# -*- coding: utf-8 -*-
"""
collatz_verify_Nstar_range.py

For n=1 to N, run Collatz trajectory until 1. Use U_step from collatz_k_core
for accelerated trajectory on odds. Output CSV: n, steps, ok.

Usage:
  python collatz_verify_Nstar_range.py --Nstar N --output CSV_PATH
"""

from __future__ import annotations
import argparse
import csv
from pathlib import Path

from collatz_k_core import U_step


def collatz_steps_to_one(n: int) -> tuple[int, bool]:
    """
    Run Collatz trajectory from n until 1.
    Returns (steps, ok) where ok=True if trajectory reached 1.
    Uses U_step for accelerated trajectory on odd numbers.
    """
    steps = 0
    while n != 1:
        if n <= 0:
            return steps, False
        if n % 2 == 1:
            n, a = U_step(n)
            steps += 1 + a  # one 3n+1, then a divisions by 2
        else:
            n = n // 2
            steps += 1
    return steps, True


def main() -> None:
    parser = argparse.ArgumentParser(
        description="Verify Collatz conjecture for n=1..N, output CSV"
    )
    parser.add_argument("--Nstar", type=int, required=True, help="Upper bound N (inclusive)")
    parser.add_argument("--output", required=True, help="Output CSV path")
    args = parser.parse_args()

    nstar = args.Nstar
    if nstar < 1:
        raise SystemExit("Nstar must be >= 1")

    out_path = Path(args.output)
    out_path.parent.mkdir(parents=True, exist_ok=True)

    with out_path.open("w", newline="", encoding="utf-8") as f:
        w = csv.writer(f)
        w.writerow(["n", "steps", "ok"])
        for n in range(1, nstar + 1):
            steps, ok = collatz_steps_to_one(n)
            w.writerow([n, steps, ok])


if __name__ == "__main__":
    main()