Application lab in Sorting and Divide-and-Conquer

Mission

Sort with recursive splitting and an explicit merge buffer.

Learning outcome: Apply recursive merge sort

Correctness contract

Invariant: A selection prefix is final; a merge emits the smallest remaining head.

Required technique: Recursively sort half-open ranges and merge them through one reusable auxiliary buffer.

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

Input and output

Input: n followed by exactly n integers. 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 and is followed by exactly n signed 32-bit 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: Recursively sort half-open ranges and merge them through one reusable auxiliary buffer.
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 8 2 7 3

Sample output

1 2 3 7 8 9

Why the sample works: Visible walkthrough for the ordinary non-trivial path. Recursive half-open ranges are sorted independently and then combined with a stable merge. Input `6 9 1 8 2 7 3` therefore produces `1 2 3 7 8 9`.

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.