Why Adjacency List Representation in DSA Typescript?

The Big Idea

Discover how organizing connections smartly can turn a messy list into a powerful tool!

The Scenario

Imagine you want to keep track of friendships in a large group of people by writing down every pair of friends on paper.

As the group grows, this list becomes huge and hard to manage.

The Problem

Writing down every connection manually is slow and confusing.

Finding all friends of a person means scanning the entire list, which wastes time.

Adding or removing friends requires rewriting many parts, increasing errors.

The Solution

An adjacency list organizes connections by listing each person with their direct friends.

This way, you quickly find all friends of anyone without scanning unrelated pairs.

It saves space and makes updates easier and faster.

Before vs After

✗ Before

const friendships = [
  ['Alice', 'Bob'],
  ['Alice', 'Charlie'],
  ['Bob', 'David']
];
// To find Alice's friends, scan all pairs

✓ After

const adjacencyList = {
  'Alice': ['Bob', 'Charlie'],
  'Bob': ['Alice', 'David'],
  'Charlie': ['Alice'],
  'David': ['Bob']
};
// Directly access Alice's friends with adjacencyList['Alice']

What It Enables

It enables fast and clear access to all connections of any node, making graph operations efficient and simple.

Real Life Example

Social media platforms use adjacency lists to quickly show your friends or followers without searching the entire user base.

Key Takeaways

Manual lists of connections grow large and slow to use.

Adjacency lists group connections by node for quick access.

This method saves time and space in managing relationships.

Practice

1. What does an adjacency list represent in graph data structures?

easy

A. A list of all nodes without connections

B. A matrix showing distances between nodes

C. A queue of nodes to visit next

D. A list where each node stores its connected neighbors

Solution

1. Step 1: Understand adjacency list concept

   An adjacency list stores each node with a list of its neighbors, showing direct connections.

2. Step 2: Compare options with definition

   Only A list where each node stores its connected neighbors correctly describes this structure; others describe different concepts.

3. Final Answer:

   A list where each node stores its connected neighbors -> Option D

4. Quick Check:

   Adjacency list = neighbors list [OK]

Hint: Adjacency list always stores neighbors per node [OK]

Common Mistakes:

• Confusing adjacency list with adjacency matrix
• Thinking it stores distances instead of neighbors
• Assuming it is a queue or unrelated structure

2. Which of the following is the correct TypeScript syntax to declare an adjacency list for a graph with nodes as numbers?

easy

A. const graph: number[][] = [];

B. const graph: Map = new Map();

C. const graph: Record = {};

D. const graph: Array<number> = [];

Solution

1. Step 1: Identify adjacency list type

   An adjacency list maps each node (number) to an array of connected nodes (number[]).

2. Step 2: Match TypeScript syntax

   Map correctly represents this; others are incorrect types or structures.

3. Final Answer:

   const graph: Map = new Map(); -> Option B

4. Quick Check:

   Map = adjacency list [OK]

Hint: Use Map with number keys and array values for adjacency list [OK]

Common Mistakes:

• Using Record which maps to single number, not array
• Using number[][] without keys for nodes
• Using Array<number> which is just a list, not adjacency

3. Given the following TypeScript code, what is the output after adding edges?

const graph: Map = new Map();
graph.set(1, [2, 3]);
graph.set(2, [1]);
graph.set(3, [1, 4]);
graph.set(4, [3]);
console.log(graph.get(3));

medium

A. [2, 3]

B. [3, 4]

C. [1, 4]

D. undefined

Solution

1. Step 1: Trace graph.set calls

   Node 3 is set with neighbors [1, 4].

2. Step 2: Check graph.get(3)

   Returns the array [1, 4] assigned to node 3.

3. Final Answer:

   [1, 4] -> Option C

4. Quick Check:

   graph.get(3) = [1, 4] [OK]

Hint: graph.get(node) returns neighbors array [OK]

Common Mistakes:

• Confusing neighbors of node 3 with node 1 or 2
• Expecting undefined if not careful with set calls
• Mixing up array contents order

4. Identify the error in this TypeScript adjacency list code snippet:

const graph: Map = new Map();
graph.set(1, [2]);
graph.set(2, [1]);
graph.get(3).push(1);

medium

A. graph.get(3) returns undefined, so push causes error

B. Map keys must be strings, not numbers

C. graph.set should use arrays of strings, not numbers

D. Missing initialization of graph variable

Solution

1. Step 1: Check graph.get(3) call

   Node 3 was never set, so graph.get(3) returns undefined.

2. Step 2: Understand push on undefined

   Calling push on undefined causes runtime error.

3. Final Answer:

   graph.get(3) returns undefined, so push causes error -> Option A

4. Quick Check:

   Accessing unset key returns undefined [OK]

Hint: Check if key exists before pushing to adjacency list [OK]

Common Mistakes:

• Assuming graph.get(3) returns empty array automatically
• Thinking Map keys must be strings (numbers are allowed)
• Ignoring runtime error from push on undefined

5. You want to represent a directed graph with nodes 1 to 4 using an adjacency list in TypeScript. Which code correctly adds an edge from node 2 to node 4 without affecting other edges?

const graph: Map = new Map();
graph.set(1, [2]);
graph.set(2, [3]);
graph.set(3, []);
graph.set(4, []);
// Add edge from 2 to 4 here

hard

A. graph.get(2)?.push(4);

B. graph.set(2, [4]);

C. graph.set(4, [2]);

D. graph.get(4)?.push(2);

Solution

1. Step 1: Understand existing edges

   Node 2 currently has neighbors [3]. We want to add 4 without removing 3.

2. Step 2: Choose correct method to add edge

   Using graph.get(2)?.push(4) adds 4 to existing array, preserving [3]. graph.set(2, [4]) replaces neighbors, removing 3.

3. Final Answer:

   graph.get(2)?.push(4); -> Option A

4. Quick Check:

   Use push to add edge without overwriting [OK]

Hint: Use push on existing neighbors to add edges safely [OK]

Common Mistakes:

• Overwriting neighbors array with set instead of pushing
• Adding edge to wrong node
• Confusing direction of edge in directed graph