class Solution:
def spiralOrder(self, matrix: List[List[int]]) -> List[int]:
"""
Returns all elements of the input 2D matrix in spiral order.
Parameters:
matrix (List[List[int]]): A 2D list of integers representing the matrix.
Returns:
List[int]: A list of integers representing the matrix elements in spiral order.
"""
# Initialize boundary pointers.
top = 0 # The top row index of the current spiral layer.
bottom = len(matrix) - 1 # The bottom row index of the current spiral layer.
left = 0 # The left column index of the current spiral layer.
right = len(matrix[0]) - 1 # The right column index of the current spiral layer.
# List to store the spiral order.
spiral = []
# Continue until all layers are processed.
while top <= bottom and left <= right:
# Traverse from left to right across the top row.
for j in range(left, right + 1):
spiral.append(matrix[top][j])
top += 1 # Move the top boundary down after processing the top row.
# Traverse from top to bottom along the right column.
for i in range(top, bottom + 1):
spiral.append(matrix[i][right])
right -= 1 # Move the right boundary left after processing the right column.
# Traverse from right to left across the bottom row if it still exists.
if top <= bottom:
for j in range(right, left - 1, -1):
spiral.append(matrix[bottom][j])
bottom -= 1 # Move the bottom boundary up.
# Traverse from bottom to top along the left column if it still exists.
if left <= right:
for i in range(bottom, top - 1, -1):
spiral.append(matrix[i][left])
left += 1 # Move the left boundary right.
return spiral
Summary of Techniques and Approaches:
Boundary Tracking: The solution utilizes four pointers (top, bottom, left, right) to mark the current boundaries of the spiral and gradually shrink them as elements are processed. This method is widely applicable in matrix problems where layers or subregions need to be traversed sequentially.
Layer-by-Layer Processing: By iteratively processing the outer layer and then moving inward, the solution keeps the logic clear and avoids unnecessary complexity. This approach is useful when problems require handling of concentric data or multi-level structures.
Conditional Traversal: The solution checks conditions (e.g., if top <= bottom or left <= right) to avoid redundant processing and ensure that boundary updates do not lead to repeated elements. Recognize when conditions must be included to handle edge cases in iterative traversals.
Efficiency: The algorithm processes each element exactly once (O(m * n) time complexity), illustrating the importance of designing solutions that balance simplicity with performance. The approach can be applied to similar problems that involve orderly data extraction from multi-dimensional structures.
These techniques are generally applicable to problems requiring systematic traversal or partitioning of data structures in varying directions.