Submission #1188234

#	Time	Username	Problem	Language	Result	Execution time	Memory
1188234		ainunnajib	Robots (APIO13_robots)	C++20	30 / 100	1599 ms	79488 KiB

robots

#include <iostream>
#include <vector>
#include <string>
#include <queue>
#include <set>
#include <map>
#include <tuple>   // For std::tie used in comparison
#include <vector>
#include <algorithm> // For std::sort
#include <cctype>    // For std::isdigit

using namespace std;

// Struct to represent a robot (original or composite)
struct Robot {
    int min_l, max_l; // Min and max labels of merged robots
    int r, c;         // Row and column position

    // Comparison operator for sorting and using in std::set/map.
    bool operator<(const Robot& other) const {
        return tie(min_l, max_l, r, c) < tie(other.min_l, other.max_l, other.r, other.c);
    }
    bool operator==(const Robot& other) const {
        return tie(min_l, max_l, r, c) == tie(other.min_l, other.max_l, other.r, other.c);
    }
};

// --- Constants and Global Variables ---
const int MAX_H = 501; // Max dimensions + 1 for safety
const int MAX_W = 501;

int N; // Number of initial robots
int W; // Grid width
int H; // Grid height
vector<string> grid; // Grid layout ('x', '.', 'A', 'C')
vector<pair<int, int>> initial_pos; // Store initial positions for robots 1 to N

// Directions: 0:Up (-1,0), 1:Right (0,1), 2:Down (1,0), 3:Left (0,-1)
int dr[] = {-1, 0, 1, 0};
int dc[] = {0, 1, 0, -1};

// --- Precomputation Data Structure ---
pair<int, int> precomputed_moves[MAX_H][MAX_W][4];

// Function to check if a cell is valid (within bounds and not an obstacle)
bool isValid(int r, int c) {
    return r >= 0 && r < H && c >= 0 && c < W && grid[r][c] != 'x';
}

// --- Precomputation Function (Revised Simulation Logic) ---
void precompute_all_moves() {
    for (int r = 0; r < H; ++r) {
        for (int c = 0; c < W; ++c) {
            // Cannot start move from an obstacle
            if (grid[r][c] == 'x') {
                 for (int start_dir = 0; start_dir < 4; ++start_dir) precomputed_moves[r][c][start_dir] = {-1, -1};
                 continue;
            }

            // Precompute for each of the 4 initial push directions
            for (int start_dir = 0; start_dir < 4; ++start_dir) {
                int nr = r, nc = c; // Current position, initialized to start
                int current_dir = start_dir; // Effective direction of travel, initialized

                // --- Determine Initial Move Direction (Revised Rule 2) ---
                bool starting_on_rotator = (grid[r][c] == 'A' || grid[r][c] == 'C');
                int first_step_dir = start_dir; // Default to original push direction

                if (starting_on_rotator) {
                    int rotated_dir = (grid[r][c] == 'A') ? (start_dir + 3) % 4 : (start_dir + 1) % 4;
                    int rotated_next_r = r + dr[rotated_dir];
                    int rotated_next_c = c + dc[rotated_dir];
                    // Prefer rotated direction if the first step is valid
                    if (isValid(rotated_next_r, rotated_next_c)) {
                        first_step_dir = rotated_dir;
                    }
                    // else: keep original push direction (first_step_dir = start_dir)
                    //       Validity of original direction step checked below.
                }

                // Check if the first step (in the determined first_step_dir) is valid
                int first_step_r = r + dr[first_step_dir];
                int first_step_c = c + dc[first_step_dir];

                if (!isValid(first_step_r, first_step_c)) {
                    // Cannot even take the first step, robot stays at (r, c)
                    precomputed_moves[r][c][start_dir] = {r, c};
                    continue; // Next start_dir
                }

                // --- Take the First Step ---
                nr = first_step_r;
                nc = first_step_c;
                current_dir = first_step_dir; // Update effective direction

                // --- Continue Simulation Loop (Rule 1 applies from now on) ---
                while (true) {
                    // Check for rotation plate at the *current* cell (nr, nc) - Rule 1
                    // This updates the direction for the *next* move.
                    if (grid[nr][nc] == 'A') {
                        current_dir = (current_dir + 3) % 4;
                    } else if (grid[nr][nc] == 'C') {
                        current_dir = (current_dir + 1) % 4;
                    }

                    // Calculate next potential cell based on current_dir
                    int next_r = nr + dr[current_dir];
                    int next_c = nc + dc[current_dir];

                    // Check if the next step is valid
                    if (!isValid(next_r, next_c)) {
                        break; // Blocked, stop at current position (nr, nc)
                    }

                    // Move to the next cell
                    nr = next_r;
                    nc = next_c;
                    // Loop continues, will check grid[nr][nc] for rotation next iteration
                }
                // Store the final resting position
                precomputed_moves[r][c][start_dir] = {nr, nc};
            }
        }
    }
}


// --- Optimized simulate_move using precomputation ---
pair<int, int> simulate_move(int r, int c, int dir) {
     return precomputed_moves[r][c][dir];
}

// Function to perform all possible merges iteratively on the current set of robots.
void perform_merges(vector<Robot>& current_robots) {
     if (current_robots.size() < 2) return;
     bool merged_in_pass = true;
     while (merged_in_pass) {
         merged_in_pass = false;
         vector<Robot> next_round_robots;
         vector<bool> processed(current_robots.size(), false);
         sort(current_robots.begin(), current_robots.end(), [](const Robot& a, const Robot& b){
              return tie(a.r, a.c, a.min_l, a.max_l) < tie(b.r, b.c, b.min_l, b.max_l);
              });
         for (int i = 0; i < current_robots.size(); ++i) {
             if (processed[i]) continue;
             bool merged_robot_i = false;
             for (int j = i + 1; j < current_robots.size(); ++j) {
                  if (processed[j]) continue;
                  if (current_robots[i].r != current_robots[j].r || current_robots[i].c != current_robots[j].c) break;
                  if (current_robots[i].max_l + 1 == current_robots[j].min_l || current_robots[j].max_l + 1 == current_robots[i].min_l) {
                      Robot merged_robot;
                      merged_robot.min_l = min(current_robots[i].min_l, current_robots[j].min_l);
                      merged_robot.max_l = max(current_robots[i].max_l, current_robots[j].max_l);
                      merged_robot.r = current_robots[i].r;
                      merged_robot.c = current_robots[i].c;
                      next_round_robots.push_back(merged_robot);
                      processed[i] = true; processed[j] = true;
                      merged_in_pass = true; merged_robot_i = true;
                      break;
                  }
             }
             if (!processed[i]) {
                 next_round_robots.push_back(current_robots[i]);
                 processed[i] = true;
             }
         }
         current_robots = next_round_robots;
          if (current_robots.size() < 2) break;
     }
     sort(current_robots.begin(), current_robots.end());
 }


// Solves the problem using BFS with precomputed moves
int solve() {
    vector<Robot> initial_state;
    for (int i = 0; i < N; ++i) {
        initial_state.push_back({i + 1, i + 1, initial_pos[i].first, initial_pos[i].second});
    }
    perform_merges(initial_state);

    queue<pair<vector<Robot>, int>> q;
    set<vector<Robot>> visited;

    q.push({initial_state, 0});
    visited.insert(initial_state);

    while (!q.empty()) {
        vector<Robot> current_robots = q.front().first;
        int current_pushes = q.front().second;
        q.pop();

        if (current_robots.size() == 1 && current_robots[0].min_l == 1 && current_robots[0].max_l == N) {
            return current_pushes;
        }

        for (int i = 0; i < current_robots.size(); ++i) {
            for (int dir_idx = 0; dir_idx < 4; ++dir_idx) {
                vector<Robot> next_robots = current_robots;
                Robot moving_robot = next_robots[i];

                pair<int, int> final_pos = simulate_move(moving_robot.r, moving_robot.c, dir_idx);

                // Check if the starting position itself was invalid (e.g., 'x')
                // simulate_move would return {-1, -1} based on precomputation
                if (final_pos.first == -1) continue;

                next_robots[i].r = final_pos.first;
                next_robots[i].c = final_pos.second;

                perform_merges(next_robots);

                if (visited.find(next_robots) == visited.end()) {
                    visited.insert(next_robots);
                    q.push({next_robots, current_pushes + 1});
                }
            }
        }
    }
    return -1;
}

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);

    cin >> N >> W >> H;

    grid.resize(H);
    initial_pos.resize(N);
    vector<bool> pos_found(N, false);

    for (int i = 0; i < H; ++i) {
        cin >> grid[i];
        for (int j = 0; j < W; ++j) {
            if (isdigit(grid[i][j])) {
                int robot_label = grid[i][j] - '0';
                int robot_id = robot_label - 1;
                if (robot_id >= 0 && robot_id < N) {
                   initial_pos[robot_id] = {i, j};
                   pos_found[robot_id] = true;
                   grid[i][j] = '.';
                } else {
                     // Silently ignore invalid digits, treat as '.'
                     grid[i][j] = '.';
                }
            }
        }
    }

    bool all_found = true;
    for(int i=0; i<N; ++i) {
        if (!pos_found[i]) {
            all_found = false;
            cerr << "Error: Robot " << (i+1) << " not found on the initial grid." << endl;
             return 1;
        }
    }

    // Call precomputation function before solving
    precompute_all_moves();

    // Call the solver function and print the result
    cout << solve() << endl;

    return 0;
}

• Subtask 1: 10 / 10
• Subtask 2: 20 / 20
• Subtask 3: 0 / 30
• Subtask 4: 0 / 40