Spiral Matrix Traversal in DSA Python - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is Spiral Matrix Traversal?

It is a way to visit all elements of a matrix by moving 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 directions are followed in Spiral Matrix Traversal?

The directions followed are: right → down → left → up, repeated in this order until all elements are covered.

intermediate

What variables help track the boundaries in Spiral Matrix Traversal?

Four variables track boundaries: top (start row), bottom (end row), left (start column), and right (end column). These shrink inward as we traverse the matrix.

intermediate

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

Updating boundaries prevents revisiting elements. After moving right, top boundary moves down; after moving down, right boundary moves left; after moving left, bottom boundary moves up; after moving up, left boundary moves right.

beginner

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

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

In Spiral Matrix Traversal, which direction do we move first?

A Left

B Down

C Right

D Up

Traversal starts from the top-left corner and moves right first.

Which boundary is updated after moving right in Spiral Matrix Traversal?

A Right boundary moves left

B Bottom boundary moves up

C Left boundary moves right

D Top boundary moves down

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

What happens when the top boundary crosses the bottom boundary during traversal?

A Traversal ends

B Continue moving right

C Reset boundaries

D Move up

When boundaries cross, all elements have been visited, so traversal ends.

What is the main purpose of tracking four boundaries in Spiral Matrix Traversal?

A To avoid revisiting elements

B To count elements

C To sort the matrix

D To find the largest element

Boundaries help keep track of visited rows and columns to avoid repeats.

How many times is each element visited in Spiral Matrix Traversal?

A Never

B Once

C Depends on matrix size

D Twice

Each element is visited exactly once in spiral order.

Explain how to perform Spiral Matrix Traversal on a 2D matrix.

Think about shrinking the edges inward as you move.

Describe the role of the top, bottom, left, and right boundaries in Spiral Matrix Traversal.

Boundaries act like walls closing in on the center.

Practice

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

easy

A. Traverse the matrix in a spiral order starting from the top-left corner

B. Traverse the matrix row by row from left to right only

C. Traverse the matrix column by column from top to bottom only

D. Traverse the matrix diagonally from top-left to bottom-right

Solution

1. Step 1: Understand traversal pattern

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

2. Step 2: Identify starting point and direction

   It starts at the top-left corner and moves right, then down, then left, then up, repeating until all elements are visited.

3. Final Answer:

   Traverse the matrix in a spiral order starting from the top-left corner -> Option A

4. Quick Check:

   Spiral traversal = circular edge-wise movement [OK]

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

Common Mistakes:

• Confusing spiral with row-wise or column-wise traversal
• Starting traversal from the wrong corner
• Ignoring direction changes after each edge

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

easy

A. top = 1; bottom = len(matrix); left = 1; right = len(matrix[0])

B. top = 0; bottom = len(matrix) - 1; left = 0; right = len(matrix[0]) - 1

C. top = 0; bottom = len(matrix); left = 0; right = len(matrix[0])

D. top = 1; bottom = len(matrix) - 1; left = 1; right = len(matrix[0]) - 1

Solution

1. Step 1: Understand matrix boundaries

   For a matrix, top and left start at 0, bottom is last row index (length - 1), right is last column index (length - 1).

2. Step 2: Check each option

   top = 0; bottom = len(matrix) - 1; left = 0; right = len(matrix[0]) - 1 correctly sets top=0, bottom=len(matrix)-1, left=0, right=len(matrix[0])-1 which matches the matrix indices.

3. Final Answer:

   top = 0; bottom = len(matrix) - 1; left = 0; right = len(matrix[0]) - 1 -> Option B

4. Quick Check:

   Boundary indices start at 0 and end at length-1 [OK]

Hint: Remember Python indexing starts at 0, so subtract 1 for last index [OK]

Common Mistakes:

• Using length instead of length - 1 for bottom and right
• Starting top or left at 1 instead of 0
• Mixing row and column lengths

3. What is the output of the following Python code?

matrix = [
  [1, 2, 3],
  [4, 5, 6],
  [7, 8, 9]
]
result = []
top, bottom = 0, 2
left, right = 0, 2
while top <= bottom and left <= right:
    for i in range(left, right + 1):
        result.append(matrix[top][i])
    top += 1
    for i in range(top, bottom + 1):
        result.append(matrix[i][right])
    right -= 1
    for i in range(right, left - 1, -1):
        result.append(matrix[bottom][i])
    bottom -= 1
    for i in range(bottom, top - 1, -1):
        result.append(matrix[i][left])
    left += 1
print(result)

medium

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

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

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

D. [1, 2, 3, 6, 9, 8, 7, 4]

Solution

1. Step 1: Traverse top row left to right

   Elements: 1, 2, 3 added to result.

2. Step 2: Traverse right column top to bottom

   Elements: 6, 9 added to result.

3. Step 3: Traverse bottom row right to left

   Elements: 8, 7 added to result.

4. Step 4: Traverse left column bottom to top

   Element: 4 added to result.

5. Step 5: Inner layer traversal

   Only element 5 remains, added last.

6. Final Answer:

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

7. Quick Check:

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

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

Common Mistakes:

• Skipping the last inner element
• Repeating elements or missing elements
• Wrong direction in bottom or left traversal

4. The following code attempts spiral traversal but produces an error. What is the main bug?

matrix = [[1,2,3],[4,5,6],[7,8,9]]
top, bottom = 0, 2
left, right = 0, 2
result = []
while top <= bottom and left <= right:
    for i in range(left, right + 1):
        result.append(matrix[top][i])
    top += 1
    for i in range(top, bottom + 1):
        result.append(matrix[i][right])
    right -= 1
    for i in range(right, left - 1, -1):
        result.append(matrix[bottom][i])
    bottom -= 1
    for i in range(bottom, top - 1, -1):
        result.append(matrix[i][left])
    left += 1
print(result)

medium

A. The code uses incorrect range in the first for loop

B. The code uses wrong indices for left and right boundaries

C. The code does not check if top <= bottom before traversing bottom row

D. The code misses incrementing the left boundary

Solution

1. Step 1: Analyze loop conditions

   The while loop checks top <= bottom and left <= right before each full cycle.

2. Step 2: Identify missing checks inside loop

   After updating top and right, the code traverses bottom row and left column without checking if top <= bottom or left <= right again, causing index errors when boundaries cross.

3. Final Answer:

   The code does not check if top <= bottom before traversing bottom row -> Option C

4. Quick Check:

   Boundary checks needed before each edge traversal [OK]

Hint: Check boundaries before each edge traversal inside the loop [OK]

Common Mistakes:

• Assuming one boundary check per loop is enough
• Not updating boundaries correctly
• Ignoring empty or single-row/column matrices

5. Given a rectangular matrix of size 3x4:

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, 11, 10, 9, 6, 5, 7]

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

C. ]6 ,7 ,5 ,9 ,01 ,11 ,21 ,8 ,4 ,3 ,2 ,1[

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

Solution

1. Step 1: Traverse top row left to right

   Elements: 1, 2, 3, 4 added.

2. Step 2: Traverse right column top to bottom

   Elements: 8, 12 added.

3. Step 3: Traverse bottom row right to left

   Elements: 11, 10, 9 added.

4. Step 4: Traverse left column bottom to top

   Element: 5 added.

5. Step 5: Traverse inner row left to right

   Elements: 6, 7 added.

6. Final Answer:

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

7. Quick Check:

   Spiral order covers all elements layer by layer [OK]

Hint: Follow edges clockwise, then move inward carefully for rectangular matrices [OK]

Common Mistakes:

• Mixing order of inner elements
• Skipping or repeating elements in inner layers
• Confusing left column traversal direction