Adjacency Matrix Representation in DSA Go - Build from Scratch

Adjacency Matrix Representation

📖 Scenario: You are working with a small network of cities connected by roads. You want to represent which cities are directly connected to each other using a simple table.

🎯 Goal: Create an adjacency matrix to represent connections between cities, then print the matrix to see which cities are connected.

📋 What You'll Learn

Create a 3x3 adjacency matrix with exact values

Add a variable for the number of cities

Use nested loops to fill the adjacency matrix

Print the adjacency matrix row by row

💡 Why This Matters

🌍 Real World

Adjacency matrices are used in network routing, social networks, and mapping connections between entities.

💼 Career

Understanding adjacency matrices is essential for roles in software development, data analysis, and network engineering.

1

Create the adjacency matrix

Create a 3x3 two-dimensional slice of integers called adjMatrix with these exact values: [[0, 1, 0], [1, 0, 1], [0, 1, 0]]

DSA Go

# Create the adjacency matrix adjMatrix with the exact values
# Your code here

Hint

Use a slice of slices to create a 2D matrix in Go.

2

Add the number of cities variable

Add an integer variable called numCities and set it to 3

DSA Go

package main

import "fmt"

func main() {
    adjMatrix := [][]int{
        {0, 1, 0},
        {1, 0, 1},
        {0, 1, 0},
    }
    // Add numCities variable here
    // Your code here
}

Hint

Use numCities := 3 to store the number of cities.

3

Print the adjacency matrix

Use nested for loops with variables i and j to iterate over adjMatrix and print each row as space-separated values

DSA Go

package main

import "fmt"

func main() {
    adjMatrix := [][]int{
        {0, 1, 0},
        {1, 0, 1},
        {0, 1, 0},
    }
    numCities := 3

    // Use nested for loops to print the adjacency matrix
    // Your code here
}

Hint

Use fmt.Print inside the inner loop and fmt.Println after the inner loop to print rows.

4

Display the adjacency matrix

Write a print statement to display the adjacency matrix rows exactly as: 0 1 0 1 0 1 0 1 0

DSA Go

package main

import "fmt"

func main() {
    adjMatrix := [][]int{
        {0, 1, 0},
        {1, 0, 1},
        {0, 1, 0},
    }
    numCities := 3

    for i := 0; i < numCities; i++ {
        for j := 0; j < numCities; j++ {
            fmt.Print(adjMatrix[i][j], " ")
        }
        fmt.Println()
    }

    // Print the adjacency matrix again here
    // Your code here
}

Hint

Use the same nested loops and fmt.Print statements to print the matrix again.

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