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

Practice - 5 Tasks

1fill in blank

easy

Complete the code to declare an adjacency matrix for a graph with 5 vertices.

DSA C

int graph[5][5] = [1];

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

A{{5}}

B{{1}}

C{{-1}}

D{{0}}

Attempts:

3 left

💡 Hint

Common Mistakes

Using 1 instead of 0 initializes all edges as present.

Using -1 is invalid for adjacency matrix initialization.

The adjacency matrix is initialized with zeros to indicate no edges initially.

2fill in blank

medium

Complete the code to add an edge from vertex 2 to vertex 4 in an adjacency matrix.

DSA C

graph[2][[1]] = 1;

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

A4

B3

C2

D5

Attempts:

3 left

💡 Hint

Common Mistakes

Using index 5 causes out-of-bounds error.

Using index 3 adds edge to wrong vertex.

Vertices are zero-indexed, so vertex 4 corresponds to index 4.

3fill in blank

hard

Fix the error in the adjacency list insertion code to add vertex 3 to vertex 1's list.

DSA C

adjList[1].push_back([1]);

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

A3

B1

C0

D4

Attempts:

3 left

💡 Hint

Common Mistakes

Pushing the source vertex instead of the destination.

Using an invalid vertex index.

To add an edge from vertex 1 to vertex 3, push 3 into vertex 1's adjacency list.

4fill in blank

hard

Fill both blanks to create an adjacency list for a graph with 4 vertices.

DSA C

std::vector<int> adjList[[1]];

adjList[0].push_back([2]);

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

A4

B3

C1

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Using wrong size for adjacency list array.

Pushing incorrect vertex number.

The graph has 4 vertices, so the array size is 4. Adding an edge from vertex 0 to vertex 1 means pushing 1 into adjList[0].

5fill in blank

hard

Fill all three blanks to check if an edge exists from vertex 2 to vertex 3 in an adjacency matrix.

DSA C

if (graph[[1]][[2]] [3] 1) {
    printf("Edge exists\n");
}

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

A2

B3

C==

D!=

Attempts:

3 left

💡 Hint

Common Mistakes

Using wrong indices for vertices.

Using '!=' instead of '==' causing wrong condition.

Check the matrix at row 2, column 3. If the value equals 1, the edge exists.

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 graph? Use adjacency list for space efficiency [OK]

Common Mistakes:

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

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

easy

A. int graph[4][4][4];

B. int graph[4];

C. int graph[][] = new int[4][4];

D. int graph[4][4];

Solution

1. Step 1: Recall C array declaration syntax

   In C, a 2D array for 4 vertices is declared as int graph[4][4];

2. Step 2: Check options for correctness

   int graph[4][4]; matches correct syntax; int graph[4]; is 1D array; int graph[][] = new int[4][4]; uses Java syntax; int graph[4][4][4]; is 3D array.

3. Final Answer:

   int graph[4][4]; -> Option D

4. Quick Check:

   C 2D array syntax = int graph[4][4]; [OK]

Hint: C 2D arrays use int name[rows][cols]; syntax [OK]

Common Mistakes:

• Using Java or other language syntax in C
• Declaring wrong array dimensions
• Confusing 1D and 2D arrays

3. Given the following adjacency matrix for a graph with 3 vertices:

int graph[3][3] = {
  {0, 1, 0},
  {1, 0, 1},
  {0, 1, 0}
};

What is the output of the code snippet that prints all neighbors of vertex 1?

for (int i = 0; i < 3; i++) {
  if (graph[1][i] == 1) {
    printf("%d ", i);
  }
}

medium

A. 0 2

B. 1 2

C. 0 1

D. 1 0 2

Solution

1. Step 1: Analyze adjacency matrix row for vertex 1

   Row 1 is {1, 0, 1}, meaning edges to vertices 0 and 2.

2. Step 2: Trace loop printing neighbors

   Loop checks graph[1][i] == 1; prints i when true. i=0 and i=2 satisfy condition.

3. Final Answer:

   0 2 -> Option A

4. Quick Check:

   Neighbors of vertex 1 = 0 and 2 [OK]

Hint: Check matrix row for 1s to find neighbors [OK]

Common Mistakes:

• Confusing row and column indices
• Printing vertex itself as neighbor
• Misreading matrix values

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

int* graph[3];
for (int i = 0; i < 3; i++) {
  graph[i] = malloc(sizeof(int));
  graph[i][0] = i;
}

What is the main issue?

medium

A. Array size should be 4 instead of 3

B. Using malloc instead of calloc

C. Memory allocated is too small for multiple neighbors

D. graph should be declared as int graph[3][3]

Solution

1. Step 1: Check memory allocation size

   malloc(sizeof(int)) allocates space for only one int, but adjacency list needs space for multiple neighbors.

2. Step 2: Understand adjacency list needs dynamic size

   Allocating only one int is insufficient; should allocate enough space or use dynamic structures like linked lists.

3. Final Answer:

   Memory allocated is too small for multiple neighbors -> Option C

4. Quick Check:

   Insufficient malloc size = Error [OK]

Hint: Allocate enough memory for all neighbors in adjacency list [OK]

Common Mistakes:

• Confusing malloc and calloc
• Wrong array declaration type
• Assuming fixed size adjacency list

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

hard

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

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

C. Edge List, because it is easiest to implement

D. Incidence Matrix, because it stores edges explicitly

Solution

1. Step 1: Analyze graph size and density

   1000 vertices and 10,000 edges means the graph is moderately dense (max edges ~499,500).

2. Step 2: Consider edge existence check speed

   Adjacency matrix allows checking edge existence in O(1) time by direct index access.

3. Step 3: Compare memory vs speed tradeoff

   Though adjacency matrix uses more memory, fast edge check is priority here.

4. Final Answer:

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

5. Quick Check:

   Fast edge check = Adjacency Matrix [OK]

Hint: Need fast edge check? Use adjacency matrix despite memory [OK]

Common Mistakes:

• Choosing adjacency list only for memory without speed need
• Ignoring graph density impact
• Confusing edge list with adjacency matrix