#include <fstream>
#include <iostream>
#include <list>
#include <vector>

class Point {
public:
    Point(int x0, int y0) : x(x0), y(y0) {}
    int x, y;
};

enum GRID_STATUS { GRID_CLEAR, GRID_BLOCKED };

void read_grid(std::istream& istr,
               std::vector<std::vector<GRID_STATUS>>& blocked_grid,
               int& start_x, int& start_y) {
    int x, y;
    int max_x = 0, max_y = 0;
    std::list<Point> blocked_points;
    while ((istr >> x >> y) && !(x == 0 && y == 0)) {
        blocked_points.push_back(Point(x, y));
        if (x > max_x) max_x = x;
        if (y > max_y) max_y = y;
    }
    istr >> start_x >> start_y;
    if (start_x > max_x) max_x = start_x;
    if (start_y > max_y) max_y = start_y;
    std::vector<GRID_STATUS> one_row_of_ys(max_y + 1, GRID_CLEAR);
    std::vector<std::vector<GRID_STATUS>> empty_grid(max_x + 1, one_row_of_ys);
    blocked_grid = empty_grid;
    for (const auto& p : blocked_points) {
        blocked_grid[p.x][p.y] = GRID_BLOCKED;
    }
}

// Modified print_grid to show the path with '$' symbols
void print_grid(const std::vector<std::vector<GRID_STATUS>>& blocked_grid,
                const std::vector<std::vector<bool>>& path_grid) {
    std::cout << "Grid with path marked (X = blocked, $ = path, . = clear):\n";
    for (unsigned int y = 0; y < blocked_grid[0].size(); ++y) {
        for (unsigned int x = 0; x < blocked_grid.size(); ++x) {
            if (path_grid[x][y]) {
                std::cout << " $";
            } else if (blocked_grid[x][y] == GRID_BLOCKED) {
                std::cout << " X";
            } else {
                std::cout << " .";
            }
        }
        std::cout << std::endl;
    }
}

std::list<Point> find_path(const std::vector<std::vector<GRID_STATUS>>& blocked_grid, int x, int y) {
    // no path
    if (x < 0 || y < 0 || blocked_grid[x][y] == GRID_BLOCKED) {
        return std::list<Point>();
    }
    // Base case
    if (x == 0 && y == 0) {
        std::list<Point> path;
        path.push_back(Point(0, 0));
        return path;
    }
    // Try moving left first
    if (x > 0) {
        std::list<Point> path_left = find_path(blocked_grid, x - 1, y);
        if (!path_left.empty()) {
            path_left.push_front(Point(x, y));
            return path_left;
        }
    }
    // If left fails, try moving up
    if (y > 0) {
        std::list<Point> path_up = find_path(blocked_grid, x, y - 1);
        if (!path_up.empty()) {
            path_up.push_front(Point(x, y));
            return path_up;
        }
    }
    // No path found
    return std::list<Point>();
}

int main(int argc, char* argv[]) {
    if (argc != 2) {
        std::cerr << "Usage: " << argv[0] << " grid-file" << std::endl;
        return 1;
    }
    std::ifstream istr(argv[1]);
    if (!istr) {
        std::cerr << "Could not open " << argv[1] << std::endl;
        return 1;
    }

    std::vector<std::vector<GRID_STATUS>> blocked_grid;
    int start_x, start_y;
    read_grid(istr, blocked_grid, start_x, start_y);

    // Find one path
    std::list<Point> path = find_path(blocked_grid, start_x, start_y);
    if (path.empty()) {
        std::cout << "No legal path exists.\n";
    } else {
        std::cout << "Path found:\n";
        for (const auto& p : path) {
            std::cout << "(" << p.x << ", " << p.y << ") ";
        }
        std::cout << "\n";

        // Create path grid for marking
        std::vector<std::vector<bool>> path_grid(blocked_grid.size(),
                                                 std::vector<bool>(blocked_grid[0].size(), false));
        for (const auto& p : path) {
            path_grid[p.x][p.y] = true;
        }
        // Print grid with path
        print_grid(blocked_grid, path_grid);
    }

    return 0;
}