Assignment 3 · Collatz Explorer — Loops + First Functions

Modules 5–7 (L09–L13) · 40 marks · due end of Week 7 Outcomes: CLO-3, CLO-4, CLO-5 (PF-5.x, PF-7.x)

The Collatz rule: for n > 1, next is n/2 if n is even, 3n+1 if odd; stop at 1. You will build a small toolkit of functions and drive it from a menu-free main.

Requirements

Implement and use these functions (signatures fixed):

1. int collatzLength(long long n); — steps from n down to 1 (n ≥ 1; return 0 for n == 1). Precondition comment required.
2. long long collatzMax(long long n); — the largest value seen on the path including n itself.
3. void printPath(long long n); — prints the path comma-separated, ending with 1 and a newline (e.g., 6, 3, 10, 5, 16, 8, 4, 2, 1).

Main:

• Read one long long n (1 ≤ n ≤ 1,000,000; else bad n, exit 1 — validate the read itself too).
• Print steps: L and max: M on separate lines, then the path.

Sample run

Input 6 →

steps: 8
max: 16
6, 3, 10, 5, 16, 8, 4, 2, 1

Constraints

• All three functions take n by value; no globals.
• The path print must not recompute the sequence differently — reuse the rule once (single loop per function is fine; duplication of the rule across functions is the defect to avoid; factor a next(n) helper if that keeps it single-sourced).
• 3n+1 must not overflow: keep the running value in long long and state why in one comment.

Deliverables

collatz.cpp (contract, zero warnings) · test_table.md — n = 1, 2, 6, 27 (steps 111, max 9232 — verify by hand for one of them), boundary 1000000, n = 0 rejected, non-numeric rejected · postmortem.md (10 marks).

Notes

• n = 1 path is just 1 with 0 steps.
• The famous n = 27 case is a good stress test for your max tracker.