Nested Loops

A nested loop is a loop placed inside the body of another loop. For each iteration of the outer loop, the entire inner loop runs from start to finish.

Nested loops are essential for any task that involves pairs of elements — comparing items in an array, printing rectangular patterns, or traversing a 2D array row by row and column by column.

On the AP exam, nested loops show up in tracing problems, output-pattern questions, and almost every 2D-array FRQ.

Basic structure

for (int i = 0; i < rows; i++) {
    for (int j = 0; j < cols; j++) {
        // executed rows * cols times
    }
}

If the outer loop runs rows times and the inner loop runs cols times, the inner body runs rows * cols times in total.

Tracing tip

Always describe nested loops with the phrase: "for every outer iteration, the inner loop runs from start to finish." This mental model prevents most tracing errors.

Pattern example

for (int i = 1; i <= 3; i++) {
    for (int j = 1; j <= i; j++) {
        System.out.print("*");
    }
    System.out.println();
}

This prints:

*
**
***

Notice how the inner loop's bound depends on the outer loop variable i — a powerful pattern used in many AP problems.

2D array 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] + " ");
    }
    System.out.println();
}

This is the standard row-major traversal pattern: the outer loop walks rows, the inner loop walks columns.