Implementation lab in ADT Contracts and Complexity

Mission

Count integer halvings until n reaches one.

Learning outcome: Implement a logarithmic halving process

Correctness contract

Invariant: An ADT contract describes observable behavior independently from implementation.

Required technique: Use an iterative integer-halving loop and count only successful reductions while the value is greater than one.

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.

Before you code

1. Restate the input and output contract, then predict the visible example without running code.
2. Implement the core state transition: Use an iterative integer-halving loop and count only successful reductions while the value is greater than one.
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

16

Sample output

4

Why the sample works: Visible walkthrough for the ordinary non-trivial path. Each successful integer division by two contributes one iteration, and counting stops once the value is no greater than one. Input `16` therefore produces `4`.

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.