2D Arrays

A 2D array is an array whose elements are themselves arrays. You reach an element with two indices: grid[row][col]. Most AP CSA problems treat 2D arrays as rectangular grids, where every row has the same length.

Two nested loops are the standard tool for traversing a 2D array. The outer loop walks rows; the inner loop walks columns. This pattern appears in nearly every 2D array FRQ.

On the AP exam, 2D arrays show up in MCQ tracing, in FRQ #4 (which is often a grid problem), and in any task involving rectangular data such as game boards, image processing, or tabular calculations.

Declaring and creating

int[][] grid = new int[3][4];          // 3 rows, 4 columns, all 0
String[][] board = new String[8][8];   // 8x8, all null

int[][] m = {{1, 2, 3},
             {4, 5, 6}};               // 2 rows, 3 columns

Accessing elements

int x = m[0][2];   // row 0, column 2  -> 3
m[1][0] = 99;      // row 1, column 0  -> now 99

The first index is the row; the second is the column. Always.

Dimensions

int rows = m.length;        // 2
int cols = m[0].length;     // 3

m.length gives the number of rows. m[r].length gives the number of columns in row r. For rectangular arrays this is the same for every row.

Row-major traversal (the standard)

for (int r = 0; r < m.length; r++) {
    for (int c = 0; c < m[r].length; c++) {
        System.out.print(m[r][c] + " ");
    }
    System.out.println();
}

This visits row 0 fully, then row 1, and so on. The println after the inner loop creates the row-by-row layout.

Column-major traversal

for (int c = 0; c < m[0].length; c++) {
    for (int r = 0; r < m.length; r++) {
        // process m[r][c]
    }
}

Swap the loops to walk all of column 0 first, then column 1, and so on.

Enhanced for over a 2D array

for (int[] row : m) {
    for (int n : row) {
        System.out.print(n + " ");
    }
}

The outer loop pulls out each row (an int[]); the inner loop walks that row's values. Cannot modify the cells through this form.