partridge-cpp/main.cc

//
// Created by Matthew Gretton-Dann on 31/08/2025.
//

#include <cassert>
#include <utility>
#include <string>
#include <string_view>
#include <vector>
#include <iostream>

using Pos = std::pair<int, int>;

auto x(Pos const &p) noexcept -> int { return p.first; }
auto y(Pos const &p) noexcept -> int { return p.second; }

struct Square {
  Square(Pos const &pos, int length) noexcept : pos_(pos), length_(length) {
  }

  Square(Square const &other) noexcept = default;

  Square(Square &&other) noexcept = default;

  Square &operator=(Square const &other) noexcept = default;

  Square &operator=(Square &&other) noexcept = default;

  ~Square() noexcept = default;

  auto x() const noexcept -> int { return ::x(pos_); }
  auto y() const noexcept -> int { return ::y(pos_); }
  auto length() const noexcept -> int { return length_; }

  Pos pos_;
  int length_;
};

struct OverlappingSquares {
  Pos pos_;
};

struct Grid {
  Grid(int length) : grid_(length * length, '.'), length_(length) {
  }

  Grid(Grid const &other) = default;

  Grid(Grid &&other) noexcept = default;

  Grid &operator=(Grid const &other) = default;

  Grid &operator=(Grid &&other) noexcept = default;

  ~Grid() noexcept = default;

  auto length() const noexcept -> int { return length_; }

  auto set(int x, int y, char c) noexcept -> void {
    assert(x < length_);
    assert(y < length_);
    assert(grid_[x + y * length_] != c);
    grid_[x + y * length_] = c;
  }

  auto get(int x, int y) const noexcept -> char {
    assert(x < length_);
    assert(y < length_);
    return grid_[x + y * length_];
  }

  auto add(Square const &sq) -> void {
    switch (sq.length()) {
      case 1: set(sq.x(), sq.y(), '*');
        break;
      case 2: set(sq.x(), sq.y(), '+');
        set(sq.x() + 1, sq.y(), '+');
        set(sq.x(), sq.y() + 1, '+');
        set(sq.x() + 1, sq.y() + 1, '+');
        break;
      default: {
        auto n = sq.length();
        set(sq.x(), sq.y(), '+');
        set(sq.x() + n - 1, sq.y(), '+');
        set(sq.x(), sq.y() + n - 1, '+');
        set(sq.x() + n - 1, sq.y() + n - 1, '+');
        for (int i = 1; i < n - 1; ++i) {
          set(sq.x() + i, sq.y(), '-');
          set(sq.x() + i, sq.y() + n - 1, '-');
          set(sq.x(), sq.y() + i, '|');
          for (int j = 1; j < n - 1; ++j) {
            set(sq.x() + j, sq.y() + i, ' ');
          }
          set(sq.x() + n - 1, sq.y() + i, '|');
        }

        int i = sq.x() + n - 1;
        while (n != 0) {
          set(--i, sq.y() + 1, '0' + (n % 10));
          n /= 10;
        }
      }
    }
  }

  auto clear(Square const &sq) {
    for (auto i = sq.x(); i < sq.x() + sq.length(); ++i) {
      for (auto j = sq.y(); j < sq.y() + sq.length(); ++j) {
        set(i, j, '.');
      }
    }
  }

  auto output() const {
    for (auto i = 0; i < length_; ++i) {
      std::cout << grid_.substr(i * length_, length_) << '\n';
    }
  }

  /** \brief Get length of the largest square that fits at \a pos in the grid.
   */
  auto largest_square(Pos const &pos, int n) const noexcept -> int {
    assert(x(pos) < length_);
    assert(y(pos) < length_);

    /* Because of how we walk through the grid (starting at 0,0 then increasing
     * x followed by y) we can assume that if the position (b, y) is clear
     * (i.e. a '.') then (b, y + i) is clear for all i > 0.
     *
     * This means we only need to look for the first non-clear position along the
     * current row.
     */
    auto b = x(pos);
    // Make sure we don't go looking in the next row.
    auto e = std::min(x(pos) + n, length_);
    while (b < e) {
      if (grid_[b + y(pos) * length_] != '.') { break; }
      ++b;
    }
    return b - x(pos);
  }

  auto next_pos(Pos const &pos) const noexcept -> Pos {
    if (const auto p = x(pos) + 1 + y(pos) * length_; p >= grid_.size()) { return std::make_pair(0, length_); } else {
      const auto next_p = grid_.find('.', p);
      if (next_p == std::string::npos) {
        return std::make_pair(0, length_);
      }
      return std::make_pair(next_p % length_, next_p / length_);
    }
  }

  std::string grid_;
  int length_;
};

auto triangle_num(int n) { return (n * (n + 1)) / 2; }

using Avail = std::vector<int>;

auto find_solution_impl(Grid &grid, int n, Pos const &pos, Avail &avail_sqs) -> bool {
  if (x(pos) == 0 && y(pos) == grid.length()) { return true; }

  /* Walk through the possible squares from the largest that will fit down to 0.
   * We don't want to walk up from 1 to the largest because we can show that a
   * 1x1 piece will never fit along an edge (or one in from the edge) - as
   * there is no other 1x1 piece to go alongside it).  This means we know the
   * first guess is definitely wrong if we start small.
   *
   * If we know a square of side length N will fit then we know a square of side length
   * N - 1 will fit.
   */
  for (auto idx = grid.largest_square(pos, n); idx != 0; --idx) {
    if (avail_sqs[idx] == 0) { continue; }

    auto const sq = Square(pos, idx);
    --avail_sqs[idx];
    grid.add(sq);
    if (find_solution_impl(grid, n, grid.next_pos(pos), avail_sqs)) { return true; }
    ++avail_sqs[idx];
    grid.clear(sq);
  }

  return false;
}

auto find_solution(int n) -> Grid {
  auto length = triangle_num(n);
  Grid grid(length);
  Avail avail_sqs;
  for (auto i = 0; i <= n; ++i) { avail_sqs.push_back(i); }
  find_solution_impl(grid, n, std::make_pair(0, 0), avail_sqs);
  return grid;
}

int main(int argc, char **argv) {
  auto n = (argc == 1) ? 8 : atoi(argv[1]);
  auto grid = find_solution(n);
  std::cout << "Partridge problem " << n << " side length " << grid.length() << '\n';
  grid.output();
  return 0;
}