The problem this code solves

A seating chart, a spreadsheet, a game board, the pixels of an image: all of them are grids, rows of columns, and the natural way to store one is a 2D array. To total a spreadsheet, find the brightest pixel, or check a winning line on a board, the program walks the grid cell by cell with a nested loop. This is the last big traversal pattern, and it is the one the exam always tests in free response.

2D arrays: a grid of rows and columns

A 2D array is an array of arrays. You reach an element with two indices: grid[r][c], the value in row r, column c. Rows come first. Almost every 2D task is a nested loop: an outer loop over rows, an inner loop over the columns in that row.

The nested traversal

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

grid.length is the row count. grid[r].length is the number of columns in that row. Mixing them up is the most common 2D bug.

Row-major vs column-major

// row-major: outer loop = rows
for (int r = 0; r < grid.length; r++)
  for (int c = 0; c < grid[r].length; c++)
    ... grid[r][c] ...

// column-major: outer loop = columns
for (int c = 0; c < grid[0].length; c++)
  for (int r = 0; r < grid.length; r++)
    ... grid[r][c] ...

Vocabulary

Predict first, then check

See the row-major traversal

Row-major order walks across row 0 first, then row 1, summing as it goes. Play it and watch the pointer move left to right, top to bottom.

int sum = 0;
for (int r = 0; r < grid.length; r++) {
  for (int c = 0; c < grid[r].length; c++) {
    sum += grid[r][c];
  }
}

Live code editor

Eight problems, six scaffolded and two open-ended. Write Java, press Run to execute it, and Check to test against the expected output. Hints and the solution are here if you need them, but using them is tracked, so try first.

Grid Walker Arcade

Six quick rounds on 2D arrays. Read the grid or the loop and type the result. Drills the nested-loop and length patterns the 2D array FRQ tests.

Multiple choice

Predict your answer before reading the options. Watch for the qualifier words. After you answer, the rationale explains every distractor.

FRQ connection: the 2D array question

Every exam has a 2D array free-response question, and it is almost always a nested-loop traversal with a condition. Practice the core move: walk the grid and count what matches.

Choose your lane