Submission #1188230

#TimeUsernameProblemLanguageResultExecution timeMemory
1188230ainunnajibRobots (APIO13_robots)C++20
30 / 100
1596 ms72948 KiB
#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. // Sort primarily by labels, then by position for a consistent canonical form. 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); } // Equality operator (needed for some container operations, though < is primary for set) 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); } }; // Global variables for grid dimensions and content 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}; // 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'; } // Function to simulate robot movement from (r, c) in direction 'dir'. // 'dir' is passed by reference as it can change due to rotation plates. // Returns the final position {final_r, final_c}. pair<int, int> simulate_move(int r, int c, int& dir) { // 1. Handle initial rotation if starting on a plate when pushed if (grid[r][c] == 'A') { // Anti-clockwise: Up->Left(3), Right->Up(0), Down->Right(1), Left->Down(2) dir = (dir + 3) % 4; } else if (grid[r][c] == 'C') { // Clockwise: Up->Right(1), Right->Down(2), Down->Left(3), Left->Up(0) dir = (dir + 1) % 4; } // 2. Move step by step until blocked int nr = r, nc = c; while (true) { int next_r = nr + dr[dir]; int next_c = nc + dc[dir]; // Check if the next step is valid (within walls/grid and not obstacle) 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') { dir = (dir + 3) % 4; // Turn anti-clockwise } else if (grid[nr][nc] == 'C') { dir = (dir + 1) % 4; // Turn clockwise } // Continue moving in the (potentially new) direction } // Return the final resting position return {nr, nc}; } // Function to perform all possible merges iteratively on the current set of robots. // Modifies the vector in place. void perform_merges(vector<Robot>& current_robots) { if (current_robots.size() < 2) return; // No merges possible with < 2 robots bool merged_in_pass = true; // Keep merging as long as a merge occurred in the previous pass while (merged_in_pass) { merged_in_pass = false; vector<Robot> next_round_robots; vector<bool> processed(current_robots.size(), false); // Sort robots primarily by position to group them for efficient checking 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; // Skip if already merged in this pass bool merged_robot_i = false; // Try merging robot 'i' with subsequent robots 'j' at the same location for (int j = i + 1; j < current_robots.size(); ++j) { if (processed[j]) continue; // Skip if already merged // Optimization: If robot j is at a different location, subsequent robots will also be (due to sorting) if (current_robots[i].r != current_robots[j].r || current_robots[i].c != current_robots[j].c) { break; } // Check compatibility (labels are consecutive) if (current_robots[i].max_l + 1 == current_robots[j].min_l || current_robots[j].max_l + 1 == current_robots[i].min_l) { // Merge robot i and j 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; // Same location merged_robot.c = current_robots[i].c; next_round_robots.push_back(merged_robot); // Add merged robot to the next round list processed[i] = true; // Mark both i and j as processed for this pass processed[j] = true; merged_in_pass = true; // Indicate that a merge occurred in this pass merged_robot_i = true; break; // Robot i has been merged, move to the next unprocessed robot } } // If robot i wasn't merged with any subsequent robot in this pass, add it directly if (!processed[i]) { next_round_robots.push_back(current_robots[i]); processed[i] = true; // Mark as processed (even though not merged) } } // Update the robot list for the next pass or for finishing current_robots = next_round_robots; if (current_robots.size() < 2) break; // Stop if only 0 or 1 robot left } // Final sort for canonical representation before returning/using in set sort(current_robots.begin(), current_robots.end()); } // Solves the problem using BFS int solve() { // 1. Create the initial state vector vector<Robot> initial_state; for (int i = 0; i < N; ++i) { // Robot labels are 1 to N initial_state.push_back({i + 1, i + 1, initial_pos[i].first, initial_pos[i].second}); } // Perform initial merges if any robots start at the same location (unlikely based on problem statement but safe) perform_merges(initial_state); // Sorts the state canonically // 2. Initialize BFS queue and visited set queue<pair<vector<Robot>, int>> q; // Stores pairs of (robot_state, pushes) set<vector<Robot>> visited; // Stores visited robot_states (canonical form) // Add initial state to queue and visited set q.push({initial_state, 0}); visited.insert(initial_state); // 3. Start BFS loop while (!q.empty()) { // Get current state from front of queue vector<Robot> current_robots = q.front().first; int current_pushes = q.front().second; q.pop(); // 4. Goal Check: Check if only one robot remains and it spans labels 1 to N if (current_robots.size() == 1 && current_robots[0].min_l == 1 && current_robots[0].max_l == N) { return current_pushes; // Found the shortest path } // 5. Generate Next States: Iterate through each robot and each possible push direction for (int i = 0; i < current_robots.size(); ++i) { for (int dir_idx = 0; dir_idx < 4; ++dir_idx) { // 4 directions: 0=Up, 1=Right, 2=Down, 3=Left // Create a copy of the current state to modify vector<Robot> next_robots = current_robots; Robot moving_robot = next_robots[i]; // The robot being pushed int current_dir = dir_idx; // Make a copy of direction for simulation // Simulate the movement of the chosen robot pair<int, int> final_pos = simulate_move(moving_robot.r, moving_robot.c, current_dir); // Update the position of the moved robot in the 'next_robots' state next_robots[i].r = final_pos.first; next_robots[i].c = final_pos.second; // Perform all possible merges in the resulting configuration // This function modifies next_robots in place and sorts it canonically. perform_merges(next_robots); // 6. Check Visited and Enqueue: If the resulting state hasn't been visited if (visited.find(next_robots) == visited.end()) { visited.insert(next_robots); // Mark as visited q.push({next_robots, current_pushes + 1}); // Add to queue } } } } // 7. Goal Not Reachable: If the queue becomes empty and goal was not found return -1; } int main() { // Faster I/O ios_base::sync_with_stdio(false); cin.tie(NULL); // Read input: N, W, H cin >> N >> W >> H; // Resize grid and initial position storage grid.resize(H); initial_pos.resize(N); vector<bool> pos_found(N, false); // To verify all robots are found // Read grid layout and find initial robot positions 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'; // Get the digit value (1-9) int robot_id = robot_label - 1; // Convert to 0-indexed id if (robot_id >= 0 && robot_id < N) { initial_pos[robot_id] = {i, j}; // Store initial position {row, col} pos_found[robot_id] = true; grid[i][j] = '.'; // Clear the robot's starting position on the grid map } else { // Handle potential invalid input (e.g., label > N) if necessary cerr << "Warning: Found digit '" << grid[i][j] << "' that is not a valid robot label (1-" << N << ")." << endl; grid[i][j] = '.'; // Treat as empty space } } } } // Sanity check: Ensure all robots 1 to N were found in the input 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; // Depending on contest rules, might need to exit or handle differently // For robustness, let's assume valid input or return error code. return 1; // Indicate an error } } // Call the solver function and print the result cout << solve() << endl; return 0; // Indicate successful execution }
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