Adjacency Matrix Representation in DSA Go - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to initialize an adjacency matrix with zeros.

DSA Go

matrix := make([][]int, n)
for i := 0; i < n; i++ {
    matrix[i] = make([]int, [1])
}

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

A1

B0

Cn

Dlen(matrix)

Attempts:

3 left

💡 Hint

Common Mistakes

Using 0 or 1 as the length of inner slices instead of n.

Using len(matrix) which is correct here but less clear than n.

The adjacency matrix is a square matrix of size n x n, so each row must have length n.

2fill in blank

medium

Complete the code to add an edge from vertex u to vertex v in the adjacency matrix.

DSA Go

matrix[u][[1]] = 1

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

Au

Bv

C0

Dn

Attempts:

3 left

💡 Hint

Common Mistakes

Using u as the second index instead of v.

Using 0 or n which are not vertex indices.

To add an edge from u to v, set matrix[u][v] to 1.

3fill in blank

hard

Fix the error in the code to check if there is an edge from vertex x to vertex y.

DSA Go

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

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

Ax

By

C0

Dn

Attempts:

3 left

💡 Hint

Common Mistakes

Using y as the first index instead of x.

Using 0 or n which are not vertex indices.

The first index is the source vertex x, so use matrix[x][y].

4fill in blank

hard

Fill both blanks to correctly iterate over all edges in the adjacency matrix.

DSA Go

for [1] := 0; [1] < n; [1]++ {
    for [2] := 0; [2] < n; [2]++ {
        if matrix[[1]][[2]] == 1 {
            fmt.Printf("Edge from %d to %d\n", [1], [2])
        }
    }
}

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

Ai

Bj

Ck

Dx

Attempts:

3 left

💡 Hint

Common Mistakes

Using the same variable for both loops.

Using variables not declared or unrelated.

Use i and j as loop variables to iterate over rows and columns of the matrix.

5fill in blank

hard

Fill all three blanks to create a function that returns true if there is an edge from a to b.

DSA Go

func hasEdge(matrix [][]int, [1] int, [2] [3]) bool {
    return matrix[[1]][[2]] == 1
}

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

Aa

Bb

Cint

Dbool

Attempts:

3 left

💡 Hint

Common Mistakes

Using wrong parameter names or missing types.

Using bool as parameter type which is incorrect here.

The function parameters are a and b of type int, used to index the matrix.

Practice

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

easy

A. A 2D array showing connections between nodes

B. A list of nodes with their neighbors

C. A sequence of edges in order

D. A tree structure of nodes

Solution

1. Step 1: Understand adjacency matrix concept

   An adjacency matrix is a 2D array where rows and columns represent nodes.

2. Step 2: Identify what the matrix stores

   Each cell shows if there is a connection (edge) between two nodes.

3. Final Answer:

   A 2D array showing connections between nodes -> Option A

4. Quick Check:

   Adjacency matrix = 2D array [OK]

Hint: Adjacency matrix is always a 2D grid of node connections [OK]

Common Mistakes:

• Confusing adjacency matrix with adjacency list
• Thinking it stores edges as a list
• Assuming it represents a tree only

2. Which of the following is the correct way to declare a 3x3 adjacency matrix in Go?

easy

A. var matrix [3][3]int

B. matrix := make([]int, 3)

C. var matrix [][]int = make([][]int, 3)

D. matrix := [3]int{3}

Solution

1. Step 1: Understand Go array declaration

   In Go, a fixed-size 2D array is declared as [rows][cols]type.

2. Step 2: Check each option

   var matrix [3][3]int declares a 3x3 int array correctly. matrix := make([]int, 3) is a 1D slice. var matrix [][]int = make([][]int, 3) is a slice of slices but incomplete. matrix := [3]int{3} is a 1D array with wrong initialization.

3. Final Answer:

   var matrix [3][3]int -> Option A

4. Quick Check:

   Fixed 2D array = [3][3]int [OK]

Hint: Use [rows][cols]type for fixed 2D arrays in Go [OK]

Common Mistakes:

• Using slices instead of arrays for fixed size
• Incorrect initialization syntax
• Confusing 1D and 2D declarations

3. Given the following Go code, what is the printed adjacency matrix?

package main
import "fmt"
func main() {
  var graph [3][3]int
  graph[0][1] = 1
  graph[1][2] = 1
  graph[2][0] = 1
  for i := 0; i < 3; i++ {
    for j := 0; j < 3; j++ {
      fmt.Print(graph[i][j], " ")
    }
    fmt.Println()
  }
}

medium

A. 0 0 1
1 0 0
0 1 0

B. 1 0 0
0 1 0
0 0 1

C. 0 1 0
0 0 1
1 0 0

D. 0 1 1
1 0 1
1 1 0

Solution

1. Step 1: Trace assignments to the matrix

   graph[0][1] = 1 means node 0 connects to 1; graph[1][2] = 1 means node 1 connects to 2; graph[2][0] = 1 means node 2 connects to 0.

2. Step 2: Print matrix row by row

   Row 0: 0 1 0; Row 1: 0 0 1; Row 2: 1 0 0.

3. Final Answer:

   0 1 0 0 0 1 1 0 0 -> Option C

4. Quick Check:

   Edges set match matrix rows [OK]

Hint: Map edges to matrix cells row-wise [OK]

Common Mistakes:

• Mixing row and column indices
• Assuming symmetric matrix for directed graph
• Forgetting zero initialization

4. Identify the error in this Go code snippet for creating an adjacency matrix:

var graph [][]int
for i := 0; i < 3; i++ {
  graph[i] = make([]int, 3)
}

medium

A. graph should be a 1D slice

B. make([]int, 3) is incorrect syntax

C. Loop should run from 1 to 3

D. graph is not initialized before assignment

Solution

1. Step 1: Check graph slice initialization

   graph is declared but not initialized with length, so graph[i] access causes runtime error.

2. Step 2: Fix initialization

   graph should be initialized with length 3 before assigning inner slices, e.g., graph = make([][]int, 3).

3. Final Answer:

   graph is not initialized before assignment -> Option D

4. Quick Check:

   Initialize outer slice before indexing [OK]

Hint: Initialize slices before indexing to avoid runtime errors [OK]

Common Mistakes:

• Forgetting to initialize outer slice
• Confusing slice length and capacity
• Incorrect loop ranges

5. You have an undirected graph with 4 nodes. Which code snippet correctly updates the adjacency matrix to add an edge between node 1 and node 3?

hard

A. graph[1][3] = 1

B. graph[1][3] = 1; graph[3][1] = 1

C. graph[3][1] = 1

D. graph[1][1] = 1; graph[3][3] = 1

Solution

1. Step 1: Understand undirected graph edge representation

   In undirected graphs, edges are bidirectional, so adjacency matrix must be symmetric.

2. Step 2: Update both directions in matrix

   Set graph[1][3] = 1 and graph[3][1] = 1 to represent the edge correctly.

3. Final Answer:

   graph[1][3] = 1; graph[3][1] = 1 -> Option B

4. Quick Check:

   Undirected edge updates both matrix cells [OK]

Hint: Update both [i][j] and [j][i] for undirected edges [OK]

Common Mistakes:

• Updating only one direction for undirected graph
• Setting diagonal elements instead of edge cells
• Confusing node indices