aocpp/2019/10.cpp

#include <algorithm>
#include <iostream>
#include <map>
#include <numeric>
#include <set>
#include <sstream>
#include <utility>

#include <doctest.h>

#include <aocpp/Startup.hpp>
#include <aocpp/Coord.hpp>
#include <aocpp/Grid.hpp>

using namespace aocpp;

namespace {

template<typename T>
struct Rational {
  T numerator, denominator;

  Rational() : numerator{0}, denominator{1} {}
  Rational(T x) : numerator{x}, denominator{1} {}
  Rational(T n, T d) {
    if (d == 0) { numerator = 1; denominator = 0; return; }
    if (d < 0) { d = -d; n = -n; }
    T m = std::gcd(n,d);
    numerator = n / m;
    denominator = d / m;
  }
  auto constexpr operator<=>(Rational const& rhs) const -> std::strong_ordering {
    return numerator * rhs.denominator <=> rhs.numerator * denominator;
  }
};

template <typename T>
auto operator<<(std::ostream & out, Rational<T> const& r) -> std::ostream & {
  return out << r.numerator << "/" << r.denominator;
}

/// Map a vector to a rational number such that the numbers are
/// ordered starting with up and proceeding clockwise.
/// Each quadrant is mapped to a whole number. Slopes in that
/// quadrant are mapped to a fraction between 0 and 1.
auto angle(Coord c) -> Rational<std::int64_t> {
  auto mk = [](std::int64_t q, std::int64_t a, std::int64_t b) {
    return Rational{q*(a+b)-b, a+b};
  };
  return
    c.x == 0 && c.y == 0 ? -1 :
    c.x >= 0 && c.y <  0 ? mk(1, c.x, -c.y) :
    c.x >  0 && c.y >= 0 ? mk(2, c.y,  c.x) :
    c.x <= 0 && c.y >  0 ? mk(3,-c.x,  c.y) :
                           mk(4, c.y,  c.x);
}

auto ClearView(Grid const& grid, Coord src, Coord dst) -> bool {
  auto vec = dst - src;
  auto steps = std::gcd(vec.x, vec.y);
  Coord delta {vec.x / steps, vec.y / steps};
  for (auto cursor = src+delta; cursor != dst; cursor+=delta) {
    if (grid[cursor] == '#') {
      return false;
    }
  }
  return true;
}

auto Part1(Grid const& grid) {
  std::size_t best = 0;
  Coord base {};
  grid.each([&](Coord src, char s) {
    if ('#' == s) {
      std::size_t visible = 0;
      grid.each([&](Coord dst, char d){
        if ('#' == d && src != dst) {
          if (ClearView(grid, src, dst)) {
            visible++;
          }
        }
      });
      
      if (visible > best) {
        best = visible;
        base = src;
      }
    }
  });
  return std::make_pair(best, base);
}

auto Part2(Grid const& grid, Coord base, std::size_t n) {
  std::map<Rational<std::int64_t>, std::vector<Coord>> targets;

  // arrange all the other asteroids by their angle relative to the base
  grid.each([&](Coord c, char v){
    if (c != base && v == '#') {
      targets[angle(c-base)].push_back(c);
    }
  });

  // Sort to vectors per angle such that the nearest asteroids are at
  // the end of the list
  for (auto & [_, vec] : targets) {
    std::sort(vec.begin(), vec.end(), [](auto const& x, auto const& y) {
      return Norm1(x) > Norm1(y);
    });
  }

  // Remove 199 asteroids from the asteroid list
  auto cursor = targets.begin();
  for (; n > 1; n--) {
    if (targets.empty()) { throw std::runtime_error{"no solution to part 2"}; }

    cursor->second.pop_back();
    if (cursor->second.empty()) {
      cursor = targets.erase(cursor);
    } else {
      cursor++;
    }

    if (cursor == targets.end()) {
      cursor = targets.begin();
    }
  }

  // Report the location of the 200th asteroid
  auto const& asteroid = cursor->second.back();
  return 100 * asteroid.x + asteroid.y;
}

} // namespace

TEST_SUITE("documented examples") {

  char const* bigexample =
    ".#..##.###...#######\n"
    "##.############..##.\n"
    ".#.######.########.#\n"
    ".###.#######.####.#.\n"
    "#####.##.#.##.###.##\n"
    "..#####..#.#########\n"
    "####################\n"
    "#.####....###.#.#.##\n"
    "##.#################\n"
    "#####.##.###..####..\n"
    "..######..##.#######\n"
    "####.##.####...##..#\n"
    ".#####..#.######.###\n"
    "##...#.##########...\n"
    "#.##########.#######\n"
    ".####.#.###.###.#.##\n"
    "....##.##.###..#####\n"
    ".#.#.###########.###\n"
    "#.#.#.#####.####.###\n"
    "###.##.####.##.#..##\n";

  TEST_CASE("part 1") {
    auto test = [](Coord base, std::size_t count, std::string text) {
      std::istringstream in {std::move(text)};
      auto [count_, base_] = Part1(Grid::Parse(in));
      REQUIRE(count_ == count);
      REQUIRE(base_ == base);
    };
    test({3,4}, 8,
      ".#..#\n"
      ".....\n"
      "#####\n"
      "....#\n"
      "...##\n");
    test({1,2}, 35,
      "#.#...#.#.\n"
      ".###....#.\n"
      ".#....#...\n"
      "##.#.#.#.#\n"
      "....#.#.#.\n"
      ".##..###.#\n"
      "..#...##..\n"
      "..##....##\n"
      "......#...\n"
      ".####.###.\n");
    test({6,3}, 41,
      ".#..#..###\n"
      "####.###.#\n"
      "....###.#.\n"
      "..###.##.#\n"
      "##.##.#.#.\n"
      "....###..#\n"
      "..#.#..#.#\n"
      "#..#.#.###\n"
      ".##...##.#\n"
      ".....#.#..\n");
    test({11,13}, 210, bigexample);
  }
  TEST_CASE("part 2") {
    auto test = [](std::size_t answer, Coord base, std::size_t nth, std::string text) {
      std::istringstream in {std::move(text)};
      REQUIRE(answer == Part2(Grid::Parse(in), base, nth));
    };
    test(1403, {8,3}, 36,
      ".#....#####...#..\n"
      "##...##.#####..##\n"
      "##...#...#.#####.\n"
      "..#.....X...###..\n"
      "..#.#.....#....##\n");
    test(802, {11,13}, 200, bigexample);
  }
}

auto Main(std::istream & in) -> void
{
  auto const grid {Grid::Parse(in)};
  auto const [part1, base] = Part1(grid);
  std::cout << "Part 1: " << part1 << std::endl;
  std::cout << "Part 2: " << Part2(grid, base, 200) << std::endl;
}