結果
| 問題 | No.2983 Christmas Color Grid (Advent Calender ver.) |
| ユーザー |
 noya2
|
| 提出日時 | 2024-12-08 20:35:44 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
MLE
|
| 実行時間 | - |
| コード長 | 22,085 bytes |
| コンパイル時間 | 4,214 ms |
| コンパイル使用メモリ | 293,600 KB |
| 実行使用メモリ | 170,820 KB |
| 最終ジャッジ日時 | 2024-12-08 20:36:03 |
| 合計ジャッジ時間 | 16,488 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge4 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 MLE * 1 |
| other | AC * 63 MLE * 1 |
ソースコード
#line 2 "/Users/noya2/Desktop/Noya2_library/template/template.hpp"using namespace std;#include<bits/stdc++.h>#line 1 "/Users/noya2/Desktop/Noya2_library/template/inout_old.hpp"namespace noya2 {template <typename T, typename U>ostream &operator<<(ostream &os, const pair<T, U> &p){os << p.first << " " << p.second;return os;}template <typename T, typename U>istream &operator>>(istream &is, pair<T, U> &p){is >> p.first >> p.second;return is;}template <typename T>ostream &operator<<(ostream &os, const vector<T> &v){int s = (int)v.size();for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];return os;}template <typename T>istream &operator>>(istream &is, vector<T> &v){for (auto &x : v) is >> x;return is;}void in() {}template <typename T, class... U>void in(T &t, U &...u){cin >> t;in(u...);}void out() { cout << "\n"; }template <typename T, class... U, char sep = ' '>void out(const T &t, const U &...u){cout << t;if (sizeof...(u)) cout << sep;out(u...);}template<typename T>void out(const vector<vector<T>> &vv){int s = (int)vv.size();for (int i = 0; i < s; i++) out(vv[i]);}struct IoSetup {IoSetup(){cin.tie(nullptr);ios::sync_with_stdio(false);cout << fixed << setprecision(15);cerr << fixed << setprecision(7);}} iosetup_noya2;} // namespace noya2#line 1 "/Users/noya2/Desktop/Noya2_library/template/const.hpp"namespace noya2{const int iinf = 1'000'000'007;const long long linf = 2'000'000'000'000'000'000LL;const long long mod998 = 998244353;const long long mod107 = 1000000007;const long double pi = 3.14159265358979323;const vector<int> dx = {0,1,0,-1,1,1,-1,-1};const vector<int> dy = {1,0,-1,0,1,-1,-1,1};const string ALP = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";const string alp = "abcdefghijklmnopqrstuvwxyz";const string NUM = "0123456789";void yes(){ cout << "Yes\n"; }void no(){ cout << "No\n"; }void YES(){ cout << "YES\n"; }void NO(){ cout << "NO\n"; }void yn(bool t){ t ? yes() : no(); }void YN(bool t){ t ? YES() : NO(); }} // namespace noya2#line 2 "/Users/noya2/Desktop/Noya2_library/template/utils.hpp"#line 6 "/Users/noya2/Desktop/Noya2_library/template/utils.hpp"namespace noya2{unsigned long long inner_binary_gcd(unsigned long long a, unsigned long long b){if (a == 0 || b == 0) return a + b;int n = __builtin_ctzll(a); a >>= n;int m = __builtin_ctzll(b); b >>= m;while (a != b) {int mm = __builtin_ctzll(a - b);bool f = a > b;unsigned long long c = f ? a : b;b = f ? b : a;a = (c - b) >> mm;}return a << std::min(n, m);}template<typename T> T gcd_fast(T a, T b){ return static_cast<T>(inner_binary_gcd(std::abs(a),std::abs(b))); }long long sqrt_fast(long long n) {if (n <= 0) return 0;long long x = sqrt(n);while ((x + 1) * (x + 1) <= n) x++;while (x * x > n) x--;return x;}template<typename T> T floor_div(const T n, const T d) {assert(d != 0);return n / d - static_cast<T>((n ^ d) < 0 && n % d != 0);}template<typename T> T ceil_div(const T n, const T d) {assert(d != 0);return n / d + static_cast<T>((n ^ d) >= 0 && n % d != 0);}template<typename T> void uniq(std::vector<T> &v){std::sort(v.begin(),v.end());v.erase(unique(v.begin(),v.end()),v.end());}template <typename T, typename U> inline bool chmin(T &x, U y) { return (y < x) ? (x = y, true) : false; }template <typename T, typename U> inline bool chmax(T &x, U y) { return (x < y) ? (x = y, true) : false; }template<typename T> inline bool range(T l, T x, T r){ return l <= x && x < r; }} // namespace noya2#line 8 "/Users/noya2/Desktop/Noya2_library/template/template.hpp"#define rep(i,n) for (int i = 0; i < (int)(n); i++)#define repp(i,m,n) for (int i = (m); i < (int)(n); i++)#define reb(i,n) for (int i = (int)(n-1); i >= 0; i--)#define all(v) (v).begin(),(v).end()using ll = long long;using ld = long double;using uint = unsigned int;using ull = unsigned long long;using pii = pair<int,int>;using pll = pair<ll,ll>;using pil = pair<int,ll>;using pli = pair<ll,int>;namespace noya2{/* ~ (. _________ . /) */}using namespace noya2;#line 2 "c.cpp"#line 2 "/Users/noya2/Desktop/Noya2_library/utility/modint.hpp"#line 4 "/Users/noya2/Desktop/Noya2_library/utility/modint.hpp"#line 2 "/Users/noya2/Desktop/Noya2_library/math/prime.hpp"#line 4 "/Users/noya2/Desktop/Noya2_library/math/prime.hpp"namespace noya2 {constexpr long long safe_mod(long long x, long long m) {x %= m;if (x < 0) x += m;return x;}constexpr long long pow_mod_constexpr(long long x, long long n, int m) {if (m == 1) return 0;unsigned int _m = (unsigned int)(m);unsigned long long r = 1;unsigned long long y = safe_mod(x, m);while (n) {if (n & 1) r = (r * y) % _m;y = (y * y) % _m;n >>= 1;}return r;}constexpr bool is_prime_constexpr(int n) {if (n <= 1) return false;if (n == 2 || n == 7 || n == 61) return true;if (n % 2 == 0) return false;long long d = n - 1;while (d % 2 == 0) d /= 2;constexpr long long bases[3] = {2, 7, 61};for (long long a : bases) {long long t = d;long long y = pow_mod_constexpr(a, t, n);while (t != n - 1 && y != 1 && y != n - 1) {y = y * y % n;t <<= 1;}if (y != n - 1 && t % 2 == 0) {return false;}}return true;}template <int n> constexpr bool is_prime_flag = is_prime_constexpr(n);constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {a = safe_mod(a, b);if (a == 0) return {b, 0};long long s = b, t = a;long long m0 = 0, m1 = 1;while (t) {long long u = s / t;s -= t * u;m0 -= m1 * u;auto tmp = s;s = t;t = tmp;tmp = m0;m0 = m1;m1 = tmp;}if (m0 < 0) m0 += b / s;return {s, m0};}constexpr int primitive_root_constexpr(int m) {if (m == 2) return 1;if (m == 167772161) return 3;if (m == 469762049) return 3;if (m == 754974721) return 11;if (m == 998244353) return 3;int divs[20] = {};divs[0] = 2;int cnt = 1;int x = (m - 1) / 2;while (x % 2 == 0) x /= 2;for (int i = 3; (long long)(i)*i <= x; i += 2) {if (x % i == 0) {divs[cnt++] = i;while (x % i == 0) {x /= i;}}}if (x > 1) {divs[cnt++] = x;}for (int g = 2;; g++) {bool ok = true;for (int i = 0; i < cnt; i++) {if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {ok = false;break;}}if (ok) return g;}}template <int m> constexpr int primitive_root_flag = primitive_root_constexpr(m);// constexpr long long primitive_root_constexpr(long long m){// if (m == (1LL << 47) - (1LL << 24) + 1) return 3;// return primitive_root_constexpr(static_cast<int>(m));// }} // namespace noya2#line 6 "/Users/noya2/Desktop/Noya2_library/utility/modint.hpp"namespace noya2{struct barrett {unsigned int _m;unsigned long long im;explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}unsigned int umod() const { return _m; }unsigned int mul(unsigned int a, unsigned int b) const {unsigned long long z = a;z *= b;unsigned long long x = (unsigned long long)((__uint128_t(z) * im) >> 64);unsigned int v = (unsigned int)(z - x * _m);if (_m <= v) v += _m;return v;}};template <int m>struct static_modint {using mint = static_modint;public:static constexpr int mod() { return m; }static mint raw(int v) {mint x;x._v = v;return x;}constexpr static_modint() : _v(0) {}template<std::signed_integral T>constexpr static_modint(T v){long long x = (long long)(v % (long long)(umod()));if (x < 0) x += umod();_v = (unsigned int)(x);}template<std::unsigned_integral T>constexpr static_modint(T v){_v = (unsigned int)(v % umod());}constexpr unsigned int val() const { return _v; }mint& operator++() {_v++;if (_v == umod()) _v = 0;return *this;}mint& operator--() {if (_v == 0) _v = umod();_v--;return *this;}mint operator++(int) {mint result = *this;++*this;return result;}mint operator--(int) {mint result = *this;--*this;return result;}constexpr mint& operator+=(const mint& rhs) {_v += rhs._v;if (_v >= umod()) _v -= umod();return *this;}constexpr mint& operator-=(const mint& rhs) {_v -= rhs._v;if (_v >= umod()) _v += umod();return *this;}constexpr mint& operator*=(const mint& rhs) {unsigned long long z = _v;z *= rhs._v;_v = (uint)(z % umod());return *this;}constexpr mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }constexpr mint operator+() const { return *this; }constexpr mint operator-() const { return mint() - *this; }constexpr mint pow(long long n) const {assert(0 <= n);mint x = *this, r = 1;while (n) {if (n & 1) r *= x;x *= x;n >>= 1;}return r;}constexpr mint inv() const {if (prime) {assert(_v);return pow(umod() - 2);} else {auto eg = inv_gcd(_v, m);assert(eg.first == 1);return eg.second;}}friend constexpr mint operator+(const mint& lhs, const mint& rhs) {return mint(lhs) += rhs;}friend constexpr mint operator-(const mint& lhs, const mint& rhs) {return mint(lhs) -= rhs;}friend constexpr mint operator*(const mint& lhs, const mint& rhs) {return mint(lhs) *= rhs;}friend constexpr mint operator/(const mint& lhs, const mint& rhs) {return mint(lhs) /= rhs;}friend constexpr bool operator==(const mint& lhs, const mint& rhs) {return lhs._v == rhs._v;}friend constexpr bool operator!=(const mint& lhs, const mint& rhs) {return lhs._v != rhs._v;}friend std::ostream &operator<<(std::ostream &os, const mint& p) {return os << p.val();}friend std::istream &operator>>(std::istream &is, mint &a) {long long t; is >> t;a = mint(t);return (is);}private:unsigned int _v;static constexpr unsigned int umod() { return m; }static constexpr bool prime = is_prime_flag<m>;};template <int id> struct dynamic_modint {using mint = dynamic_modint;public:static int mod() { return (int)(bt.umod()); }static void set_mod(int m) {assert(1 <= m);bt = barrett(m);}static mint raw(int v) {mint x;x._v = v;return x;}dynamic_modint() : _v(0) {}template<std::signed_integral T>dynamic_modint(T v){long long x = (long long)(v % (long long)(umod()));if (x < 0) x += umod();_v = (unsigned int)(x);}template<std::unsigned_integral T>dynamic_modint(T v){_v = (unsigned int)(v % umod());}uint val() const { return _v; }mint& operator++() {_v++;if (_v == umod()) _v = 0;return *this;}mint& operator--() {if (_v == 0) _v = umod();_v--;return *this;}mint operator++(int) {mint result = *this;++*this;return result;}mint operator--(int) {mint result = *this;--*this;return result;}mint& operator+=(const mint& rhs) {_v += rhs._v;if (_v >= umod()) _v -= umod();return *this;}mint& operator-=(const mint& rhs) {_v += mod() - rhs._v;if (_v >= umod()) _v -= umod();return *this;}mint& operator*=(const mint& rhs) {_v = bt.mul(_v, rhs._v);return *this;}mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }mint operator+() const { return *this; }mint operator-() const { return mint() - *this; }mint pow(long long n) const {assert(0 <= n);mint x = *this, r = 1;while (n) {if (n & 1) r *= x;x *= x;n >>= 1;}return r;}mint inv() const {auto eg = noya2::inv_gcd(_v, mod());assert(eg.first == 1);return eg.second;}friend mint operator+(const mint& lhs, const mint& rhs) {return mint(lhs) += rhs;}friend mint operator-(const mint& lhs, const mint& rhs) {return mint(lhs) -= rhs;}friend mint operator*(const mint& lhs, const mint& rhs) {return mint(lhs) *= rhs;}friend mint operator/(const mint& lhs, const mint& rhs) {return mint(lhs) /= rhs;}friend bool operator==(const mint& lhs, const mint& rhs) {return lhs._v == rhs._v;}friend bool operator!=(const mint& lhs, const mint& rhs) {return lhs._v != rhs._v;}friend std::ostream &operator<<(std::ostream &os, const mint& p) {return os << p.val();}friend std::istream &operator>>(std::istream &is, mint &a) {long long t; is >> t;a = mint(t);return (is);}private:unsigned int _v;static barrett bt;static unsigned int umod() { return bt.umod(); }};template <int id> noya2::barrett dynamic_modint<id>::bt(998244353);using modint998244353 = static_modint<998244353>;using modint1000000007 = static_modint<1000000007>;using modint = dynamic_modint<-1>;template<typename T>concept Modint = requires (T &a){T::mod();a.inv();a.val();a.pow(declval<int>());};} // namespace noya2#line 4 "c.cpp"using mint = modint;#line 2 "/Users/noya2/Desktop/Noya2_library/math/binomial.hpp"#line 4 "/Users/noya2/Desktop/Noya2_library/math/binomial.hpp"namespace noya2 {template<typename mint>struct binomial {binomial(int len = 300000){ extend(len); }static mint fact(int n){if (n < 0) return 0;while (n >= (int)_fact.size()) extend();return _fact[n];}static mint ifact(int n){if (n < 0) return 0;while (n >= (int)_fact.size()) extend();return _ifact[n];}static mint inv(int n){return ifact(n) * fact(n-1);}static mint C(int n, int r){if (!(0 <= r && r <= n)) return 0;return fact(n) * ifact(r) * ifact(n-r);}static mint P(int n, int r){if (!(0 <= r && r <= n)) return 0;return fact(n) * ifact(n-r);}inline mint operator()(int n, int r) { return C(n, r); }template<class... Cnts>static mint M(const Cnts&... cnts){return multinomial(0,1,cnts...);}static void initialize(int len = 2){_fact.clear();_ifact.clear();extend(len);}private:static mint multinomial(const int& sum, const mint& div_prod){if (sum < 0) return 0;return fact(sum) * div_prod;}template<class... Tail>static mint multinomial(const int& sum, const mint& div_prod, const int& n1, const Tail&... tail){if (n1 < 0) return 0;return multinomial(sum+n1,div_prod*ifact(n1),tail...);}static inline std::vector<mint> _fact, _ifact;static void extend(int len = -1){if (_fact.empty()){_fact = _ifact = {1,1};}int siz = _fact.size();if (len == -1) len = siz * 2;len = (int)min<long long>(len, mint::mod() - 1);if (len < siz) return ;_fact.resize(len+1), _ifact.resize(len+1);for (int i = siz; i <= len; i++) _fact[i] = _fact[i-1] * i;_ifact[len] = _fact[len].inv();for (int i = len; i > siz; i--) _ifact[i-1] = _ifact[i] * i;}};} // namespace noya2#line 2 "/Users/noya2/Desktop/Noya2_library/graph/grid.hpp"#line 5 "/Users/noya2/Desktop/Noya2_library/graph/grid.hpp"#include <ranges>namespace noya2 {struct grid {int h, w;grid (int _h = 0, int _w = 0) : h(_h), w(_w) {}int idx(int x, int y) const {return x * w + y;}std::pair<int,int> pos(int id) const {return {id / w, id % w};}bool operator()(int x, int y) const {return 0 <= x && x < h && 0 <= y && y < w;}bool operator()(int id) const {return operator()(id / w, id % w);}static constexpr std::array<std::pair<int,int>, 4> dxys = {std::pair<int,int>{0, 1}, {-1, 0}, {0, -1}, {1, 0}};auto adj4(int x, int y) const {return dxys | std::views::transform([x, y](std::pair<int,int> dxy){return std::pair<int,int>(dxy.first + x, dxy.second + y);}) | std::views::filter([this](std::pair<int,int> xy){return operator()(xy.first, xy.second);});}auto adj4(int id) const {return adj4(id / w, id % w) | std::ranges::views::transform([this](std::pair<int,int> xy){return idx(xy.first, xy.second);});}};} // namespace noya2#line 7 "c.cpp"namespace noya2{struct dsu {public:dsu() : _n(0) {}dsu(int n) : _n(n) {fill(all(parent_or_size),-1);}int8_t merge(int8_t a, int8_t b) {assert(0 <= a && a < _n);assert(0 <= b && b < _n);int8_t x = leader(a), y = leader(b);if (x == y) return x;if (-parent_or_size[x] < -parent_or_size[y]) std::swap(x, y);parent_or_size[x] += parent_or_size[y];parent_or_size[y] = x;return x;}bool same(int8_t a, int8_t b) {assert(0 <= a && a < _n);assert(0 <= b && b < _n);return leader(a) == leader(b);}int8_t leader(int8_t a) {assert(0 <= a && a < _n);if (parent_or_size[a] < 0) return a;return parent_or_size[a] = leader(parent_or_size[a]);}int8_t size(int8_t a) {assert(0 <= a && a < _n);return -parent_or_size[leader(a)];}private:int _n;// root node: -1 * component size// otherwise: parentstd::array<int8_t, 25> parent_or_size;};} // namespace noya2void solve(){int h, w; in(h,w);ll kk; in(kk);{int p; in(p);mint::set_mod(p);}binomial<mint> bnm(2); bnm.initialize(100);const int hw = h*w;mint coef = 0;const mint i2 = mint(2).inv();for (int i = 1; i <= hw; i++){coef += bnm.inv(hw-i+1);}coef *= i2.pow(hw);vector<mint> pows(hw+1);for (int c = 1; c <= hw; c++){pows[c] = mint(c).pow(kk);}vector<mint> p2(hw+1);rep(i,hw+1){p2[i] = mint(2).pow(i);}if (h < w) swap(h,w);grid g(h,w);auto connected = [&](dsu &d, int s) -> bool {if (s == 0) return false;int cnt = popcount<uint32_t>(s);rep(id,hw){if (d.size(id) == cnt){return true;}}return false;};using pdi = pair<dsu,int>;auto proc = [&](dsu d, int s, int add, int i) -> pdi {s ^= (add << (i*w));bool lastempty = true;rep(j,w){int id = g.idx(i,j);if (~s >> id & 1) continue;lastempty = false;if (i > 0){int jd = g.idx(i-1,j);if (s >> jd & 1){d.merge(id,jd);}}if (j > 0){int jd = g.idx(i,j-1);if (s >> jd & 1){d.merge(id,jd);}}}if (lastempty){if (s == 0){return {d, s};}return {d, ~s};}rep(id,i*w){if (~s >> id & 1) continue;bool con = false;rep(j,w){int jd = g.idx(i,j);if (d.same(id,jd)){con = true;}}if (!con){return {d, INT_MAX};}}return {d, s};};vector<pdi> a = {{dsu(hw),0}};vector<pdi> adone;rep(i,h){vector<pdi> b;for (auto [d, s] : a){rep(add,1<<w){auto [nd, ns] = proc(d, s, add, i);if (ns == INT_MAX) continue;if (ns < 0){adone.emplace_back(nd, ~ns);}else {b.emplace_back(nd, ns);}}}swap(a,b);}a.insert(a.end(),all(adone));// cout << "OK" << endl;// return ;mint ans = 0;int tot = 0;for (auto [d, s] : a){if (!connected(d, s)){continue;}tot++;int cnt = 0;array<bool,25> ex = {};rep(i,h) rep(j,w){int id = g.idx(i, j);if (~s >> id & 1) continue;ex[id] = true;cnt++;for (auto [ni, nj] : g.adj4(i, j)){ex[g.idx(ni,nj)] = true;}}int other = h*w;rep(i,h) rep(j,w){if (ex[g.idx(i,j)]){other--;}}// out(s);ans += p2[other] * pows[cnt];}// out(tot);// out(ans);ans *= coef;out(ans);}int main(){int t = 1; //in(t);while (t--) { solve(); }}