Implementation lab in Queues and Fair Scheduling

Mission

Move the front item to the rear k times.

Learning outcome: Implement queue rotation

Correctness contract

Invariant: Dequeue returns the oldest live item while preserving the relative order of all others.

Required technique: Move front to rear repeatedly, reducing the rotation count modulo queue size.

Complexity target: time O(n+k); space O(n).

Input and output

Input: n, then n integers, then a non-negative rotation count k. Whitespace may be spaces or line breaks.

Output: Print the requested sequence on one line with single spaces and no trailing space. Return it as a String; Main.java prints it without adding other text.

Assumptions:

• n is positive.
• The rotation count is non-negative.

Before you code

1. Restate the input and output contract, then predict the visible example without running code.
2. Implement the core state transition: Move front to rear repeatedly, reducing the rotation count modulo queue size.
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

5 1 2 3 4 5 2

Sample output

3 4 5 1 2

Why the sample works: Visible walkthrough for the ordinary non-trivial path. Each move transfers the current front to the rear while retaining every queue member. Input `5 1 2 3 4 5 2` therefore produces `3 4 5 1 2`.

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.