Implementation lab in Call Stacks and Recursion

Mission

Compute n factorial from a terminating recurrence.

Learning outcome: Implement a base-case recurrence

Correctness contract

Invariant: Every recursive call moves strictly closer to a reachable base case.

Required technique: Use the recurrence factorial(n) = n * factorial(n - 1) with factorial(0) = 1.

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

Input and output

Input: One integer n. Whitespace may be spaces or line breaks.

Output: Print the single exact numeric result with no label. Return it as a String; Main.java prints it without adding other text.

Assumptions:

• n is in the range 0 through 20 so the result fits in signed 64-bit storage.

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 the recurrence factorial(n) = n * factorial(n - 1) with factorial(0) = 1.
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

0

Sample output

1

Why the sample works: Visible walkthrough for the ordinary non-trivial path. The recurrence multiplies n by the factorial of n - 1 until factorial(0) returns one. Input `0` therefore produces `1`.

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.