2D Array Algorithms in AP CSA: Row Sums, Column Sums, and Matrix Patterns

FRQ 4 on the AP CSA exam almost always involves a 2D array. This page covers the exact algorithmic patterns you need: summing rows and columns, finding extremes, counting with conditions, and processing subregions of a matrix.

📈 Row Sum Pattern

To compute the sum of a single row, hold the row index constant and iterate across columns:

public static int rowSum(int[][] grid, int row)
{
    int sum = 0;
    for (int c = 0; c < grid[row].length; c++)
    {
        sum += grid[row][c];
    }
    return sum;
}

To get ALL row sums, wrap this in an outer loop:

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

📉 Column Sum Pattern

Column sums flip the loop order. Hold the column constant, iterate down the rows:

public static int colSum(int[][] grid, int col)
{
    int sum = 0;
    for (int r = 0; r < grid.length; r++)
    {
        sum += grid[r][col];
    }
    return sum;
}

🔎 Finding Max/Min in a Matrix

public static int findMax(int[][] grid)
{
    int max = grid[0][0];
    for (int r = 0; r < grid.length; r++)
    {
        for (int c = 0; c < grid[r].length; c++)
        {
            if (grid[r][c] > max)
            {
                max = grid[r][c];
            }
        }
    }
    return max;
}

Critical: Initialize max to grid[0][0], not to 0. If all values are negative, initializing to 0 gives a wrong answer. Same logic applies to finding the minimum.

🔢 Counting with Conditions

// Count how many elements are greater than a threshold
public static int countAbove(int[][] grid, int threshold)
{
    int count = 0;
    for (int r = 0; r < grid.length; r++)
    {
        for (int c = 0; c < grid[r].length; c++)
        {
            if (grid[r][c] > threshold)
            {
                count++;
            }
        }
    }
    return count;
}

This pattern appears on nearly every FRQ 4. The condition inside the if statement changes, but the nested loop structure stays the same.

❌ Common Pitfalls

✏ Practice Questions

❓ Frequently Asked Questions