Trace lab in Hash Tables and Collision Reasoning

Mission

Print floor-mod hash indexes for integer keys.

Learning outcome: Trace deterministic bucket placement

Correctness contract

Invariant: Equal keys produce equal hashes, and collision handling preserves every distinct key.

Required technique: Use Math.floorMod(key, bucketCount) so negative keys still map to valid buckets.

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

Input and output

Input: A positive bucket count, then key count n, then n integer keys. 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:

• The hash-table size is greater than zero.

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 Math.floorMod(key, bucketCount) so negative keys still map to valid buckets.
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 3 12 7 5

Sample output

2 2 0

Why the sample works: Visible walkthrough for the ordinary non-trivial path. floorMod maps each signed key into the valid range from zero through bucketCount - 1. Input `5 3 12 7 5` therefore produces `2 2 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.