Adjacency List vs Matrix When to Choose Which in DSA Python - Interactive Comparison Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to initialize an adjacency list for a graph with 3 nodes.

DSA Python

graph = {i: [] for i in range([1])}

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

A3

B5

C0

D1

Attempts:

3 left

💡 Hint

Common Mistakes

Using the wrong number of nodes in range.

The graph has 3 nodes, so we create keys from 0 to 2 with empty lists.

2fill in blank

medium

Complete the code to add an edge from node 0 to node 2 in the adjacency list.

DSA Python

graph[0].[1](2)

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

Aremove

Binsert

Cpop

Dappend

Attempts:

3 left

💡 Hint

Common Mistakes

Using remove or pop which delete elements.

We use append to add node 2 to the adjacency list of node 0.

3fill in blank

hard

Fix the error in the code to create an adjacency matrix for 3 nodes.

DSA Python

matrix = [[0 for _ in range([1])] for _ in range(3)]

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

A2

B4

C3

D1

Attempts:

3 left

💡 Hint

Common Mistakes

Using a different size for rows and columns.

The matrix must be 3x3 for 3 nodes, so range(3) is correct.

4fill in blank

hard

Fill both blanks to set an edge from node 1 to node 2 in the adjacency matrix.

DSA Python

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

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

A1

B2

C0

D3

Attempts:

3 left

💡 Hint

Common Mistakes

Swapping the indices or using out-of-range indices.

Set matrix[1][2] = 1 to represent an edge from node 1 to node 2.

5fill in blank

hard

Fill both blanks to create a dictionary comprehension that maps nodes to their degree (number of edges) in an adjacency list.

DSA Python

degree = {node: len([1]) for node, [2] in graph.items()}

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

A{

Bneighbors

Cadjacency

D}

Attempts:

3 left

💡 Hint

Common Mistakes

Using wrong variable names or missing braces.

Use a dictionary comprehension with braces {}, and 'neighbors' as the variable name for the adjacency list in both places: {node: len(neighbors) for node, neighbors in graph.items()}.

Practice

1. Which data structure is generally better 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

   A graph with very few edges compared to vertices is called a sparse graph.

2. Step 2: Choose efficient representation for sparse graphs

   Adjacency lists store only existing edges, saving space for sparse graphs, unlike adjacency matrices which use space for all possible edges.

3. Final Answer:

   Adjacency List -> Option A

4. Quick Check:

   Sparse graph = Adjacency List [OK]

Hint: Sparse graphs use adjacency lists for space efficiency [OK]

Common Mistakes:

• Choosing adjacency matrix for sparse graphs wastes space
• Confusing edge list with adjacency matrix
• Assuming adjacency matrix is always better

2. Which of the following is the correct way to initialize an adjacency matrix for a graph with 4 vertices in Python?

easy

A. matrix = [[0 for _ in range(4)] for _ in range(4)]

B. matrix = [[0]*4]*4

C. matrix = [0]*4

D. matrix = [[None]*4 for _ in range(4)]

Solution

1. Step 1: Understand matrix initialization

   Using list comprehension with nested loops creates independent inner lists.

2. Step 2: Avoid shallow copies

   matrix = [[0]*4]*4 creates shallow copies causing all rows to reference the same list, leading to bugs.

3. Final Answer:

   matrix = [[0 for _ in range(4)] for _ in range(4)] -> Option A

4. Quick Check:

   Independent rows = matrix = [[0 for _ in range(4)] for _ in range(4)] [OK]

Hint: Use nested list comprehension for independent rows [OK]

Common Mistakes:

• Using [[0]*4]*4 causes all rows to be the same object
• Initializing with single list for matrix
• Using None instead of 0 for adjacency matrix

3. Consider the following Python code for a graph with 3 vertices using adjacency list representation:

graph = {0: [1, 2], 1: [2], 2: []}
print(graph[1])

What is the output?

medium

A. [1, 2]

B. []

C. [2]

D. KeyError

Solution

1. Step 1: Understand adjacency list structure

   Key 1 maps to list [2], meaning vertex 1 connects to vertex 2.

2. Step 2: Print value for key 1

   graph[1] returns [2], so print outputs [2].

3. Final Answer:

   [2] -> Option C

4. Quick Check:

   graph[1] = [2] [OK]

Hint: Access adjacency list by vertex key [OK]

Common Mistakes:

• Confusing keys and values in dictionary
• Expecting all vertices in output
• Assuming KeyError for existing key

4. The following code attempts to create an adjacency matrix for a graph with 3 vertices but has a bug:

matrix = [[0]*3]*3
matrix[0][1] = 1
print(matrix)

What is the output and what is the bug?

medium

A. IndexError; Wrong indexing

B. [[0, 1, 0], [0, 0, 0], [0, 0, 0]]; No bug

C. [[0, 0, 0], [0, 0, 0], [0, 0, 0]]; Assignment failed

D. [[0, 1, 0], [0, 1, 0], [0, 1, 0]]; Rows are shallow copies

Solution

1. Step 1: Understand matrix initialization

   Using [[0]*3]*3 creates 3 references to the same inner list.

2. Step 2: Modify one element affects all rows

   Setting matrix[0][1] = 1 changes the second element in all rows because they share the same list.

3. Final Answer:

   [[0, 1, 0], [0, 1, 0], [0, 1, 0]]; Rows are shallow copies -> Option D

4. Quick Check:

   Shallow copy rows cause all rows to change [OK]

Hint: Avoid [[0]*n]*n; use nested list comprehension [OK]

Common Mistakes:

• Assuming only first row changes
• Ignoring shallow copy behavior
• Confusing IndexError with shallow copy bug

5. You have a graph with 1000 vertices and about 10,000 edges. You need to frequently check if an edge exists between two vertices. Which representation is best and why?

hard

A. Edge List, because it is simplest to implement

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

C. Adjacency List, because it uses less memory for sparse graphs

D. Incidence Matrix, because it stores edges explicitly

Solution

1. Step 1: Analyze graph density and operations

   Graph has 1000 vertices and 10,000 edges, which is moderately sparse but not very sparse.

2. Step 2: Consider operation speed for edge checks

   Adjacency matrix allows checking edge existence in constant time O(1), while adjacency list requires searching neighbors.

3. Step 3: Balance memory and speed

   Though adjacency matrix uses more memory, the speed benefit for frequent edge checks outweighs memory cost here.

4. Final Answer:

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

5. Quick Check:

   Frequent edge check = Adjacency Matrix [OK]

Hint: For fast edge checks, adjacency matrix is best despite memory [OK]

Common Mistakes:

• Choosing adjacency list only for memory without considering speed
• Ignoring operation frequency in choice
• Confusing edge list with adjacency matrix for fast checks