/* #region Head */ // #include #include #include #include #include // assert.h #include // math.h #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using ll = long long; using ull = unsigned long long; using ld = long double; using pll = pair; template using vc = vector; template using vvc = vc>; using vll = vc; using vvll = vvc; using vld = vc; using vvld = vvc; using vs = vc; using vvs = vvc; template using um = unordered_map; template using pq = priority_queue; template using pqa = priority_queue, greater>; template using us = unordered_set; #define TREP(T, i, m, n) for (T i = (m), i##_len = (T)(n); i < i##_len; ++(i)) #define TREPM(T, i, m, n) for (T i = (m), i##_max = (T)(n); i <= i##_max; ++(i)) #define TREPR(T, i, m, n) for (T i = (m), i##_min = (T)(n); i >= i##_min; --(i)) #define TREPD(T, i, m, n, d) for (T i = (m), i##_len = (T)(n); i < i##_len; i += (d)) #define TREPMD(T, i, m, n, d) for (T i = (m), i##_max = (T)(n); i <= i##_max; i += (d)) #define REP(i, m, n) for (ll i = (m), i##_len = (ll)(n); i < i##_len; ++(i)) #define REPM(i, m, n) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; ++(i)) #define REPR(i, m, n) for (ll i = (m), i##_min = (ll)(n); i >= i##_min; --(i)) #define REPD(i, m, n, d) for (ll i = (m), i##_len = (ll)(n); i < i##_len; i += (d)) #define REPMD(i, m, n, d) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; i += (d)) #define REPI(itr, ds) for (auto itr = ds.begin(); itr != ds.end(); itr++) #define REPIR(itr, ds) for (auto itr = ds.rbegin(); itr != ds.rend(); itr++) #define ALL(x) begin(x), end(x) #define SIZE(x) ((ll)(x).size()) #define ISIZE(x) ((int)(x).size()) #define PERM(c) \ sort(ALL(c)); \ for (bool c##p = 1; c##p; c##p = next_permutation(ALL(c))) #define UNIQ(v) v.erase(unique(ALL(v)), v.end()); #define CEIL(a, b) (((a) + (b)-1) / (b)) #define endl '\n' constexpr ll INF = 1'010'000'000'000'000'017LL; constexpr int IINF = 1'000'000'007LL; constexpr ll MOD = 1'000'000'007LL; // 1e9 + 7 // constexpr ll MOD = 998244353; constexpr ld EPS = 1e-12; constexpr ld PI = 3.14159265358979323846; template istream &operator>>(istream &is, vc &vec) { // vector 入力 for (T &x : vec) is >> x; return is; } template ostream &operator<<(ostream &os, const vc &vec) { // vector 出力 (for dump) os << "{"; REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "" : ", "); os << "}"; return os; } template ostream &operator>>(ostream &os, const vc &vec) { // vector 出力 (inline) REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "\n" : " "); return os; } template istream &operator>>(istream &is, array &arr) { // array 入力 REP(i, 0, SIZE(arr)) is >> arr[i]; return is; } template ostream &operator<<(ostream &os, const array &arr) { // array 出力 (for dump) os << "{"; REP(i, 0, SIZE(arr)) os << arr[i] << (i == i_len - 1 ? "" : ", "); os << "}"; return os; } template istream &operator>>(istream &is, pair &pair_var) { // pair 入力 is >> pair_var.first >> pair_var.second; return is; } template ostream &operator<<(ostream &os, const pair &pair_var) { // pair 出力 os << "(" << pair_var.first << ", " << pair_var.second << ")"; return os; } // map, um, set, us 出力 template ostream &out_iter(ostream &os, const T &map_var) { os << "{"; REPI(itr, map_var) { os << *itr; auto itrcp = itr; if (++itrcp != map_var.end()) os << ", "; } return os << "}"; } template ostream &operator<<(ostream &os, const map &map_var) { return out_iter(os, map_var); } template ostream &operator<<(ostream &os, const um &map_var) { os << "{"; REPI(itr, map_var) { auto [key, value] = *itr; os << "(" << key << ", " << value << ")"; auto itrcp = itr; if (++itrcp != map_var.end()) os << ", "; } os << "}"; return os; } template ostream &operator<<(ostream &os, const set &set_var) { return out_iter(os, set_var); } template ostream &operator<<(ostream &os, const us &set_var) { return out_iter(os, set_var); } template ostream &operator<<(ostream &os, const pq &pq_var) { pq pq_cp(pq_var); os << "{"; if (!pq_cp.empty()) { os << pq_cp.top(), pq_cp.pop(); while (!pq_cp.empty()) os << ", " << pq_cp.top(), pq_cp.pop(); } return os << "}"; } // tuple 出力 template ostream &operator<<(ostream &os, tuple &a) { if constexpr (N < std::tuple_size_v>) { os << get(a); if constexpr (N + 1 < std::tuple_size_v>) { os << ' '; } else if constexpr (end_line) { os << '\n'; } return operator<<(os, a); } return os; } template void print_tuple(tuple &a) { operator<<<0, true>(cout, a); } void pprint() { cout << endl; } template void pprint(Head &&head, Tail &&...tail) { cout << head; if (sizeof...(Tail) > 0) cout << ' '; pprint(move(tail)...); } // dump #define DUMPOUT cerr void dump_func() { DUMPOUT << endl; } template void dump_func(Head &&head, Tail &&...tail) { DUMPOUT << head; if (sizeof...(Tail) > 0) DUMPOUT << ", "; dump_func(move(tail)...); } // chmax (更新「される」かもしれない値が前) template > bool chmax(T &xmax, const U &x, Comp comp = {}) { if (comp(xmax, x)) { xmax = x; return true; } return false; } // chmin (更新「される」かもしれない値が前) template > bool chmin(T &xmin, const U &x, Comp comp = {}) { if (comp(x, xmin)) { xmin = x; return true; } return false; } // ローカル用 #ifndef ONLINE_JUDGE #define DEBUG_ #endif #ifndef MYLOCAL #undef DEBUG_ #endif #ifdef DEBUG_ #define DEB #define dump(...) \ DUMPOUT << " " << string(#__VA_ARGS__) << ": " \ << "[" << to_string(__LINE__) << ":" << __FUNCTION__ << "]" << endl \ << " ", \ dump_func(__VA_ARGS__) #else #define DEB if (false) #define dump(...) #endif #define VAR(type, ...) \ type __VA_ARGS__; \ assert((cin >> __VA_ARGS__)); template istream &operator,(istream &is, T &rhs) { return is >> rhs; } template ostream &operator,(ostream &os, const T &rhs) { return os << ' ' << rhs; } struct AtCoderInitialize { static constexpr int IOS_PREC = 15; static constexpr bool AUTOFLUSH = true; AtCoderInitialize() { ios_base::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr); cout << fixed << setprecision(IOS_PREC); if (AUTOFLUSH) cout << unitbuf; } } ATCODER_INITIALIZE; void Yn(bool p) { cout << (p ? "Yes" : "No") << endl; } void YN(bool p) { cout << (p ? "YES" : "NO") << endl; } template constexpr void operator--(vc &v, int) noexcept { for (int i = 0; i < ISIZE(v); ++i) v[i]--; } template constexpr void operator++(vc &v, int) noexcept { for (int i = 0; i < ISIZE(v); ++i) v[i]++; } /* #endregion */ // #include // using namespace atcoder; using coord_t = short; constexpr coord_t H = 20; constexpr coord_t W = 20; /* #region dijkstra_f_restore */ constexpr double dinf = double(INF); using Weight = double; Weight inf = dinf; /** * @param N ノード数 * @param delta 隣接行列を生成する関数.delta(Node v, fn(Node t)). * fn は現在の頂点 current と隣接する頂点を探索する関数. * @param index 頂点→頂点インデックス,のマップ関数.(index(Node v) -> int) * @return 距離テーブル */ template pair> dijkstra_f_restore(int N, const vc &starts, const Node &terminal, Delta delta, Index index, Weight init = 0) { struct state { Weight cost; Node dst; state(Weight cost, Node dst) : cost(cost), dst(dst) {} bool operator<(const state &o) const { return cost > o.cost; } // bool operator>(const state &o) const { return cost > o.cost; } }; vc bs(N, -1); // 経路復元用 vc dist(N, inf); // 距離テーブル priority_queue que; // 「訪問予定」頂点リスト for (const Node &start : starts) { int idx = index(start); assert(0 <= idx && idx < N); dist[idx] = init; // 初期条件 (頂点 start を初期頂点とする) que.emplace(init, start); } while (!que.empty()) { state cur = que.top(); // tie(d, v) = que.top(); que.pop(); Node current = cur.dst; Weight cur_dist = cur.cost; int ci = index(current); // 隣接ノードに関するループは外に出す delta(current, [&](Node dst, Weight weight) -> void { Weight nxt_dist = cur_dist + weight; int idx = index(dst); assert(0 <= idx && idx < N); if (chmin(dist[idx], nxt_dist)) { que.emplace(nxt_dist, dst); bs[idx] = ci; } }); } // dump(dist); // 経路復元 vc res; int dst = index(terminal); int dst_bak = dst; // if (bs[dst] < 0) return res; while (~dst) res.emplace_back(dst), dst = bs[dst]; reverse(ALL(res)); // return res; return {dist[dst_bak], res}; } /* #endregion */ // Problem void solve() { VAR(int, h, w, p); // assert(h == H); // assert(w == W); assert(6 <= p && p <= 15); double P = double(p) / 100; int wall_place_sum = (h * (w - 1)) + ((h - 1) * w); int wall_cnt = 11; // これくらい壁がある // int wall_cnt = 150; // これくらい壁がある int ok_cnt = 0; // 壁がないことが確定した箇所の個数 vc> ok_horizontal(h, vc(w - 1, 0)); // 横移動可能が確定したかどうか vc> ok_vertical(h - 1, vc(w, 0)); // 縦移動可能が確定したかどうか vc> ng_cnt_horizontal(h, vc(w - 1, 0)); // 横移動できなかった回数(一度でも移動できたらクリア) vc> ng_cnt_vertical(h - 1, vc(w, 0)); // 縦移動できなかった回数(一度でも移動できたらクリア) using Node = pair; // row, col const static vc dx{1, 0, -1, 0}; Node start = {0, 0}; Node goal = {h - 1, w - 1}; // 隣接行列生成関数 auto delta = [&](const Node ¤t, function transit) -> void { auto [r, c] = current; // 隣接ノードに関するループ for (short q = 0; q < 4; q++) { coord_t nr = r + dx[q]; coord_t nc = c + dx[q ^ 1]; if (nr < 0 || nr >= h || nc < 0 || nc >= w) continue; double cost = 0; if (nr == r) { // 横移動 if (ok_horizontal[r][min(c, nc)] == 1) { // コスト 0 確定 } else { if (ng_cnt_horizontal[r][min(c, nc)] == 0) { cost += double(wall_cnt) / (wall_place_sum - ok_cnt) / 100; } else { cost += 1.0 - powl(P, ng_cnt_horizontal[r][min(c, nc)]); } } } else { // 縦移動 if (ok_vertical[min(r, nr)][c] == 1) { // コスト 0 確定 } else { if (ng_cnt_vertical[min(r, nr)][c] == 0) { cost += double(wall_cnt) / (wall_place_sum - ok_cnt) / 100; } else { cost += 1.0 - powl(P, ng_cnt_vertical[min(r, nr)][c]); } } } // if (r == 1 && c == 4 && nr == 2) { // dump(cost); // } transit(Node(nr, nc), cost); // コスト 1 で遷移 } }; // インデックス生成関数 auto index = [&](const Node &v) -> int { return v.first * w + v.second; }; TREP(int, trial, 0, 1001) { // dump(double(wall_cnt) / (wall_place_sum - ok_cnt)); // dump(ng_cnt_vertical); auto [dist, res] = dijkstra_f_restore(h * w, vc{start}, goal, delta, index, double(0)); // dump(res); const int len = ISIZE(res); string ans; TREP(int, i, 1, len) { int r = res[i] / w; int c = res[i] % w; int pr = res[i - 1] / w; int pc = res[i - 1] % w; if (r == pr) { if (c > pc) ans.push_back('R'); else ans.push_back('L'); } else { if (r > pr) ans.push_back('D'); else ans.push_back('U'); } } pprint(ans); // break; VAR(int, ok_len); if (ok_len == -1) break; // ok_cnt += ok_len; TREPM(int, i, 1, ok_len) { int r = res[i] / w; int c = res[i] % w; int pr = res[i - 1] / w; int pc = res[i - 1] % w; if (r == pr) { if (ok_horizontal[r][min(c, pc)] == 0) { ok_horizontal[r][min(c, pc)] = 1; ok_cnt++; } } else { if (ok_vertical[min(r, pr)][c] == 0) { ok_vertical[min(r, pr)][c] = 1; ok_cnt++; } } } { int r = res[ok_len + 1] / w; int c = res[ok_len + 1] % w; int pr = res[ok_len] / w; int pc = res[ok_len] % w; if (r == pr) { ng_cnt_horizontal[r][min(c, pc)]++; } else { ng_cnt_vertical[min(r, pr)][c]++; } } } } // entry point int main() { solve(); return 0; }