Spiral Matrix Traversal in DSA C++ - Build from Scratch

Spiral Matrix Traversal

📖 Scenario: You are working on a robot that needs to clean a room by moving in a spiral path. The room is represented as a grid of numbers, where each number shows the dirt level. The robot must visit each cell in a spiral order to clean efficiently.

🎯 Goal: Build a program that takes a 3x3 matrix and prints the elements in spiral order, starting from the top-left corner and moving clockwise.

📋 What You'll Learn

Create a 3x3 matrix with exact values

Use variables to track the boundaries of the matrix

Implement the spiral traversal logic using loops

Print the elements in the correct spiral order

💡 Why This Matters

🌍 Real World

Spiral traversal is useful in image processing, robot path planning, and printing matrix data in a readable pattern.

💼 Career

Understanding matrix traversal algorithms helps in technical interviews and solving problems related to grids and 2D data structures.

1

Create the 3x3 matrix

Create a 3x3 integer matrix called matrix with these exact rows: {1, 2, 3}, {4, 5, 6}, {7, 8, 9}.

DSA C++

# Create the 3x3 matrix called matrix
# Your code here

Hint

Use a 2D array with 3 rows and 3 columns. Each row is enclosed in curly braces.

2

Set up boundary variables

Add four integer variables: top set to 0, bottom set to 2, left set to 0, and right set to 2. These will track the current edges of the matrix during traversal.

DSA C++

int matrix[3][3] = {
    {1, 2, 3},
    {4, 5, 6},
    {7, 8, 9}
};
// Add boundary variables top, bottom, left, right
# Your code here

Hint

These variables mark the current edges of the matrix rows and columns.

3

Implement spiral traversal logic

Write a while loop that runs while top <= bottom and left <= right. Inside the loop, use for loops to traverse from left to right on the top row, top to bottom on the right column, right to left on the bottom row, and bottom to top on the left column. Update the top, bottom, left, and right variables accordingly after each traversal. Store the visited elements in a vector called result.

DSA C++

int matrix[3][3] = {
    {1, 2, 3},
    {4, 5, 6},
    {7, 8, 9}
};

int top = 0;
int bottom = 2;
int left = 0;
int right = 2;

#include 
std::vector result;
// Add while loop and for loops to traverse the matrix in spiral order
# Your code here

Hint

Use four loops inside the while loop to cover each side of the current rectangle. Update the boundaries after each side is processed.

4

Print the spiral order result

Use a for loop to print each element in the result vector separated by spaces on a single line.

DSA C++

#include 
#include 

int matrix[3][3] = {
    {1, 2, 3},
    {4, 5, 6},
    {7, 8, 9}
};

int top = 0;
int bottom = 2;
int left = 0;
int right = 2;

std::vector result;

while (top = left; i--) {
            result.push_back(matrix[bottom][i]);
        }
        bottom--;
    }

    if (left = top; i--) {
            result.push_back(matrix[i][left]);
        }
        left++;
    }
}

// Print the elements in result separated by spaces
# Your code here

Hint

Use a for loop to print each element in result followed by a space.

Practice

1. What is the main idea behind Spiral Matrix Traversal?

easy

A. Traverse only the diagonal elements of the matrix

B. Traverse the matrix row by row from top to bottom

C. Traverse the matrix column by column from left to right

D. Traverse the matrix in a circular pattern starting from the outer layer moving inward

Solution

1. Step 1: Understand traversal pattern

   Spiral traversal means moving around the edges of the matrix and then moving inward layer by layer.

2. Step 2: Compare options

   Only Traverse the matrix in a circular pattern starting from the outer layer moving inward describes moving in a circular pattern from outer to inner layers, which matches spiral traversal.

3. Final Answer:

   Traverse the matrix in a circular pattern starting from the outer layer moving inward -> Option D

4. Quick Check:

   Spiral traversal = circular outer to inner [OK]

Hint: Spiral means circle around edges then go inside [OK]

Common Mistakes:

• Confusing spiral with row-wise or column-wise traversal
• Thinking spiral means diagonal traversal
• Ignoring the inward movement after outer layer

2. Which of the following C++ code snippets correctly initializes the boundaries for spiral traversal of an m x n matrix?

easy

A. int top = 0, bottom = n - 1, left = 0, right = m - 1;

B. int top = 0, bottom = m - 1, left = 0, right = n - 1;

C. int top = 1, bottom = m, left = 1, right = n;

D. int top = m - 1, bottom = 0, left = n - 1, right = 0;

Solution

1. Step 1: Understand boundary variables

   Top and bottom represent row boundaries, left and right represent column boundaries. For an m x n matrix, top starts at 0, bottom at m-1, left at 0, right at n-1.

2. Step 2: Check each option

   int top = 0, bottom = m - 1, left = 0, right = n - 1; correctly sets top=0, bottom=m-1, left=0, right=n-1. Others have reversed or incorrect assignments.

3. Final Answer:

   int top = 0, bottom = m - 1, left = 0, right = n - 1; -> Option B

4. Quick Check:

   Boundaries = top=0, bottom=m-1, left=0, right=n-1 [OK]

Hint: Top/left start at 0; bottom/right at size minus one [OK]

Common Mistakes:

• Swapping m and n in boundary initialization
• Starting boundaries at 1 instead of 0
• Confusing row and column boundaries

3. What is the output of the following C++ code snippet for spiral traversal?

int matrix[3][3] = {
  {1, 2, 3},
  {4, 5, 6},
  {7, 8, 9}
};

int top = 0, bottom = 2, left = 0, right = 2;

while (top <= bottom && left <= right) {
  for (int i = left; i <= right; i++)
    std::cout << matrix[top][i] << " ";
  top++;
  for (int i = top; i <= bottom; i++)
    std::cout << matrix[i][right] << " ";
  right--;
  if (top <= bottom) {
    for (int i = right; i >= left; i--)
      std::cout << matrix[bottom][i] << " ";
    bottom--;
  }
  if (left <= right) {
    for (int i = bottom; i >= top; i--)
      std::cout << matrix[i][left] << " ";
    left++;
  }
}

medium

A. 1 2 3 4 5 6 7 8 9

B. 1 4 7 8 9 6 3 2 5

C. 1 2 3 6 9 8 7 4 5

D. 9 8 7 6 5 4 3 2 1

Solution

1. Step 1: Trace the spiral traversal

   First top row: 1 2 3
   Right column down: 6 9
   Bottom row left: 8 7
   Left column up: 4
   Next inner layer top row: 5

2. Step 2: Combine all elements in order

   Combined output: 1 2 3 6 9 8 7 4 5

3. Final Answer:

   1 2 3 6 9 8 7 4 5 -> Option C

4. Quick Check:

   Spiral order = 1 2 3 6 9 8 7 4 5 [OK]

Hint: Follow edges clockwise, then move inward [OK]

Common Mistakes:

• Printing rows or columns in wrong order
• Skipping inner elements like 5
• Repeating elements or missing boundaries update

4. Identify the bug in this spiral traversal code snippet:

int top = 0, bottom = m - 1, left = 0, right = n - 1;
while (top < bottom && left < right) {
  for (int i = left; i <= right; i++) cout << matrix[top][i] << " ";
  top++;
  for (int i = top; i <= bottom; i++) cout << matrix[i][right] << " ";
  right--;
  for (int i = right; i >= left; i--) cout << matrix[bottom][i] << " ";
  bottom--;
  for (int i = bottom; i >= top; i--) cout << matrix[i][left] << " ";
  left++;
}

medium

A. The while loop condition should use <= instead of < to include all layers

B. The for loops should use < instead of <= to avoid out-of-bound errors

C. The variables top, bottom, left, right are not initialized correctly

D. The code misses printing the diagonal elements

Solution

1. Step 1: Analyze loop condition

   The while loop uses 'top < bottom && left < right', which skips the last layer when top == bottom or left == right.

2. Step 2: Correct condition for full traversal

   Changing to 'top <= bottom && left <= right' ensures the last single row or column is included in traversal.

3. Final Answer:

   The while loop condition should use <= instead of < to include all layers -> Option A

4. Quick Check:

   Use <= in loop condition to cover all layers [OK]

Hint: Use <= in while condition to cover last layer [OK]

Common Mistakes:

• Using < causes missing last row or column
• Changing for loops to < causes skipping elements
• Not updating boundaries after each traversal

5. Given a non-square matrix:

int matrix[3][4] = {
  {1, 2, 3, 4},
  {5, 6, 7, 8},
  {9, 10, 11, 12}
};

Which is the correct spiral traversal output?

hard

A. 1 2 3 4 8 12 11 10 9 5 6 7

B. 1 2 3 4 8 12 11 10 9 5 6 7 0

C. 1 5 9 10 11 12 8 4 3 2 6 7

D. 1 2 3 4 8 12 11 10 9 5 7 6

Solution

1. Step 1: Trace spiral on 3x4 matrix

   Top row: 1 2 3 4
   Right column down: 8 12
   Bottom row left: 11 10 9
   Left column up: 5
   Inner top row: 6 7

2. Step 2: Combine elements in order

   Combined output: 1 2 3 4 8 12 11 10 9 5 6 7

3. Final Answer:

   1 2 3 4 8 12 11 10 9 5 6 7 -> Option A

4. Quick Check:

   Spiral order for 3x4 matrix = 1 2 3 4 8 12 11 10 9 5 6 7 [OK]

Hint: Follow edges carefully, handle rectangular shape [OK]

Common Mistakes:

• Adding extra elements like 0
• Mixing inner elements order
• Swapping 6 and 7 positions