Column-Major Traversal and Diagonals

Normal row-major traversal uses an outer loop over rows and an inner loop over columns, so you finish an entire row before moving to the next. Column-major traversal just swaps which loop sits outside: the outer loop fixes a column, and the inner loop walks down the rows of that column before moving to the next column. The code pattern barely changes — you still write grid[row][col] — but now row is the inner variable that changes fast, and col is the outer variable that changes slow. That swap is the whole trick: the loop nesting controls the order of visits, not the array itself.

On a non-square grid the bounds have to swap too, not just the loop order. A 3 by 5 grid has 3 rows and 5 columns. Row-major loops outer over rows (0 to 2) and inner over columns (0 to 4). Column-major must loop outer over columns (0 to 4) and inner over rows (0 to 2) — the outer bound becomes the column count, the inner bound becomes the row count. Copying row-major's bounds unchanged is a common setup that throws an ArrayIndexOutOfBoundsException on anything but a square grid.

Diagonals are a special case that needs no nested loop at all. The main diagonal of a square grid always has equal row and column index, so a single loop with one counter i walks grid[i][i] from i = 0 up to the last row. This connects column-major and diagonal traversal back to the bigger idea of the unit: once you're comfortable treating the loop structure itself as something you design, you can visit a grid's cells in whatever order a problem needs — rows, columns, diagonals, or something else entirely.