Complex traversals are boundary management

Complex traversals (spirals, diagonals, borders) are boundary management problems. The spiral keeps four walls (top, bottom, left, right) and shrinks them after each side — with two re-checks (if (top <= bottom), if (left <= right)) that exist only for single-row and single-column remainders. Drop a re-check and a 3×1 grid double-counts.

Rules for writing any complex traversal:

1. Write the loop invariants in the margin: "top row fully filled", "right column fully filled", etc.
2. After each side, move the corresponding wall and say why the next side's bounds are still valid.
3. Test 1×n, n×1, and 1×1 before anything else. Rectangular (non-square) inputs break symmetric-looking code.

That last rule is the advanced habit: the bug is never in the middle of the grid. It is on the last column, the single row, or the already-shrunk wall.