Allow users to override the default HCN search limit by passing one optional
positive integer argument. Bad input now exits with status 2 and prints a clear
message instead of silently using a fixed range.
Keep the existing one-billion default when no argument is provided, so current
usage remains unchanged.
Test Plan:
- cargo clippy
- cargo clippy --benches
- cargo clippy --tests
- cargo test
Refs: N/A
Replace the range scan and trial division with a search over prime exponent
vectors. Highly composite records only need candidates whose exponents are
non-increasing across ascending primes, so the program can compute divisor
counts directly while pruning branches above the search limit.
Remove the sieve module because the new search no longer factors each number.
This makes the current one-billion limit finish in microseconds after startup
instead of scanning hundreds of millions of inputs.
Test Plan:
- cargo clippy
- cargo clippy --benches
- cargo clippy --tests
- cargo test
Refs: N/A
* readability: changing variable names/adding variables for clarity
* initialize primes Vec with reasonable space to reduce allocations
* return type of find_next_prime more idiomatic (Option)
* avoid overflow by using checked_mul
ddidderr
