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

Practice - 5 Tasks

1fill in blank

easy

Complete the code to declare an adjacency list for a graph with 5 nodes.

DSA Go

graph := make([][]int, [1])

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

A1

B0

C10

D5

Attempts:

3 left

💡 Hint

Common Mistakes

Using 0 or 1 which creates no or too small a list.

Using 10 which is unrelated to the number of nodes.

The adjacency list is created with a slice of slices, one for each node. Since there are 5 nodes, we use 5.

2fill in blank

medium

Complete the code to initialize an adjacency matrix for a graph with 4 nodes.

DSA Go

matrix := make([][]int, [1])
for i := range matrix {
    matrix[i] = make([]int, [1])
}

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

A0

B4

C5

D3

Attempts:

3 left

💡 Hint

Common Mistakes

Using 3 or 5 which do not match the number of nodes.

Using 0 which creates an empty matrix.

An adjacency matrix for a graph with 4 nodes is a 4x4 matrix, so both dimensions are 4.

3fill in blank

hard

Fix the error in the code that adds an edge from node 1 to node 3 in an adjacency list.

DSA Go

graph[[1]] = append(graph[1], 3)

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

A2

B3

C1

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Using the destination node index instead of the source.

Using 0 or 2 which are unrelated here.

The index before append must be the node number where the edge starts, which is 1 here.

4fill in blank

hard

Fill both blanks to check if there is an edge from node 2 to node 4 in an adjacency matrix.

DSA Go

if matrix[[1]][[2]] == 1 {
    fmt.Println("Edge exists")
}

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

A2

B3

C4

D1

Attempts:

3 left

💡 Hint

Common Mistakes

Swapping source and destination indices.

Using indices outside the matrix range.

To check edge from node 2 to 4, use matrix[2][4].

5fill in blank

hard

Fill all three blanks to create a map of node to neighbors using adjacency list style.

DSA Go

neighbors := map[int][]int{
    [1]: {2, 3},
    [2]: {1},
    [3]: {1, 4},
}

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

A1

B2

C3

D4

Attempts:

3 left

💡 Hint

Common Mistakes

Mixing up keys and values.

Using nodes not in the graph.

Keys are node numbers. Node 1 connects to 2 and 3, node 2 connects to 1, node 4 connects to 1 and 4.

Practice

1. Which data structure is generally better for representing a graph with very few edges compared to the number of nodes?

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 nodes is called a sparse graph.

2. Step 2: Choose data structure for sparse graphs

   Adjacency lists store only existing edges, saving space for sparse graphs.

3. Final Answer:

   Adjacency List -> Option A

4. Quick Check:

   Sparse graph = Adjacency List [OK]

Hint: Sparse graph? Use adjacency list 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 declare an adjacency matrix for a graph with 4 nodes in Go?

easy

A. var graph [4][4]int

B. graph := make([][]int, 4)

C. var graph []int

D. graph := map[int][]int{}

Solution

1. Step 1: Understand adjacency matrix declaration

   An adjacency matrix is a 2D fixed-size array representing edges between nodes.

2. Step 2: Check Go syntax for fixed 2D array

   "var graph [4][4]int" declares a 4x4 integer matrix correctly.

3. Final Answer:

   var graph [4][4]int -> Option A

4. Quick Check:

   Fixed 2D array = var graph [4][4]int [OK]

Hint: Adjacency matrix = fixed 2D array declaration [OK]

Common Mistakes:

• Using slice of slices without initialization for matrix
• Declaring 1D slice instead of 2D array
• Using map which is adjacency list style

3. Given the following Go code using an adjacency list, what will be printed?

graph := map[int][]int{
  0: {1, 2},
  1: {2},
  2: {0},
  3: {},
}
fmt.Println(graph[1])

medium

A. [0 2]

B. [2]

C. [1 2]

D. []

Solution

1. Step 1: Identify adjacency list entries for node 1

   Node 1 has edges to node 2 only, so graph[1] = {2}.

2. Step 2: Understand fmt.Println output

   Printing graph[1] outputs the slice [2].

3. Final Answer:

   [2] -> Option B

4. Quick Check:

   graph[1] = [2] [OK]

Hint: Print adjacency list for node key directly [OK]

Common Mistakes:

• Confusing keys and values in map
• Assuming node 1 connects to node 0
• Expecting adjacency matrix output

4. The following Go code attempts to create an adjacency matrix but has a bug. What is the bug?

graph := make([][]int, 3)
for i := range graph {
  graph[i] = make([]int, 3)
}
graph[0][1] = 1
graph[1][2] = 1
fmt.Println(graph[0][2])

medium

A. The matrix is not initialized properly

B. graph[0][2] should be 1 but prints 0

C. Index out of range error

D. No bug, code runs correctly

Solution

1. Step 1: Check matrix initialization

   Each row is initialized with make([]int, 3), so matrix is properly created.

2. Step 2: Check assigned values and print

   graph[0][1] and graph[1][2] are set to 1; graph[0][2] was never set, so prints 0.

3. Step 3: Verify no runtime errors

   All indices are within range; no errors occur.

4. Final Answer:

   No bug, code runs correctly -> Option D

5. Quick Check:

   Proper initialization and indexing = No bug [OK]

Hint: Check initialization and index ranges carefully [OK]

Common Mistakes:

• Assuming unassigned entries print 1
• Thinking initialization is missing
• Expecting index errors without out-of-range access

5. You need to represent a dense graph with 1000 nodes where you frequently check if an edge exists between any two nodes. Which data structure is best and why? A) Adjacency Matrix for constant-time edge checks B) Adjacency List for memory efficiency C) Edge List for simple iteration D) Map of maps for flexible keys

hard

A. Edge List for simple iteration

B. Adjacency List for memory efficiency

C. Adjacency Matrix for constant-time edge checks

D. Map of maps for flexible keys

Solution

1. Step 1: Understand graph density and operations

   A dense graph has many edges, close to the maximum possible.

2. Step 2: Choose data structure for fast edge existence checks

   Adjacency matrix allows O(1) time to check if edge exists between any two nodes.

3. Step 3: Consider memory tradeoff

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

4. Final Answer:

   Adjacency Matrix for constant-time edge checks -> Option C

5. Quick Check:

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

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

Common Mistakes:

• Choosing adjacency list for dense graphs slows edge checks
• Ignoring memory vs speed tradeoff
• Confusing edge list with adjacency matrix