Grid layout and nested traversal

A 2D array is an array of arrays — rows first, then columns:

int[][] grid = new int[3][4];      // 3 rows, 4 columns, all zeros
int[][] g2 = { {1, 2, 3}, {4, 5, 6} };   // 2 rows, 3 columns

Indexing is grid[row][col], both zero-based. grid[0] is the whole first row (it is itself an int[]), grid[0][2] is one element.

The lengths trick: grid.length is the number of rows, grid[0].length is the number of columns. They are NOT the same variable, and mixing them up is the classic bounds bug:

for (int r = 0; r < grid.length; r++) {          // rows
    for (int c = 0; c < grid[0].length; c++) {   // columns of that row
        System.out.print(grid[r][c] + " ");
    }
    System.out.println();
}

Row-major order — this outer-rows / inner-columns pattern — is how almost every AP 2D problem starts. Say the loop bounds out loud: "r goes over rows, c goes over the columns of row r."