Submission #1188233

#	Time	Username	Problem	Language	Result	Execution time	Memory
1188233		ainunnajib	Robots (APIO13_robots)	C++20	0 / 100	0 ms	320 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 ---
// Stores the final {row, col} after pushing from grid[r][c] in direction start_dir
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 ---
// Simulates all possible moves once and stores the results.
void precompute_all_moves() {
    cout << "Precomputing moves..." << endl; // Debug output
    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}; // Indicate invalid start
                 }
                 continue;
            }

            // Precompute for each of the 4 initial push directions
            for (int start_dir = 0; start_dir < 4; ++start_dir) {
                 int current_dir = start_dir; // This is the initial push direction

                // --- Simulation Logic (copied from original simulate_move) ---
                // 1. Handle initial rotation if starting on a plate when pushed
                if (grid[r][c] == 'A') {
                    current_dir = (current_dir + 3) % 4; // Effective direction after rotation
                } else if (grid[r][c] == 'C') {
                    current_dir = (current_dir + 1) % 4; // Effective direction after rotation
                }

                // 2. Move step by step until blocked
                int nr = r, nc = c; // Current position starts at the initial cell
                while (true) {
                    int next_r = nr + dr[current_dir]; // Calculate next potential cell
                    int next_c = nc + dc[current_dir];

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

                    // Move to the next cell
                    nr = next_r;
                    nc = next_c;

                    // Check for rotation plate at the new cell and update direction for subsequent steps
                    if (grid[nr][nc] == 'A') {
                        current_dir = (current_dir + 3) % 4; // Turn anti-clockwise
                    } else if (grid[nr][nc] == 'C') {
                        current_dir = (current_dir + 1) % 4; // Turn clockwise
                    }
                    // Continue moving in the (potentially new) direction
                }
                // --- End Simulation Logic ---

                // Store the final resting position {nr, nc} for this starting cell and initial push direction
                precomputed_moves[r][c][start_dir] = {nr, nc};
            }
        }
    }
     cout << "Precomputation finished." << endl; // Debug output
}


// --- Optimized simulate_move using precomputation ---
// Returns the final {r, c} after pushing robot at (r, c) in initial direction 'dir'.
// Assumes precompute_all_moves() has been called.
pair<int, int> simulate_move(int r, int c, int dir) {
     // Directly return the precomputed result
     // Ensure r, c, dir are within bounds - should be guaranteed by caller
     return precomputed_moves[r][c][dir];
}

// Function to perform all possible merges iteratively on the current set of robots.
// Modifies the vector in place and sorts it canonically.
// (No changes needed in this function for the precomputation optimization)
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() {
    // 1. Create the initial state vector
    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); // Handle initial merges and sort

    // 2. Initialize BFS queue and visited set
    queue<pair<vector<Robot>, int>> q;
    set<vector<Robot>> visited;

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

    // 3. Start BFS loop
    while (!q.empty()) {
        vector<Robot> current_robots = q.front().first;
        int current_pushes = q.front().second;
        q.pop();

        // 4. Goal Check
        if (current_robots.size() == 1 && current_robots[0].min_l == 1 && current_robots[0].max_l == N) {
            return current_pushes;
        }

        // 5. Generate Next States
        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];

                // *** Use precomputed move result ***
                pair<int, int> final_pos = simulate_move(moving_robot.r, moving_robot.c, dir_idx);

                // Check if the move was valid (precomputation might return {-1,-1} if start was invalid)
                // Although the loop should only consider robots at valid positions. Add check for safety?
                // if (final_pos.first == -1) continue; // Should not happen if robot starts validly

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

                // Perform merges
                perform_merges(next_robots);

                // 6. Check Visited and Enqueue
                if (visited.find(next_robots) == visited.end()) {
                    visited.insert(next_robots);
                    q.push({next_robots, current_pushes + 1});
                }
            }
        }
    }

    // 7. Goal Not Reachable
    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 {
                     cerr << "Warning: Found digit '" << grid[i][j] << "' that is not a valid robot label (1-" << N << ")." << endl;
                     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: 0 / 10
• Subtask 2: 0 / 20
• Subtask 3: 0 / 30
• Subtask 4: 0 / 40