Spiral Matrix Traversal in DSA Java - 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

What variables help track the boundaries during Spiral Matrix Traversal?

Four variables: top (start row), bottom (end row), left (start column), right (end column) to keep track of the current edges of the matrix to traverse.

intermediate

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

Because after traversing one edge, 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.

In Spiral Matrix Traversal, which boundary moves down after traversing the top row?

A left

B bottom

C right

D top

After traversing the top row, the top boundary moves down to avoid revisiting that row.

What direction do you move after traversing the rightmost column in Spiral Matrix Traversal?

A Left

B Up

C Down

D Right

After moving down the rightmost column, the next direction is left along the bottom row.

Which variable tracks the left boundary in Spiral Matrix Traversal?

A left

B bottom

C top

D right

The 'left' variable tracks the leftmost column boundary.

When does the Spiral Matrix Traversal stop?

A When all columns are visited

B When all rows are visited

C When top > bottom or left > right

D After one full spiral

Traversal stops when the top boundary crosses the bottom or the left boundary crosses the right, meaning all elements are visited.

What is the first direction to move in Spiral Matrix Traversal?

A Down

B Right

C Up

D Left

Traversal starts by moving right along the top row.

Explain how you would traverse a 3x3 matrix in spiral order using boundary variables.

Think about moving along edges and shrinking the matrix boundaries step by step.

Describe the role of boundary variables in preventing revisiting elements during Spiral Matrix Traversal.

Boundaries act like fences that close in as you move.

Practice

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

easy

A. Traverse the matrix in a circular pattern from outer to inner layers

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

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

D. Traverse only the diagonal elements of the matrix

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 A

4. Quick Check:

   Spiral traversal = circular outer to inner [OK]

Hint: Spiral means circle inward from edges [OK]

Common Mistakes:

• Confusing spiral with row-wise traversal
• Thinking spiral means diagonal only
• Mixing column-wise with spiral

2. Which of the following Java code snippets correctly initializes the boundaries for spiral traversal of a matrix int[][] matrix?

easy

A. int top = 1, bottom = matrix.length, left = 1, right = matrix[0].length;

B. int top = 0, bottom = matrix.length - 1, left = 0, right = matrix[0].length - 1;

C. int top = 0, bottom = matrix[0].length - 1, left = 0, right = matrix.length - 1;

D. int top = matrix.length, bottom = 0, left = matrix[0].length, right = 0;

Solution

1. Step 1: Identify matrix dimensions

   For a 2D array, rows = matrix.length, columns = matrix[0].length.

2. Step 2: Set boundaries correctly

   Top and left start at 0, bottom is last row index (length-1), right is last column index (length-1). int top = 0, bottom = matrix.length - 1, left = 0, right = matrix[0].length - 1; matches this.

3. Final Answer:

   int top = 0, bottom = matrix.length - 1, left = 0, right = matrix[0].length - 1; -> Option B

4. Quick Check:

   Boundaries start at 0 and end at length-1 [OK]

Hint: Boundaries start at 0, end at length-1 [OK]

Common Mistakes:

• Using 1-based indices instead of 0-based
• Swapping rows and columns in boundaries
• Setting bottom or right greater than max index

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

int[][] matrix = {
  {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++) System.out.print(matrix[top][i] + " ");
  top++;
  for (int i = top; i <= bottom; i++) System.out.print(matrix[i][right] + " ");
  right--;
  if (top <= bottom) {
    for (int i = right; i >= left; i--) System.out.print(matrix[bottom][i] + " ");
    bottom--;
  }
  if (left <= right) {
    for (int i = bottom; i >= top; i--) System.out.print(matrix[i][left] + " ");
    left++;
  }
}

medium

A. 1 4 7 8 9 6 3 2 5

B. 1 2 3 4 5 6 7 8 9

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 first outer layer

   Top row: 1 2 3, right column down: 6 9, bottom row left: 8 7, left column up: 4

2. Step 2: Trace inner layer

   Now top=1, bottom=1, left=1, right=1, print center element: 5

3. Final Answer:

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

4. Quick Check:

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

Hint: Follow boundaries and print edges inward [OK]

Common Mistakes:

• Printing rows or columns in wrong order
• Missing center element in odd-sized matrix
• Not updating boundaries correctly

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

int top = 0, bottom = matrix.length - 1;
int left = 0, right = matrix[0].length - 1;
while (top < bottom && left < right) {
  for (int i = left; i <= right; i++) System.out.print(matrix[top][i] + " ");
  top++;
  for (int i = top; i <= bottom; i++) System.out.print(matrix[i][right] + " ");
  right--;
  for (int i = right; i >= left; i--) System.out.print(matrix[bottom][i] + " ");
  bottom--;
  for (int i = bottom; i >= top; i--) System.out.print(matrix[i][left] + " ");
  left++;
}

medium

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

B. The for loops should use < instead of <= to avoid index errors

C. The boundaries are initialized incorrectly

D. The print statements should be inside if conditions to avoid duplicates

Solution

1. Step 1: Analyze while loop condition

   Using < excludes the case when top == bottom or left == right, missing last layer in odd-sized matrices.

2. Step 2: Correct condition to include all layers

   Changing to <= ensures the center or last layer is processed.

3. Final Answer:

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

4. Quick Check:

   Use <= in while to cover all layers [OK]

Hint: Use <= in while to cover all matrix layers [OK]

Common Mistakes:

• Using < excludes center element in odd matrices
• Not updating boundaries after each loop
• Missing if checks for inner loops

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 5 9 10 11 12 8 4 3 2 6 7

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

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

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

Solution

1. Step 1: Traverse top row left to right

   Print 1 2 3 4

2. Step 2: Traverse right column top to bottom

   Print 8 12

3. Step 3: Traverse bottom row right to left

   Print 11 10 9

4. Step 4: Traverse left column bottom to top

   Print 5

5. Step 5: Traverse inner row left to right

   Print 6 7

6. Final Answer:

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

7. Quick Check:

   Follow edges inward for rectangular matrix [OK]

Hint: Print edges clockwise, move inward layer by layer [OK]

Common Mistakes:

• Mixing order of inner elements
• Skipping last inner row
• Confusing left column traversal direction