Rust

use log::debug;
use std::collections::HashSet;

use regex::Regex;

#[derive(PartialEq, Eq, Hash, Clone)]
struct Number(isize, isize);

impl Number {

  fn add(self: &Number, b: &Number) -> Number {
    Number(self.0 + b.0, self.1 + b.1)
  }

  fn mul(self: &Number, b: &Number) -> Number {
    Number(self.0 * b.0 - self.1 * b.1, self.0 * b.1 + self.1 * b.0)
  }

  fn div(self: &Number, b: &Number) -> Number {
    Number(self.0 / b.0, self.1 / b.1)
  }
}

pub fn solve_part_1(input: &str) -> String {
  let re = Regex::new(r"A=\[(\d+),(\d+)\]").unwrap();
  let (_, [x, y]) = re.captures(input).unwrap().extract();
  let a = Number(x.parse().unwrap(), y.parse().unwrap());
  let mut res = Number(0, 0);
  for _ in 0..3 {
    res = res.mul(&res);
    res = res.div(&Number(10, 10));
    res = res.add(&a);
  }
  format!("[{},{}]", res.0, res.1)
}

pub fn solve_part_2(input: &str) -> String {
  let re = Regex::new(r"A=\[([-0-9]+),([-0-9]+)\]").unwrap();
  let (_, [x, y]) = re.captures(input).unwrap().extract();
  let a = Number(x.parse().unwrap(), y.parse().unwrap());
  let mut engraved_points = 0;
  let mut pts: HashSet<_> = HashSet::new();
  for i in 0..=100 {
    for j in 0..=100 {
      let pt = Number(a.0 + 10 * i, a.1 + 10 * j);
      let mut res = Number(0, 0);
      engraved_points += 1;
      pts.insert(pt.clone());
      for _ in 0..100 {
        res = res.mul(&res);
        res = res.div(&Number(100_000, 100_000));
        res = res.add(&pt);
        if res.0.abs() > 1_000_000 || res.1.abs() > 1_000_000 {
          engraved_points -= 1;
          pts.remove(&pt);
          break;
        }
      }
    }
  }
  for i in 0..=100 {
    debug!("{}", (0..=100).map(|j| if pts.contains(&Number(a.0 + 10*i, a.1 + 10*j)) { 'X' } else {'.'}).collect::<String>());
  }
  engraved_points.to_string()
}

pub fn solve_part_3(input: &str) -> String {
  let re = Regex::new(r"A=\[([-0-9]+),([-0-9]+)\]").unwrap();
  let (_, [x, y]) = re.captures(input).unwrap().extract();
  let a = Number(x.parse().unwrap(), y.parse().unwrap());
  let mut engraved_points = 0;
  for i in 0..=1000 {
    for j in 0..=1000 {
      let pt = Number(a.0 + i, a.1 + j);
      let mut res = Number(0, 0);
      engraved_points += 1;
      for _ in 0..100 {
        res = res.mul(&res);
        res = res.div(&Number(100_000, 100_000));
        res = res.add(&pt);
        if res.0.abs() > 1_000_000 || res.1.abs() > 1_000_000 {
          engraved_points -= 1;
          break;
        }
      }
    }
  }
  engraved_points.to_string()
}