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A rat searching for cheese in a maze, via DFS search.\n#include \n#include \n#include \n#include \n#include \n\nnamespace {\n\n// Specifies the direction we're facing.\nstruct Direction {\n enum direction {\n Up, Down, Left, Right, // Actual directions.\n First = Up, Last = Right // Useful aliases.\n } dir;\n\n // Allows conversion between the enum and the class. Purposefully\n // not an explicit construtor.\n constexpr Direction(direction d) : dir{d} {}\n\n // Returns the successor for the current direction, cycling back to the\n // beginning when reaching the end.\n Direction succ() const {\n if (dir == Last) {\n return Direction{ First };\n } else {\n return Direction{ direction(int(dir) + 1) };\n }\n }\n\n // Returns the predecessor for the current direction, cycling back to the\n // end when reaching the beginning.\n Direction pred() const {\n if (dir == First) {\n return Direction{ Last };\n } else {\n return Direction{ direction(int(dir) - 1) };\n }\n }\n\n // Equality test.\n bool operator==(const Direction rhs) const { return dir == rhs.dir; }\n\n // Human-readable names for the directions.\n constexpr static std::array name = {\n \"Up\", \"Down\", \"Left\", \"Right\"\n };\n\n // Stringifies a Direction, so we can print it easily.\n std::string to_string() const {\n return name[int(dir) % 4];\n }\n};\n\n// Represents a discrete point on a grid.\nstruct Position {\n int x, y;\n\n // Creates a new point that is a step in the specified direction.\n Position step(Direction d) const {\n switch (d.dir) {\n case Direction::Up: return Position{ x, y - 1 };\n case Direction::Down: return Position{ x, y + 1 };\n case Direction::Left: return Position{ x - 1, y };\n case Direction::Right: return Position{ x + 1, y };\n }\n throw std::logic_error(\"Invalid value for direction\");\n }\n\n // Equality test.\n bool operator==(const Position& rhs) const {\n return x == rhs.x && y == rhs.y;\n }\n\n // Stringifies a Position, so we can print it easily.\n std::string to_string() const {\n return std::string(\"(\") + std::to_string(x) + \",\" + std::to_string(y) + \")\";\n }\n};\n\n// Represents a maze as a bitmap of pathways.\n//\n// For now, use a vector of vectors. This could be wrapped in a class,\n// but for now, keep it simple.\nusing Maze = std::vector>;\n\n// Returns true if Position represents an open path in the maze.\n// Returns false if Position is outside the maze\nbool canGo(const Maze& maze, const Position pos) {\n if (pos.y < 0 || pos.x < 0 || std::size_t(pos.y) >= maze.size() ||\n std::size_t(pos.x) >= maze[pos.y].size()) {\n return false;\n }\n return maze[pos.y][pos.x];\n};\n\n// Represents the location and orientation of our \"rat\" in the maze.\n// A solution consists of a progression of MazeSteps. The direction on\n// each step indicates the direction used to exit a grid-point. Thus,\n// the direction on the last step is meaningless.\nstruct MazeStep {\n Position pos;\n Direction dir;\n\n MazeStep(Position p, Direction d) : pos(p), dir(d) {}\n\n std::string to_string() const {\n return pos.to_string() + \":\" + dir.to_string();\n }\n};\n\n// Finds a path through the provided maze, and returns it as a vector\n// of MazeSteps. An empty vector means we found no solution.\nstd::vector findPath(\n const Maze& maze, // What to search.\n const Position start, // Where we're starting.\n const Position goal // What we're looking for.\n) {\n std::vector solution;\n std::vector> visited;\n\n // Sanity check: Ensure our starting and ending positions are in open\n // pathways. If not, return an empty solution.\n if (!canGo(maze, start) || !canGo(maze, goal)) {\n return solution;\n }\n\n // Initialize the visited array to have identical dimensions to the maze.\n // Default-constructed bools are false.\n visited.resize(maze.size());\n for (size_t y = 0; y != maze.size(); ++y) {\n visited[y].resize(maze[y].size());\n }\n\n solution.emplace_back(start, Direction::First);\n visited[start.y][start.x] = true;\n\n // If we started at the goal, just return the single step.\n if (start == goal) {\n return solution;\n }\n\n // Keep iterating until either we reach the goal, or we backtrack to\n // the start.\n while (solution.size()) {\n MazeStep& curr = solution.back();\n\n // Try to move in the current direction. If we can go that way,\n // make it part of our partial solution. Reorient to the \"First\"\n // direction on each step.\n // \n // Note: Test \"canGo\" first as it also includes a bounds check.\n const MazeStep next{ curr.pos.step(curr.dir), Direction::First };\n if (canGo(maze, next.pos) && !visited[next.pos.y][next.pos.x]) {\n visited[next.pos.y][next.pos.x] = true;\n solution.push_back(next);\n\n // If we happened to reach the goal, return what we found.\n if (next.pos == goal) {\n return solution;\n }\n\n // Otherwise continue trying to expand the solution.\n continue;\n }\n \n // If we couldn't move that direction, turn.\n curr.dir = curr.dir.succ();\n\n // If we ran out of turns, backtrack.\n if (curr.dir == Direction::First) {\n solution.pop_back();\n }\n }\n\n // If we reach here, there was no solution. Return the empty solution.\n return solution;\n}\n\n} // namespace\n\nint main() {\n Maze maze = {\n { 1, 0, 1, 1, 0 },\n { 1, 1, 1, 0, 1 },\n { 0, 1, 0, 1, 0 },\n { 1, 1, 1, 1, 1 }\n };\n\n Position start = { 0, 0 };\n Position goal = { 4, 3 };\n\n std::vector solution = findPath(maze, start, goal);\n\n if (solution.empty()) {\n std::cout << \"No path found.\\n\";\n } else {\n std::cout << \"Found this path:\\n\";\n for (const auto& step : solution) {\n std::cout << step.to_string() << '\\n';\n }\n }\n\n return 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