4.13 Implementing 2D Array Algorithms

1. Example 1

   Write a method: column totals

   Write a method columnTotals that returns an array with the sum of each column of grid. One solution:Javapublic static int[] columnTotals(int[][] grid) { int[] totals = new int[grid[0].length]; for (int c = 0; c < grid[0].length; c++) { for (int r = 0; r < grid.length; r++) { totals[c] += grid[r][c]; } } return totals; }

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   1. 1Step 1: The result needs one total per column, so its length is grid[0].length. A new int array starts full of 0s, which is exactly where totals should start.
   2. 2Step 2: The outer loop picks a column; the inner loop moves down the rows and adds each element to that column's total.
   3. 3Step 3: For { {3, 1, 4}, {1, 5, 9}, {2, 6, 5} }: column 0 is 3 + 1 + 2 = 6, column 1 is 1 + 5 + 6 = 12, column 2 is 4 + 9 + 5 = 18.

   Answer: The method above; for that grid it returns {6, 12, 18}.

2. Example 2

   Write a method: counting peaks

   A cell is a peak if it's higher than every neighbor that exists above, below, left and right. Write countPeaks to count the peaks in land. One solution:Javapublic static int countPeaks(int[][] land) { int count = 0; for (int r = 0; r < land.length; r++) { for (int c = 0; c < land[0].length; c++) { int h = land[r][c]; boolean peak = true; if (r > 0 && land[r - 1][c] >= h) { peak = false; } if (r < land.length - 1 && land[r + 1][c] >= h) { peak = false; } if (c > 0 && land[r][c - 1] >= h) { peak = false; } if (c < land[0].length - 1 && land[r][c + 1] >= h) { peak = false; } if (peak) { count++; } } } return count; }

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   1. 1Step 1: Visit every cell with nested loops, and assume it's a peak until a neighbor proves otherwise.
   2. 2Step 2: Each neighbor check starts with a bounds test, like r > 0 before looking at row r - 1, so edge cells never go out of bounds.
   3. 3Step 3: Trace { {5, 2, 3}, {1, 4, 8}, {2, 6, 3} }. The 5 at the top-left beats its neighbors 2 and 1. The 8 beats 3, 4 and 3. The 6 beats 4, 2 and 3. Every other cell has a neighbor at least as high.
   4. 4Step 4: That's 3 peaks.

   Answer: The method above; it returns 3 for that grid.

Common mistakes

• !Forgetting to reset a row total to 0 at the start of each row, so totals pile up across rows.
• !Checking a neighbor before checking that its index is in range.
• !Mixing up grid.length and grid[0].length in the bounds of a column loop.

On the exam

• ✓Free-response Question 4 (2D Array) is worth 6 points since the 2025 course update, down from 9. Typical tasks are counting or totaling over part of the grid, finding a best element, checking neighbors, or building a new 1D or 2D array from the grid.