Implementation lab in Heaps and Priority Queues

Mission

Keep only the k smallest values in a max-heap and print them sorted.

Learning outcome: Implement bounded top-k selection

Correctness contract

Invariant: Every parent has priority over its children, and the root is the next item removed.

Required technique: Maintain a max-heap containing at most k retained candidates.

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

Input and output

Input: n, then n integers, then 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:

• k satisfies 1 <= k <= n.

Before you code

1. Restate the input and output contract, then predict the visible example without running code.
2. Implement the core state transition: Maintain a max-heap containing at most k retained candidates.
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

6 9 1 7 3 2 8 3

Sample output

1 2 3

Why the sample works: Visible walkthrough for the ordinary non-trivial path. The bounded max-heap retains only the k smallest candidates seen, after which those candidates are printed in order. Input `6 9 1 7 3 2 8 3` therefore produces `1 2 3`.

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.