Spiral Matrix Traversal in DSA C - Build from Scratch

Spiral Matrix Traversal

📖 Scenario: You are working with a 2D grid of numbers, like a map of city blocks with house numbers. You want to walk around the blocks in a spiral path, starting from the top-left corner and moving inward, collecting the house numbers in the order you visit them.

🎯 Goal: Build a program that takes a fixed 3x3 matrix and prints the numbers in the order they appear when traversed in a spiral pattern.

📋 What You'll Learn

Create a 3x3 integer matrix with exact values

Use variables to track the boundaries of the matrix

Implement the spiral traversal logic using loops

Print the elements in spiral order separated by spaces

💡 Why This Matters

🌍 Real World

Spiral traversal is useful in image processing, games, and UI layouts where you need to process elements in a circular inward pattern.

💼 Career

Understanding matrix traversal techniques is important for software engineers working with grids, graphics, and algorithm optimization.

1

Create the 3x3 matrix

Create a 3x3 integer matrix called matrix with these exact values: 1, 2, 3 in the first row, 4, 5, 6 in the second row, and 7, 8, 9 in the third row.

DSA C

# Your code here

Hint

Use a 2D array with three rows and three columns. Each row is enclosed in braces and separated by commas.

2

Set up boundary variables

Add four integer variables called top, bottom, left, and right. Initialize top to 0, bottom to 2, left to 0, and right to 2.

DSA C

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

Hint

These variables will help you keep track of the current edges of the matrix as you spiral inward.

3

Implement spiral traversal logic

Write a while loop that continues as long as top <= bottom and left <= right. Inside the loop, use for loops to traverse from left to right on the top row, then increment top. Next, traverse from top to bottom on the right column, then decrement right. Then traverse from right to left on the bottom row, then decrement bottom. Finally, traverse from bottom to top on the left column, then increment left. For each element visited, print it followed by a space.

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;

// Your code here

Hint

Follow the edges in order: top row left to right, right column top to bottom, bottom row right to left, left column bottom to top. Update boundaries after each edge.

4

Print the spiral traversal result

Add a printf statement to print a newline character '\n' after the spiral traversal is complete.

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;

while (top = left; i--) {
            printf("%d ", matrix[bottom][i]);
        }
        bottom--;
    }

    if (left = top; i--) {
            printf("%d ", matrix[i][left]);
        }
        left++;
    }
}

// Print a newline character

Hint

After printing all elements, print a newline to move the cursor to the next line.

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 from outer to inner layers

Solution

1. Step 1: Understand traversal pattern

   Spiral traversal means moving around the edges of the matrix and gradually moving inward in a circular way.

2. Step 2: Compare options

   Only Traverse the matrix in a circular pattern from outer to inner layers 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 from outer to inner layers -> Option D

4. Quick Check:

   Spiral traversal = circular outer to inner [OK]

Hint: Think of peeling an onion layer by layer [OK]

Common Mistakes:

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

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

easy

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

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

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

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

Solution

1. Step 1: Identify correct boundary initialization

   For spiral traversal, top starts at 0, bottom at last row (m-1), left at 0, right at last column (n-1).

2. Step 2: Match with options

   int top = 0, bottom = m-1, left = 0, right = n-1; matches this initialization exactly; others swap or mix row and column indices incorrectly.

3. Final Answer:

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

4. Quick Check:

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

Hint: Top and left start at 0; bottom and right at max index [OK]

Common Mistakes:

• Swapping m and n in bottom or right
• Starting top or left at max index
• Confusing row and column boundaries

3. What is the output of the following C code snippet for spiral traversal of a 3x3 matrix?

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++) printf("%d ", matrix[top][i]);
  top++;
  for(int i=top; i<=bottom; i++) printf("%d ", matrix[i][right]);
  right--;
  if(top <= bottom) {
    for(int i=right; i>=left; i--) printf("%d ", matrix[bottom][i]);
    bottom--;
  }
  if(left <= right) {
    for(int i=bottom; i>=top; i--) printf("%d ", matrix[i][left]);
    left++;
  }
}

medium

A. 1 4 7 8 9 6 3 2 5

B. 1 2 3 6 9 8 7 4 5

C. 1 2 3 4 5 6 7 8 9

D. 1 3 5 7 9 2 4 6 8

Solution

1. Step 1: Trace first outer layer traversal

   Top row left to right: 1 2 3; then right column top to bottom: 6 9; bottom row right to left: 8 7; left column bottom to top: 4.

2. Step 2: Move inward and print center

   Now top=1, bottom=1, left=1, right=1; print center element matrix[1][1] = 5.

3. Final Answer:

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

4. Quick Check:

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

Hint: Follow boundaries and print edges clockwise [OK]

Common Mistakes:

• Skipping center element
• Mixing row and column indices
• Not updating boundaries correctly

4. Find the error in this spiral traversal code snippet for a 3x3 matrix:

int top=0, bottom=2, left=0, right=2;
while(top < bottom && left < right) {
  for(int i=left; i<=right; i++) printf("%d ", matrix[top][i]);
  top++;
  for(int i=top; i<=bottom; i++) printf("%d ", matrix[i][right]);
  right--;
  for(int i=right; i>=left; i--) printf("%d ", matrix[bottom][i]);
  bottom--;
  for(int i=bottom; i>=top; i--) printf("%d ", matrix[i][left]);
  left++;
}

medium

A. The variables top and bottom are swapped

B. The for loops should use < instead of <=

C. The while loop condition should use <= instead of <

D. The matrix indices are accessed incorrectly

Solution

1. Step 1: Analyze loop condition

   The condition top < bottom && left < right stops before the center element is processed in odd-sized matrices.

2. Step 2: Correct condition for full traversal

   Using <= allows the loop to run when top equals bottom or left equals right, ensuring center elements are included.

3. Final Answer:

   The while loop condition should use <= instead of < -> Option C

4. Quick Check:

   Use <= in while condition for complete spiral [OK]

Hint: Use <= in while to include center elements [OK]

Common Mistakes:

• Stopping traversal too early
• Changing for loop bounds incorrectly
• Swapping top and bottom variables

5. Given a 4x4 matrix:

int matrix[4][4] = {
  {1, 2, 3, 4},
  {5, 6, 7, 8},
  {9, 10, 11, 12},
  {13, 14, 15, 16}
};

Write the spiral traversal output if you start from the bottom-left corner and move clockwise inward.

hard

A. 13 9 5 1 2 3 4 8 12 16 15 14 10 6 7 11

B. 1 2 3 4 8 12 16 15 14 13 9 5 6 7 11 10

C. 13 14 15 16 12 8 4 3 2 1 5 9 10 11 7 6

D. 16 15 14 13 9 5 1 2 3 4 8 12 11 10 6 7

Solution

1. Step 1: Understand starting point and direction

   Start at bottom-left (matrix[3][0] = 13) and move clockwise: up, right, down, left, inward.

2. Step 2: Trace spiral clockwise from bottom-left

   Up column: 13 9 5 1; right row: 2 3 4; down column: 8 12 16; left row: 15 14 10 6; then inner spiral: 7 11.

3. Final Answer:

   13 9 5 1 2 3 4 8 12 16 15 14 10 6 7 11 -> Option A

4. Quick Check:

   Start bottom-left clockwise spiral = 13 9 5 1 2 3 4 8 12 16 15 14 10 6 7 11 [OK]

Hint: Change start and direction, then trace edges inward [OK]

Common Mistakes:

• Starting from top-left instead of bottom-left
• Moving counter-clockwise instead of clockwise
• Mixing row and column indices