Unit 2 Cycle 1 Day 14: For Loop Tracing
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For Loop Tracing
Section 2.9 — For Loops
Key Concept
A for loop combines initialization, condition, and update into a single line: for (init; condition; update). The initialization runs once before the loop starts, the condition is checked before each iteration, and the update runs after each iteration's body completes. A standard counting loop for (int i = 0; i < n; i++) executes exactly n times, with i taking values 0 through n - 1. The variable i is only in scope within the loop.
Consider the following code segment.
What is printed as a result of executing the code segment?
Answer: (B) 30
Trace: i=1: result=1. i=2: result=1+4=5. i=3: result=5+9=14. i=4: result=14+16=30. Sum of squares: 1+4+9+16=30.
Why Not the Others?
(A) 16 is just i*i when i=4, not the accumulated sum.
(C) 10 would be the sum of 1+2+3+4 (sum of i, not i*i).
(D) 20 is not the sum of any standard pattern with these values.
Common Mistake
Trace each iteration carefully. The accumulator adds i * i, not i. Sum of squares (1+4+9+16) differs from sum of integers (1+2+3+4).
AP Exam Tip
For accumulator loops, write a table with columns for i and result. Update after each iteration. This prevents arithmetic errors on multi-step traces.