Application lab in Call Stacks and Recursion

Mission

Compute the greatest common divisor recursively.

Learning outcome: Apply Euclid recursive reduction

Correctness contract

Invariant: Every recursive call moves strictly closer to a reachable base case.

Required technique: Use Euclid’s recursive remainder reduction until the second value is zero.

Complexity target: time O(log min(a,b)); space O(log min(a,b)).

Input and output

Input: Two integers a and b. 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:

• At least one input is nonzero.

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 Euclid’s recursive remainder reduction until the second value is zero.
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

48 18

Sample output

6

Why the sample works: Visible walkthrough for the ordinary non-trivial path. Euclid repeatedly replaces the pair with (second, first mod second) until the remainder is zero. Input `48 18` therefore produces `6`.

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.