Understanding the Problem
We are given a 2D matrix and asked to print its elements in a spiral order. That means starting from the top-left corner, we go right along the top row, then down the rightmost column, then left along the bottom row, then up the leftmost column—repeating this process inward like peeling layers of an onion until all elements are visited.
For a beginner, think of walking around the boundary of the matrix, one layer at a time, and collecting the numbers in the order you walk.
Step-by-Step Solution with Example
step 1: Initialize boundaries
We define four variables to represent the current unvisited part of the matrix:
top
– the index of the first row not yet printed
bottom
– the index of the last row not yet printed
left
– the index of the first column not yet printed
right
– the index of the last column not yet printed
step 2: Traverse in spiral order
We use a loop and at each iteration, follow this order:
- Go left to right across the top row
- Go top to bottom along the rightmost column
- If rows remain, go right to left along the bottom row
- If columns remain, go bottom to top along the leftmost column
After completing a side, update the boundary variables to move inward (e.g., top++
, right--
, etc.).
step 3: Continue until all elements are visited
The loop continues as long as top ≤ bottom
and left ≤ right
. This ensures we don't go beyond the unvisited region.
step 4: Example walk-through
Consider this 3x3 matrix:
[ [1, 2, 3],
[4, 5, 6],
[7, 8, 9] ]
Spiral order traversal:
- Top row: 1, 2, 3
- Right column: 6, 9
- Bottom row (reversed): 8, 7
- Left column (upward): 4
- Remaining element: 5
Output: [1, 2, 3, 6, 9, 8, 7, 4, 5]
Edge Cases
- Empty matrix: No elements to print. Return an empty list.
- Single element: Just return that one value.
- Single row: Only traverse left to right.
- Single column: Only traverse top to bottom.
- More rows than columns: Spiral will loop deeper vertically.
- More columns than rows: Spiral will loop wider horizontally.
Finally
This spiral traversal technique ensures we visit each element exactly once. It's intuitive when we think in terms of peeling layers, and it works efficiently in O(m × n)
time for an m x n
matrix. For beginners, always visualize the movement and update of boundaries, and use dry runs with small matrices to build confidence.
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