Application lab in Searching Ordered and Unordered Data

Mission

Find the first index whose value is at least target.

Learning outcome: Apply lower-bound search

Correctness contract

Invariant: The active interval contains every remaining position where the target could occur.

Required technique: Use a half-open [lo, hi) binary search for the first value that is at least the target.

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

Input and output

Input: n, then n integers, then one target integer. Whitespace may be spaces or line breaks.

Output: Print the required zero-based index as one integer. Return it as a String; Main.java prints it without adding other text.

Assumptions:

• The array is sorted in nondecreasing order.

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 a half-open [lo, hi) binary search for the first value that is at least the target.
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 3 5 7 9 6

Sample output

3

Why the sample works: Visible walkthrough for the ordinary non-trivial path. The half-open search keeps the first not-smaller position, including n when no stored value qualifies. Input `5 1 3 5 7 9 6` therefore produces `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: Write the meaning of lo and hi above the loop and verify that every update shrinks the interval.

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.