Columns, swaps, transposes

Column aggregation — the classic "compute per-column totals" task:

public static int[] colSums(int[][] g) {
    int[] sums = new int[g[0].length];
    for (int c = 0; c < g[0].length; c++) {
        for (int r = 0; r < g.length; r++) {
            sums[c] += g[r][c];
        }
    }
    return sums;
}

The output array is sized by COLUMNS; the loops read column-major. Two orientations in one method — draw which loop walks which direction until it is automatic.

Transformations that read and write the same array need care: swapping rows uses a temporary one-row array:

int[] tmp = g[a];
g[a] = g[b];
g[b] = tmp;

That is O(1) — row references swap, no element copying. Compare with transposing (rows become columns), which needs element-by-element copy into a NEW array of swapped dimensions:

int[][] t = new int[g[0].length][g.length];
for (int r = 0; r < g.length; r++) {
    for (int c = 0; c < g[r].length; c++) {
        t[c][r] = g[r][c];
    }
}

Both directions appear on exams; the swap copies nothing, the transpose copies everything. Know which question you are answering.