2.8 for Loops

What you need to know

• for (init; condition; update) { body }. Execution: init once → check condition → body → update → check condition → … until the condition is false.
• A variable declared in the init (int i = 0) exists only inside the loop. Using it after the loop is a compile error.
• for (int i = 0; i < n; i++) runs exactly n times, i = 0 through n−1. i <= n runs n + 1 times.
• Number of iterations for i = a; i < b; i++ is b − a (if b > a). For i <= b, it's b − a + 1.
• The update can be anything: i += 2, i--, i *= 2. Counting down: for (int i = 10; i > 0; i--).
• Any for loop can be rewritten as a while loop by moving the init above and the update to the end of the body. The difference: scope of the loop variable.
• Modifying the loop variable inside the body is legal but confusing and a source of trick questions.

Worked example

for (int i = 2; i <= 10; i += 3)
{
    System.out.print(i + " ");
}
// prints: 2 5 8
// i would be 11 after, but i doesn't exist outside the loop

// equivalent while loop:
int i = 2;
while (i <= 10)
{
    System.out.print(i + " ");
    i += 3;
}
System.out.println(i);   // 11 — i is in scope here

Going deeper

The nuance, edge cases, and connections that turn a 3 into a 5.

• Execution order of for (init; cond; update): init once → cond → body → update → cond → body → update → … → cond false → exit. The update runs after the body, before the next check.
• Loop variable scope: a variable declared in the init exists only inside the loop. After the loop it's gone — using it is a compile error. To use it after, declare it before the loop and initialize in the init: int i; for (i = 0; …).
• Iteration counts: i = a; i < b → b − a iterations. i = a; i <= b → b − a + 1. With step s: ⌈(b − a) / s⌉ for <. When in doubt, list the values.
• Counting down: for (int i = n; i >= 0; i--) runs n + 1 times (n down to 0). i > 0 runs n times (n down to 1). The exam tests the boundary.
• Multiplicative steps: for (int i = 1; i < 100; i *= 2) → 1, 2, 4, 8, 16, 32, 64: seven iterations. No formula; list them.
• for ↔ while conversion: for (A; B; C) { D } ≡ A; while (B) { D; C }. The only difference is the loop variable's scope. Equivalence questions between the two forms hinge on the placement of C (must be at the end of the body) and on scope.
• Modifying the loop variable inside the body is legal and confusing. If the body does i += 2 and the header does i++, i increases by 3 per iteration.

Mistakes that cost points

• < vs <= off-by-one. One full extra iteration. Count the endpoints.
• Using the loop variable after the loop. Out of scope if declared in the header.
• Converting for to while with the update at the top of the body. It goes at the bottom, or the first iteration sees the wrong value.
• Applying a formula to a non-unit step. List the values instead.

Practice questions

Written in the style of the real exam. Try each one before revealing the answer.

for (int i = 10; i > 0; i -= 4)
{
    System.out.print(i + " ");
}