Adjacency List Representation in DSA Typescript - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is an adjacency list in graph representation?

An adjacency list is a way to represent a graph where each node stores a list of its neighbors. It shows which nodes are directly connected to each node.

intermediate

How does an adjacency list differ from an adjacency matrix?

An adjacency list stores neighbors only, saving space for sparse graphs. An adjacency matrix uses a 2D array showing connections between all pairs, using more space.

beginner

TypeScript code snippet: How to declare an adjacency list for a graph with 3 nodes?

const graph: Map<number, number[]> = new Map();
graph.set(0, [1, 2]);
graph.set(1, [0]);
graph.set(2, [0]);

intermediate

Why is adjacency list preferred for sparse graphs?

Because it only stores existing edges, saving memory and making traversal faster compared to adjacency matrix which stores all possible edges.

intermediate

What is the time complexity to find all neighbors of a node in adjacency list?

It is O(k), where k is the number of neighbors of that node, because the list directly stores neighbors.

What data structure is commonly used to implement an adjacency list?

A Queue

B 2D array

C Stack

D Array of lists or Map of lists

An adjacency list is usually implemented as an array or map where each element stores a list of neighbors.

Which graph representation uses less space for a graph with few edges?

A Adjacency matrix

B Adjacency list

C Edge list

D Incidence matrix

Adjacency list stores only existing edges, so it uses less space for sparse graphs.

In an adjacency list, how do you find neighbors of a node?

A Look up the node's list of neighbors

B Scan the entire matrix row

C Check all nodes in the graph

D Use a stack to traverse

Neighbors are stored directly in the node's list in adjacency list representation.

What is the main disadvantage of adjacency matrix compared to adjacency list?

A Uses more memory for sparse graphs

B Slower to find neighbors

C Cannot represent directed graphs

D Hard to implement

Adjacency matrix uses memory for all possible edges, even if many don't exist.

Which of these is a valid TypeScript type for an adjacency list?

A string[]

B number[][]

C Map<number, number[]>

D Set<number>

Map maps each node to a list of neighbor nodes.

Explain how an adjacency list represents a graph and why it is efficient for sparse graphs.

Think about how you store only connected nodes, not all possible pairs.

Describe how you would implement an adjacency list in TypeScript for an undirected graph.

Remember undirected means two-way connections.

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