],[0,0,0]]; [OK]

Hint: Use explicit 2D array for adjacency matrix initialization [OK]

Common Mistakes:

• Using fill with nested arrays causing shared references
• Declaring 1D array instead of 2D
• Using map on empty array without initialization

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

const graph = {
  0: [1, 2],
  1: [2],
  2: [0, 3],
  3: []
};
console.log(graph[2]);

What will be the output?

medium

A. [2]

B. [1, 2]

C. undefined

D. [0, 3]

Solution

1. Step 1: Identify the adjacency list for vertex 2

   In the graph object, key '2' maps to the array [0, 3].

2. Step 2: Understand console.log output

   Logging graph[2] prints the array [0, 3] representing edges from vertex 2.

3. Final Answer:

   [0, 3] -> Option D

4. Quick Check:

   graph[2] = [0, 3] [OK]

Hint: Access adjacency list by vertex key to get connected nodes [OK]

Common Mistakes:

• Confusing keys and values in adjacency list
• Expecting adjacency matrix output
• Assuming undefined for existing keys

4. Consider this TypeScript code snippet for creating an adjacency matrix for a graph with 3 vertices:

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. All rows refer to the same inner array, so all rows change when one element changes

B. The matrix is not initialized with zeros

C. The matrix is not a 2D array

D. The size variable is not used correctly

Solution

1. Step 1: Analyze the fill method usage

   Using fill with new Array(size).fill(0) creates one inner array and fills outer array with references to the same inner array.

2. Step 2: Understand effect of modifying one element

   Changing matrix[0][1] changes that element in all rows because they share the same inner array reference.

3. Final Answer:

   All rows refer to the same inner array, so all rows change when one element changes -> Option A

4. Quick Check:

   Shared inner array reference causes unexpected changes [OK]

Hint: Avoid fill with nested arrays; use map to create separate arrays [OK]

Common Mistakes:

• Thinking fill creates separate inner arrays
• Ignoring shared reference problem
• Assuming matrix is 1D array

5. You need to represent a dense graph with 1000 vertices where you frequently check if an edge exists between any two vertices. Which representation is best and why?

hard

A. Adjacency List, because it uses less space for dense graphs

B. Adjacency Matrix, because it allows O(1) edge existence checks

C. Edge List, because it is fastest for dense graphs

D. Incidence Matrix, because it uses less space than adjacency matrix

Solution

1. Step 1: Understand graph density and operation needs

   Dense graph means many edges; checking edge existence frequently requires fast lookup.

2. Step 2: Compare adjacency list and matrix for edge checks

   Adjacency matrix allows direct O(1) access to check if edge exists between two vertices. Adjacency list requires searching neighbors, which can be slower in dense graphs.

3. Step 3: Consider space tradeoff

   Though adjacency matrix uses more space, for dense graphs this is acceptable and beneficial for speed.

4. Final Answer:

   Adjacency Matrix, because it allows O(1) edge existence checks -> Option B

5. Quick Check:

   Dense graph + frequent edge check = Adjacency Matrix [OK]

Hint: Dense graph + frequent edge check? Use adjacency matrix [OK]

Common Mistakes:

• Choosing adjacency list for dense graphs needing fast edge checks
• Ignoring time complexity of edge existence queries
• Confusing edge list with adjacency matrix benefits