Spiral Matrix Traversal in DSA C# - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is Spiral Matrix Traversal?

It is a way to visit all elements of a matrix in a spiral order, starting from the top-left corner and moving right, down, left, and up repeatedly until all elements are visited.

beginner

Which four directions are used in Spiral Matrix Traversal?

Right → Down → Left → Up, repeated in this order until all elements are covered.

intermediate

In Spiral Matrix Traversal, what do the variables 'top', 'bottom', 'left', and 'right' represent?

'top' and 'bottom' represent the current row boundaries, while 'left' and 'right' represent the current column boundaries of the matrix section that is yet to be traversed.

intermediate

Why do we update the boundaries after each direction in Spiral Matrix Traversal?

Because after traversing one side of the matrix, that row or column is fully visited and should not be visited again, so boundaries are moved inward to avoid repetition.

beginner

What is the time complexity of Spiral Matrix Traversal for an m x n matrix?

O(m * n), because every element in the matrix is visited exactly once.

What is the first direction followed in Spiral Matrix Traversal?

A Right

B Down

C Left

D Up

The traversal starts moving right from the top-left corner.

After moving right in Spiral Matrix Traversal, which boundary is updated?

A left boundary moves right

B bottom boundary moves up

C top boundary moves down

D right boundary moves left

After moving right, the top row is fully visited, so top boundary moves down.

Which condition stops the Spiral Matrix Traversal loop?

A When all directions are visited once

B When top > bottom or left > right

C When top == bottom and left == right

D When matrix is empty

Traversal stops when the boundaries cross, meaning all elements are visited.

What data structure is commonly used to store the result of Spiral Matrix Traversal?

A List or array

B Stack

C Queue

D Dictionary

A list or array is used to store elements in the order they are visited.

If the matrix has 3 rows and 4 columns, how many elements will Spiral Matrix Traversal visit?

A 7

B 4

C 3

D 12

3 rows * 4 columns = 12 elements total.

Explain how the boundaries (top, bottom, left, right) change during Spiral Matrix Traversal.

Think about how each side of the matrix is removed after traversal.

Describe the step-by-step process to traverse a matrix in spiral order.

Imagine peeling layers of an onion from outside to inside.

Practice

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

easy

A. To visit all elements of a matrix in a spiral order starting from the top-left corner

B. To sort the matrix elements in ascending order

C. To find the maximum element in each row of the matrix

D. To transpose the matrix by swapping rows and columns

Solution

1. Step 1: Understand traversal pattern

   Spiral traversal means visiting matrix elements starting from the outer layer and moving inward in a circular pattern.

2. Step 2: Identify the traversal goal

   The goal is to visit every element exactly once in a spiral order, usually starting from the top-left corner.

3. Final Answer:

   To visit all elements of a matrix in a spiral order starting from the top-left corner -> Option A

4. Quick Check:

   Spiral traversal = visiting elements in spiral order [OK]

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

Common Mistakes:

• Confusing spiral traversal with sorting
• Thinking it only visits diagonal elements
• Assuming it transposes the matrix

2. Which of the following C# code snippets correctly initializes the boundaries for spiral traversal of a matrix named matrix?

easy

A. int top = 0, bottom = matrix.Length - 1, left = 0, right = matrix.GetLength(0) - 1;

B. int top = 1, bottom = matrix.Length, left = 1, right = matrix.Length;

C. int top = matrix.GetLength(1), bottom = 0, left = matrix.GetLength(0), right = 0;

D. int top = 0, bottom = matrix.GetLength(0) - 1, left = 0, right = matrix.GetLength(1) - 1;

Solution

1. Step 1: Understand matrix dimensions in C#

   matrix.GetLength(0) gives number of rows, matrix.GetLength(1) gives number of columns.

2. Step 2: Set boundaries correctly

   Top and left start at 0; bottom and right are last indices (length - 1) for rows and columns respectively.

3. Final Answer:

   int top = 0, bottom = matrix.GetLength(0) - 1, left = 0, right = matrix.GetLength(1) - 1; -> Option D

4. Quick Check:

   Correct boundary initialization = int top = 0, bottom = matrix.GetLength(0) - 1, left = 0, right = matrix.GetLength(1) - 1; [OK]

Hint: Use GetLength(0) for rows, GetLength(1) for columns [OK]

Common Mistakes:

• Using matrix.Length which is total elements, not rows or columns
• Swapping rows and columns in GetLength calls
• Starting boundaries at 1 instead of 0

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

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

List<int> result = new List<int>();
int top = 0, bottom = 2, left = 0, right = 2;

while (top <= bottom && left <= right) {
  for (int i = left; i <= right; i++) result.Add(matrix[top, i]);
  top++;
  for (int i = top; i <= bottom; i++) result.Add(matrix[i, right]);
  right--;
  if (top <= bottom) {
    for (int i = right; i >= left; i--) result.Add(matrix[bottom, i]);
    bottom--;
  }
  if (left <= right) {
    for (int i = bottom; i >= top; i--) result.Add(matrix[i, left]);
    left++;
  }
}
Console.WriteLine(string.Join(", ", result));

medium

A. 1, 2, 3, 6, 9, 8, 7, 4, 5

B. 1, 4, 7, 8, 9, 6, 3, 2, 5

C. 1, 2, 3, 4, 5, 6, 7, 8, 9

D. 9, 8, 7, 6, 5, 4, 3, 2, 1

Solution

1. Step 1: Traverse top row left to right

   Elements added: 1, 2, 3; then top moves from 0 to 1.

2. Step 2: Traverse right column top to bottom

   Elements added: 6, 9; right moves from 2 to 1.

3. Step 3: Traverse bottom row right to left

   Elements added: 8, 7; bottom moves from 2 to 1.

4. Step 4: Traverse left column bottom to top

   Elements added: 4; left moves from 0 to 1.

5. Step 5: Repeat for inner layer

   Now top=1, bottom=1, left=1, right=1; add element 5.

6. Final Answer:

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

7. Quick Check:

   Spiral order of 3x3 matrix = 1, 2, 3, 6, 9, 8, 7, 4, 5 [OK]

Hint: Follow boundaries and shrink after each side [OK]

Common Mistakes:

• Not updating boundaries correctly after each side
• Skipping the inner elements
• Reversing traversal directions incorrectly

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

int top = 0, bottom = matrix.GetLength(0), left = 0, right = matrix.GetLength(1) - 1;
while (top <= bottom && left <= right) {
  for (int i = left; i <= right; i++) Console.Write(matrix[top, i] + " ");
  top++;
  for (int i = top; i <= bottom; i++) Console.Write(matrix[i, right] + " ");
  right--;
  if (top <= bottom) {
    for (int i = right; i >= left; i--) Console.Write(matrix[bottom, i] + " ");
    bottom--;
  }
  if (left <= right) {
    for (int i = bottom; i >= top; i--) Console.Write(matrix[i, left] + " ");
    left++;
  }
}

medium

A. Change right to matrix.GetLength(1) to include last column

B. Change bottom to matrix.GetLength(0) - 1 to avoid index out of range

C. Remove the if conditions checking top <= bottom and left <= right

D. Initialize top and left to 1 instead of 0

Solution

1. Step 1: Check boundary initialization

   bottom is set to matrix.GetLength(0), which is out of index range since indexing is zero-based.

2. Step 2: Correct bottom boundary

   bottom should be matrix.GetLength(0) - 1 to point to the last valid row index.

3. Final Answer:

   Change bottom to matrix.GetLength(0) - 1 to avoid index out of range -> Option B

4. Quick Check:

   Zero-based indexing means last index = length - 1 [OK]

Hint: Remember zero-based indexing means last index = length - 1 [OK]

Common Mistakes:

• Using length instead of length - 1 for last index
• Removing boundary checks causing infinite loops
• Starting indices at 1 instead of 0

5. Given a rectangular matrix of size 3x4:

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

What is the spiral traversal output?

hard

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

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

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

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

Solution

1. Step 1: Traverse top row left to right

   Elements: 1, 2, 3, 4; top moves from 0 to 1.

2. Step 2: Traverse right column top to bottom

   Elements: 8, 12; right moves from 3 to 2.

3. Step 3: Traverse bottom row right to left

   Elements: 11, 10, 9; bottom moves from 2 to 1.

4. Step 4: Traverse left column bottom to top

   Elements: 5; left moves from 0 to 1.

5. Step 5: Traverse inner row left to right

   Elements: 6, 7; top moves from 1 to 2.

6. Final Answer:

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

7. Quick Check:

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

Hint: Shrink boundaries after each side, watch rectangular shape [OK]

Common Mistakes:

• Mixing order of inner elements
• Skipping last inner row or column
• Confusing left and right boundaries