Bound the frontier. I.e., do beam search.

[slidingtile] / sliding_tile_lib.cc

#include "sliding_tile_lib.h"

#include <cstdlib>
#include <istream>
#include <map>
#include <memory>
#include <ostream>
#include <queue>
#include <set>
#include <sstream>
#include <stdexcept>
#include <vector>

#include <iostream>

int Step::count = 0;
signed char Step::adjacent[BOARD_SIZE][5] = {
  1,   4,   -1,  -1,  -1,
  0,   2,   5,   -1,  -1,
  1,   3,   6,   -1,  -1,
  2,   7,   -1,  -1,  -1,
  0,   5,   8,   -1,  -1,
  1,   4,   6,   9,   -1,
  2,   5,   7,   10,  -1,
  3,   6,   11,  -1,  -1,
  4,   9,   12,  -1,  -1,
  5,   8,   10,  13,  -1,
  6,   9,   11,  14,  -1,
  7,   10,  15,  -1,  -1,
  8,   13,  -1,  -1,  -1,
  9,   12,  14,  -1,  -1,
  10,  13,  15,  -1,  -1,
  11,  14,  -1,  -1,  -1,
};

bool Board::is_valid() const {
  bool seen[BOARD_SIZE];
  for (int i = 0; i < BOARD_SIZE; i++) {
    seen[i] = false;
  }

  for (int i = 0; i < BOARD_SIZE; i++) {
    if (board[i] < 0 || board[i] >= BOARD_SIZE || seen[board[i]]) {
      return false;
    }
    seen[board[i]] = true;
  }

  // Redundant because pigeon-hole-principle, but check anyway
  for (int i = 0; i < BOARD_SIZE; i++) {
    if (!seen[i]) {
      return false;
    }
  }

  return true;
}

bool Board::operator==(const Board& o) const {
  for (int i = 0; i < BOARD_SIZE; i++) {
    if (board[i] != o.board[i]) {
      return false;
    }
  }
  return true;
}

bool Board::operator!=(const Board& o) const {
  return !operator==(o);
}

bool Board::operator<(const Board& o) const {
  for (int i = 0; i < BOARD_SIZE; i++) {
    if (board[i] < o.board[i]) {
      return true;
    } else if (board[i] > o.board[i]) {
      return false;
    }
  }
  return false;
}

std::istream& operator>>(std::istream& is, Board& board) {
  for (int i = 0; i < BOARD_SIZE; i++) {
    if (!is.good()) {
      is.setstate(std::istream::failbit);
      break;
    }
    if (i > 0 && is.get() != ',') {
      is.setstate(std::istream::failbit);
      break;
    }
    int numeric;
    is >> numeric;
    board.board[i] = numeric;
  }
  if (!board.is_valid()) {
    is.setstate(std::istream::failbit);
  }
  return is;
}

std::ostream& operator<<(std::ostream& os, const Board& board) {
  for (int i = 0; i < BOARD_SIZE; i++) {
    if (i > 0) {
      os << " ";
    }
    os << int(board.board[i]);
  }
  return os;
}

signed char Board::hole() const {
  for (int i = 0; i < BOARD_SIZE; i++) {
    if (board[i] == 0) {
      return i;
    }
  }
  throw std::runtime_error("Board with no hole");
}

InvertedBoard Board::invert() const {
  InvertedBoard inv;
  for (int i = 0; i < BOARD_SIZE; i++) {
    inv.pos[board[i]] = i;
  }
  return inv;
}

int Board::distance(const Board& o) const {
  return distance(o.invert());
}

int Board::distance(const InvertedBoard& invo) const {
  int dist = 0;
  for (int i = 0; i < BOARD_SIZE; i++) {
    if (board[i] != 0) {
      dist += std::abs(i % BOARD_DIM - invo.pos[board[i]] % BOARD_DIM) +
              std::abs(i / BOARD_DIM - invo.pos[board[i]] / BOARD_DIM);
    }
  }
  return dist;
}

Step::Step(Board board, std::shared_ptr<Step> prev) : board(board), prev(prev) {
  count++;
}

Step::~Step() {
  count--;
}

std::vector<std::shared_ptr<Step>> Step::successors(std::shared_ptr<Step> shared_this) const {
  std::vector<std::shared_ptr<Step>> suc;
  signed char hole_pos = board.hole();
  for (int i = 0; adjacent[hole_pos][i] >= 0; i++) {
    suc.emplace_back(std::make_shared<Step>(board, shared_this));
    std::swap(suc.back()->board.board[hole_pos], suc.back()->board.board[adjacent[hole_pos][i]]);
  }
  return suc;
}

int Step::length() const {
  if (prev.get() == nullptr) {
    return 0;
  }
  return 1 + prev->length();
}

int Step::cost(const InvertedBoard& invgoal) const {
  return length() + board.distance(invgoal) / 2;
}

std::ostream& operator<<(std::ostream& os, const Step& step) {
  if (step.prev != nullptr) {
    os << *step.prev;
    signed char this_hole = step.board.hole();
    signed char prev_hole = step.prev->board.hole();
    os << int(step.board.board[prev_hole]) << " ";
    switch (this_hole - prev_hole) {
      case -1:         os << "right";    break;
      case  1:         os << "left";     break;
      case -BOARD_DIM: os << "down";     break;
      case BOARD_DIM:  os << "up";       break;
      default:         os << "somehow!"; break;
    }
    os << std::endl;
  }
  return os;
}

std::shared_ptr<Step> find_path(const std::string& start, const std::string& goal, unsigned max_frontier) {
  std::istringstream iss_start{start}, iss_goal{goal};
  Board board_start, board_goal;
  iss_start >> board_start;
  iss_goal >> board_goal;
  if (iss_start.fail() || !iss_start.eof()) {
    throw std::runtime_error("Could not parse the start board: " + start);
  }
  if (iss_goal.fail() || !iss_goal.eof()) {
    throw std::runtime_error("Could not parse the goal board: " + goal);
  }
  return find_path(board_start, board_goal, max_frontier);
}

std::shared_ptr<Step> find_path(const Board& start, const Board& goal, unsigned max_frontier) {
  InvertedBoard invgoal = goal.invert();
  std::multimap<int, std::shared_ptr<Step>> todo;
  std::set<Board> seen;

  seen.insert(start);
  auto start_step = std::make_shared<Step>(start, nullptr);
  todo.emplace(start_step->cost(invgoal), start_step);
  while (!todo.empty()) {
    auto cur = todo.begin()->second;
    todo.erase(todo.begin());
    if (cur->board == goal) {
      return cur;
    }
    std::vector<std::shared_ptr<Step>> successors = cur->successors(cur);
    for (const std::shared_ptr<Step>& s : successors) {
      if (seen.find(s->board) == seen.end()) {
        seen.insert(s->board);
        todo.emplace(s->cost(invgoal), s);
        if (seen.size() % 10000 == 0) {
          std::cerr << "Examined " << seen.size() << " boards.  Tracking "
                    << Step::count << " steps.  " << todo.size()
                    << " waiting.  Considering paths of length "
                    << cur->cost(invgoal) << std::endl;
        }
      }
    }
    while (todo.size() > max_frontier) {
      todo.erase(--todo.end());
    }
  }
  throw std::runtime_error("No path from start to goal");
}