Spiral Matrix

FizzBuzz

Length of Last Word

Generate an n-by-n matrix filled clockwise in spiral order.

Generate an `n x n` matrix containing the integers from `1` through `n²` in clockwise spiral order, starting at the top-left corner.

**Input / output**
- Input: `n: integer`
- Output: `integer[][]`

**Examples**
1. `n = 3` returns `[[1,2,3],[8,9,4],[7,6,5]]`.
2. `n = 1` returns `[[1]]`.

**Constraints**
- `1 <= n <= 50`

**Follow-up**
Can you describe the loop invariant for the four moving boundaries and avoid special-case center logic?

- Create an `n x n` matrix and place values from `1` to `n²`.
- The direction starts moving right, then turns down, left, and up.
- After each side is filled, the active boundary moves inward.

Understand the Spiral Fill

- Keep `top`, `bottom`, `left`, and `right` boundaries for the unfilled rectangle.
- Fill the top row left-to-right, then move `top` down.
- Fill the right column top-to-bottom, then move `right` left, and continue around.

Track Four Boundaries

- One loop iteration fills the outer ring of the current rectangle.
- After a ring is finished, the boundaries describe the next inner ring.
- Continue while `top <= bottom` and `left <= right`.

Fill One Ring at a Time

- Odd-sized matrices eventually have a single center cell, which the boundary loop fills naturally.
- Some test inputs may provide `n` as a string after JSON parsing.
- Convert `n` to an integer before creating the matrix.

Handle Center Cells and Input Type

- The final solution fills each cell exactly once while shrinking the boundaries.
- Time complexity is O(n²).
- Space complexity is O(n²) for the returned matrix.