Application lab in Hash Tables and Collision Reasoning

Mission

Return the first value encountered for the second time.

Learning outcome: Apply a set to detect repetition

Correctness contract

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

Required technique: Insert into a HashSet and return the first value whose insertion reports that it was already present.

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

Input and output

Input: n followed by exactly n integers. Whitespace may be spaces or line breaks.

Output: Print the first repeated value, or NONE when no value repeats. Return it as a String; Main.java prints it without adding other text.

Assumptions:

• n is positive and is followed by exactly n signed integers.

Before you code

1. Restate the input and output contract, then predict the visible example without running code.
2. Implement the core state transition: Insert into a HashSet and return the first value whose insertion reports that it was already present.
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 4 7 9 7 4

Sample output

7

Why the sample works: Visible walkthrough for the ordinary non-trivial path. The first value rejected by set insertion is the earliest value encountered for a second time. Input `5 4 7 9 7 4` therefore produces `7`.

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.