Challenge lab in Arrays and Dynamic Lists

Mission

Count capacity doublings from one until n items fit.

Learning outcome: Analyze geometric capacity growth

Correctness contract

Invariant: Elements occupy indexes 0 through size - 1, and size never exceeds capacity.

Required technique: Simulate geometric capacity growth from one until the requested logical size fits.

Complexity target: time O(log n); space O(1).

Input and output

Input: One integer n. Whitespace may be spaces or line breaks.

Output: Print the single exact numeric result with no label. Return it as a String; Main.java prints it without adding other text.

Assumptions:

• n is at least 1 and the next power of two fits in a signed 32-bit integer.

Before you code

1. Restate the input and output contract, then predict the visible example without running code.
2. Implement the core state transition: Simulate geometric capacity growth from one until the requested logical size fits.
3. Trace the smallest boundary case, verify exact formatting, and justify the authored time and auxiliary-space bounds.

Implement Practice.solve(Scanner sc). Keep every provided filename and public class name unchanged.

Sample input

1

Sample output

0

Why the sample works: Visible walkthrough for the ordinary non-trivial path. Capacity starts at one and doubles only while it is smaller than the requested logical size. Input `1` therefore produces `0`.

Progressive hints

Try the trace and first milestone before opening a hint. Open them in order.

Hint 1 — Contract: identify what each parsed variable represents and write the invariant beside the loop or recursive method.

Hint 2 — Next step: Trace the smallest non-trivial input and write the structure state after the operation before coding the loop.

Hint 3 — Verification: compare the structure state before and after one operation, then test the smallest valid input and a duplicate or unreachable case when allowed.