Topic 2.11 — Nested Iteration

Goal: trace and write nested loops (a loop inside another loop), and recognize how the number of iterations grows when loops are nested.

The big idea

Nested iteration means you have a loop inside another loop. For each iteration of the outer loop, the inner loop runs completely.

Think: “For each row, do all the columns.”

for (int r = 0; r < rows; r++) {
  for (int c = 0; c < cols; c++) {
    // runs rows * cols times total
  }
}

Total executions of the inner body ≈ (outer iterations) × (inner iterations).

(Even if you don’t “print” on your site, this pattern is common for 2D work later.)

for (int r = 0; r < 3; r++) {
  for (int c = 0; c < 4; c++) {
    // do something for (r, c)
  }
}

Another common use: compare every item with every other item.

for (int i = 0; i < n; i++) {
  for (int j = i + 1; j < n; j++) {
    // work with pair (i, j)
  }
}

Starting j at i + 1 avoids duplicate pairs and avoids comparing an element with itself.

for (int i = 1; i <= 2; i++) {
  for (int j = 1; j <= 3; j++) {
    // body
  }
}
// i=1 with j=1,2,3 then i=2 with j=1,2,3

// Bug: accidentally increments i inside inner loop
for (int i = 0; i < n; i++) {
  for (int j = 0; j < n; j++) {
    i++; // ❌
  }
}