Submission #1189251

#	Time	Username	Problem	Language	Result	Execution time	Memory
1189251		Zakir060	Robots (APIO13_robots)	C++20	30 / 100	1596 ms	66940 KiB

robots

#include <iostream>
#include <vector>
#include <string>
#include <queue> // Need priority_queue
#include <map>
#include <set>
#include <algorithm>
#include <tuple>
#include <functional>

using namespace std;

// --- Constants, Globals, Robot struct, State typedef (unchanged) ---
const int MAX_N = 9;
const int MAX_W = 50;
const int MAX_H = 50;
int N, W, H;
vector<string> grid;

struct Robot {
    int min_label; int max_label; int r; int c;
    bool operator<(const Robot& other) const { /* ... unchanged ... */
        if (min_label != other.min_label) return min_label < other.min_label;
        if (max_label != other.max_label) return max_label < other.max_label;
        if (r != other.r) return r < other.r;
        return c < other.c;
    }
     bool operator==(const Robot& other) const { /* ... unchanged ... */
        return min_label == other.min_label && max_label == other.max_label && r == other.r && c == other.c;
     }
};
using State = vector<Robot>;

// --- Helper Functions (is_valid, get_grid_char, simulate_move, merge_robots_at_location, canonicalize - unchanged) ---
bool is_valid(int r, int c) { return r >= 0 && r < H && c >= 0 && c < W; }
char get_grid_char(int r, int c) { if (!is_valid(r, c)) return 'x'; return grid[r][c]; }
int dr[] = {-1, 0, 1, 0}; int dc[] = {0, 1, 0, -1};
pair<int, int> simulate_move(int start_r, int start_c, int push_dir) { /* ... unchanged ... */
    int r = start_r; int c = start_c; int current_dir = push_dir;
    char start_plate = get_grid_char(r, c);
    if (start_plate == 'A') { current_dir = (push_dir + 3) % 4; } else if (start_plate == 'C') { current_dir = (push_dir + 1) % 4; }
    while (true) {
        int next_r = r + dr[current_dir]; int next_c = c + dc[current_dir]; char next_cell = get_grid_char(next_r, next_c);
        if (next_cell == 'x' || !is_valid(next_r, next_c)) { break; } r = next_r; c = next_c;
        if (next_cell == 'A') { current_dir = (current_dir + 3) % 4; } else if (next_cell == 'C') { current_dir = (current_dir + 1) % 4; }
    } return {r, c};
}
State merge_robots_at_location(const State& robots_at_loc) { /* ... unchanged (using the safer map version) ... */
    if (robots_at_loc.size() <= 1) return robots_at_loc;
    State current_robots = robots_at_loc; bool merged;
    do {
        merged = false; if (current_robots.size() <= 1) break;
        State next_robots; vector<bool> used(current_robots.size(), false);
        sort(current_robots.begin(), current_robots.end()); // Ensure sorted for reliable merging check
        for (int i = 0; i < current_robots.size(); ++i) {
            if (used[i]) continue; bool i_merged_this_pass = false;
            for (int j = i + 1; j < current_robots.size(); ++j) {
                if (used[j]) continue;
                if (current_robots[i].max_label + 1 == current_robots[j].min_label) {
                    next_robots.push_back({current_robots[i].min_label, current_robots[j].max_label, current_robots[i].r, current_robots[i].c});
                    used[i] = used[j] = true; merged = i_merged_this_pass = true; break;
                } else if (current_robots[j].max_label + 1 == current_robots[i].min_label) {
                     next_robots.push_back({current_robots[j].min_label, current_robots[i].max_label, current_robots[i].r, current_robots[i].c});
                    used[i] = used[j] = true; merged = i_merged_this_pass = true; break;
                }
            } if (!i_merged_this_pass && !used[i]) { next_robots.push_back(current_robots[i]); }
        } current_robots = next_robots; sort(current_robots.begin(), current_robots.end());
    } while (merged); return current_robots;
}
State canonicalize(State s) { sort(s.begin(), s.end()); return s; }

// --- A* Heuristic ---
int calculate_heuristic(const State& s) {
    // h = number of robot groups - 1
    // Goal is 1 group, so need at least size-1 merges.
    if (s.empty()) return 0; // Or some large value? Should not happen.
    return max(0, (int)s.size() - 1);
}

// --- A* Search ---
int solve() {
    State initial_state;
    for (int r = 0; r < H; ++r) { for (int c = 0; c < W; ++c) { if (isdigit(grid[r][c])) { int label = grid[r][c] - '0'; initial_state.push_back({label, label, r, c}); } } }
    initial_state = canonicalize(initial_state);

    // Priority Queue for A*: Stores { f_cost, g_cost, state }
    // We want the minimum f_cost, so use std::greater for min-heap.
    using PQElement = tuple<int, int, State>;
    priority_queue<PQElement, vector<PQElement>, greater<PQElement>> pq;

    // Map to store the minimum g_cost (pushes) found so far to reach a state
    map<State, int> g_costs;

    // Initial state
    int initial_g = 0;
    int initial_h = calculate_heuristic(initial_state);
    int initial_f = initial_g + initial_h;

    pq.push({initial_f, initial_g, initial_state});
    g_costs[initial_state] = initial_g;

    while (!pq.empty()) {
        auto [current_f, current_g, current_state] = pq.top();
        pq.pop();

        // If we found a shorter path to this state already, ignore this one
        // Check required because priority queue might hold multiple entries for the same state
        // with different costs discovered at different times.
        if (current_g > g_costs[current_state]) {
            continue;
        }

        // Goal check
        if (current_state.size() == 1 && current_state[0].min_label == 1 && current_state[0].max_label == N) {
            return current_g; // Found the optimal solution (due to admissible heuristic)
        }

        // Explore neighbors (moves)
        for (int i = 0; i < current_state.size(); ++i) {
            Robot robot_to_move = current_state[i];
            for (int push_dir = 0; push_dir < 4; ++push_dir) {
                pair<int, int> final_pos = simulate_move(robot_to_move.r, robot_to_move.c, push_dir);
                if (final_pos.first == robot_to_move.r && final_pos.second == robot_to_move.c) { continue; }

                // Create next state (grouping/merging - same logic as before)
                map<pair<int,int>, State> robots_by_location;
                for(int k=0; k < current_state.size(); ++k) { if (k == i) continue; const auto& orob = current_state[k]; robots_by_location[{orob.r, orob.c}].push_back(orob); }
                Robot moved_robot = robot_to_move; moved_robot.r = final_pos.first; moved_robot.c = final_pos.second;
                robots_by_location[{moved_robot.r, moved_robot.c}].push_back(moved_robot);

                State next_state_unmerged;
                for(auto& loc_pair : robots_by_location) { sort(loc_pair.second.begin(), loc_pair.second.end()); State merged = merge_robots_at_location(loc_pair.second); next_state_unmerged.insert(next_state_unmerged.end(), merged.begin(), merged.end()); }

                State next_state = canonicalize(next_state_unmerged);

                // Calculate costs for the next state
                int next_g = current_g + 1;
                int next_h = calculate_heuristic(next_state);
                int next_f = next_g + next_h;

                // Check if this state is new or we found a shorter path to it
                auto it = g_costs.find(next_state);
                if (it == g_costs.end() || next_g < it->second) {
                    g_costs[next_state] = next_g; // Update minimum cost
                    pq.push({next_f, next_g, next_state}); // Add to priority queue
                }
            }
        }
    }

    return -1; // Goal not reachable
}

// --- Main Function (unchanged) ---
int main() {
    ios_base::sync_with_stdio(false); cin.tie(NULL);
    cin >> N >> W >> H; grid.resize(H);
    for (int i = 0; i < H; ++i) { cin >> grid[i]; }
    int result = solve(); cout << result << endl;
    return 0;
}

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