4.12 2D Array Traversals

What you need to know

• Row-major traversal: outer loop over rows, inner over columns. Visits row 0 left to right, then row 1, etc. This is the default.
• Column-major traversal: outer loop over columns, inner over rows. Visits column 0 top to bottom, then column 1.
• Nested enhanced for: for (int[] row : grid) { for (int v : row) { ... } } — row-major, read only.
• Use grid.length for the row bound and grid[0].length (or grid[r].length) for the column bound.
• Partial traversals: a single row (grid[r][c] for c), a single column (grid[r][c] for r), the diagonal (grid[i][i]), or a sub-region.
• Traversal order matters when output is printed in sequence or when elements are appended to a list.

Worked example

int[][] g = {{1, 2, 3},
             {4, 5, 6}};

// row-major: 1 2 3 4 5 6
for (int r = 0; r < g.length; r++)
{
    for (int c = 0; c < g[0].length; c++)
    {
        System.out.print(g[r][c] + " ");
    }
}

// column-major: 1 4 2 5 3 6
for (int c = 0; c < g[0].length; c++)
{
    for (int r = 0; r < g.length; r++)
    {
        System.out.print(g[r][c] + " ");
    }
}

Going deeper

The nuance, edge cases, and connections that turn a 3 into a 5.

• Row-major (outer r, inner c) visits row 0 fully, then row 1, etc. Reading order for English text. Column-major (outer c, inner r) visits column 0 top to bottom, then column 1. The loop nesting order determines which.
• Nested enhanced for: for (int[] row : g) for (int v : row) — row-major only, read-only. To modify cells you need indices.
• Single row: for (int c = 0; c < g[r].length; c++) g[r][c]. Single column: for (int r = 0; r < g.length; r++) g[r][c]. There's no g[][c] — a column has to be assembled by looping rows.
• Diagonals: main diagonal g[i][i]; anti-diagonal g[i][n - 1 - i] for a square grid.
• Bounds: row bound is g.length, column bound g[0].length (or g[r].length). Swapping them works only for square grids and fails otherwise — the exam uses non-square grids to catch it.
• Output order questions: write the grid, then read it in the traversal order (across rows or down columns). Trust the loop nesting, not the variable names.
• Traversal with a running index: when copying between a 1D array and a 2D array, keep a separate counter k that increments once per cell.

Mistakes that cost points

• Assuming the outer loop is always rows. Check which variable it controls.
• Swapping bounds on a non-square grid. Exception or missed cells.
• Trying to grab a column as an array. No such thing. Loop rows.

Practice questions

Written in the style of the real exam. Try each one before revealing the answer.

int[][] m = {{1, 2}, {3, 4}, {5, 6}};
for (int c = 0; c < m[0].length; c++)
{
    for (int r = 0; r < m.length; r++)
    {
        System.out.print(m[r][c]);
    }
}