1. Introduction

The "Spiral Matrix" problem is a classic in matrix manipulation challenges. It involves traversing a 2D matrix in a spiral pattern, starting from the top left corner and gradually moving inward. This problem tests one's ability to handle complex iteration patterns and boundary conditions in arrays.

Problem

Given an m x n matrix, the task is to return all elements of the matrix in spiral order. This involves traversing the matrix in a clockwise spiral, starting from the top left corner and collecting elements until all have been traversed.

2. Solution Steps

1. Initialize variables for the boundaries of the matrix: top, bottom, left, and right.

2. Traverse the matrix within these boundaries, adjusting them after each spiral rotation.

3. Move right across the top row, then move down the right column.

4. Move left across the bottom row, then move up the left column.

5. Repeat the process until all elements are covered.

6. Handle edge cases like single-row or single-column matrices within the loop.

7. Append each element encountered to a result list.

8. Return the result list once the spiral traversal is complete.

3. Code Program

``````def spiralOrder(matrix):
result = []
if not matrix:
return result

top, bottom, left, right = 0, len(matrix), 0, len(matrix[0])

while left < right and top < bottom:
# Move right
for i in range(left, right):
result.append(matrix[top][i])
top += 1

# Move down
for i in range(top, bottom):
result.append(matrix[i][right - 1])
right -= 1

if not (left < right and top < bottom):
break

# Move left
for i in range(right - 1, left - 1, -1):
result.append(matrix[bottom - 1][i])
bottom -= 1

# Move up
for i in range(bottom - 1, top - 1, -1):
result.append(matrix[i][left])
left += 1

return result

# Example Usage
matrix = [
[1, 2, 3],
[4, 5, 6],
[7, 8, 9]
]
print(spiralOrder(matrix))  # Output: [1, 2, 3, 6, 9, 8, 7, 4, 5]

``````

Output:

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

Explanation:

1. Initial Setup: Variables are initialized to represent the boundaries of the matrix.

2. Spiral Traversal: The matrix is traversed in a spiral manner, starting from the top left corner.

3. Directional Movement: Movement is carried out right, down, left, and up, adjusting boundaries after each direction.

4. Boundary Conditions: The traversal checks if the current direction is still valid within the adjusted boundaries.

5. Edge Cases: Special cases like single rows or columns are handled implicitly by the boundary conditions.

6. Collecting Elements: Each traversed element is added to the result list.

7. Complete Coverage: The process continues until all elements are added to the result.

8. Result: The function returns a list of elements in spiral order.