AP CS A: 2D Arrays and Nested Loops (the patterns that show up)

The 2D array FRQ is one of the four AP CS A FRQ types and shows up every year. The traversal patterns are limited — learn these 4 and you've covered everything the exam can ask.

Pattern 1 — Full row-major traversal

The standard traversal. Visit every element row by row.

for (int r = 0; r < arr.length; r++) {
  for (int c = 0; c < arr[r].length; c++) {
    // do something with arr[r][c]
  }
}

Used for: summing all elements, finding max/min, applying an operation to every cell.

Pattern 2 — Column-major traversal

Visit by column, then row.

for (int c = 0; c < arr[0].length; c++) {
  for (int r = 0; r < arr.length; r++) {
    // do something with arr[r][c]
  }
}

Used for: column sums, finding the ‘heaviest’ column, transposing.

Pattern 3 — Diagonal traversal

The main diagonal where row index equals column index. For a square 2D array:

for (int i = 0; i < arr.length; i++) {
  // arr[i][i] is on the main diagonal
}

For the anti-diagonal (top-right to bottom-left): arr[i][arr.length - 1 - i].

Pattern 4 — Neighbor traversal

Visit each cell and its neighbors. Tricky because neighbors might not exist at edges.

for (int r = 0; r < arr.length; r++) {
  for (int c = 0; c < arr[r].length; c++) {
    // check each neighbor with bounds check
    if (r > 0) { /* arr[r-1][c] is north neighbor */ }
    if (r < arr.length - 1) { /* south */ }
    if (c > 0) { /* west */ }
    if (c < arr[r].length - 1) { /* east */ }
  }
}

Used for: cellular-automata-style problems, “count neighbors with property X”.

Common 2D array FRQ mistakes

1. Confusing rows and columns. arr[r][c] is row r, column c. NOT column r, row c.
2. Using arr.length for columns. arr.length is the number of rows. arr[0].length (or arr[r].length) is the number of columns.
3. Forgetting that 2D arrays in Java are arrays of arrays. Rows can technically have different lengths (jagged arrays). The exam rarely tests this but it's worth knowing.
4. Off-by-one on neighbor bounds. if (r < arr.length - 1), not if (r <= arr.length).

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