Implementing 2D Array Algorithms

Grid algorithms

• 2-D algorithms combine the array patterns with nested-loop 嵌套循环 traversal.
• Sum / count / max over the whole grid: accumulate inside the inner loop.
• Search a grid: return the [row][col] where found (or a "not found" signal).
• The same accumulator/max logic, now over rows × columns cells.

Row and column sums

• One row: fix r, loop c over the columns, summing g[r][c].
• One column: fix c, loop r over the rows, summing g[r][c].
• Choosing which index to fix and which to loop is the key decision.
• A row sum sweeps across; a column sum sweeps down.

Row-major and column-major traversal of a 2D array

The diagonal

• The main diagonal 主对角线 of a square grid is the cells where row == column.
• Loop one index: for (int i = 0; i < g.length; i++) { ... g[i][i] ... }
• g[0][0], g[1][1], g[2][2], … — a single loop, both indices equal.
• Useful for square grids (identity checks, board diagonals).

Modifying cells

• To change a cell, use the indexed 带下标 nested loops and assign g[r][c] = ....
• The for-each version can't write back to the grid.
• Watch the two bounds — a wrong length reads or writes the wrong cell.
• Trace [r][c] carefully, especially when rows and columns differ in count.