結果
問題 | No.2747 Permutation Adjacent Sum |
ユーザー | rogi52 |
提出日時 | 2024-04-20 12:19:35 |
言語 | C++23 (gcc 12.3.0 + boost 1.83.0) |
結果 |
TLE
|
実行時間 | - |
コード長 | 21,357 bytes |
コンパイル時間 | 3,209 ms |
コンパイル使用メモリ | 261,920 KB |
実行使用メモリ | 263,140 KB |
最終ジャッジ日時 | 2024-10-12 07:38:42 |
合計ジャッジ時間 | 12,848 ms |
ジャッジサーバーID (参考情報) |
judge3 / judge2 |
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テストケース
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testcase_00 | TLE | - |
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ソースコード
#line 2 "cp-library/src/cp-template.hpp" #include <bits/stdc++.h> using namespace std; using ll = long long; using ld = long double; using uint = unsigned int; using ull = unsigned long long; using i32 = int; using u32 = unsigned int; using i64 = long long; using u64 = unsigned long long; using i128 = __int128_t; template < class T > bool chmin(T& a, T b) { if(a > b) { a = b; return true; } return false; } template < class T > bool chmax(T& a, T b) { if(a < b) { a = b; return true; } return false; } template < class T, class U > T ceil (T x, U y) { return (x > 0 ? (x + y - 1) / y : x / y); } template < class T, class U > T floor(T x, U y) { return (x > 0 ? x / y : (x - y + 1) / y); } int popcnt(i32 x) { return __builtin_popcount(x); } int popcnt(u32 x) { return __builtin_popcount(x); } int popcnt(i64 x) { return __builtin_popcountll(x); } int popcnt(u64 x) { return __builtin_popcountll(x); } #line 2 "cp-library/src/utility/rep_itr.hpp" template < class T > struct itr_rep { T i, d; constexpr itr_rep(const T i) noexcept : i(i), d(1) {} constexpr itr_rep(const T i, const T d) noexcept : i(i), d(d) {} void operator++() noexcept { i += d; } constexpr int operator*() const noexcept { return i; } constexpr bool operator!=(const itr_rep x) const noexcept { return d > 0 ? i < x.i : i > x.i; } }; template < class T > struct rep { const itr_rep< T > s, t; constexpr rep(const T t) noexcept : s(0), t(t) {} constexpr rep(const T s, const T t) noexcept : s(s), t(t) {} constexpr rep(const T s, const T t, const T d) noexcept : s(s, d), t(t, d) {} constexpr auto begin() const noexcept { return s; } constexpr auto end () const noexcept { return t; } }; template < class T > struct revrep { const itr_rep < T > s, t; constexpr revrep(const T t) noexcept : s(t - 1, -1), t(-1, -1) {} constexpr revrep(const T s, const T t) noexcept : s(t - 1, -1), t(s - 1, -1) {} constexpr revrep(const T s, const T t, const T d) noexcept : s(t - 1, -d), t(s - 1, -d) {} constexpr auto begin() const noexcept { return s; } constexpr auto end () const noexcept { return t; } }; #line 3 "cp-library/src/utility/io.hpp" /* 128bit integer */ istream& operator>>(istream& is, i128& x) { std::string s; is >> s; int pm = (s[0] == '-'); x = 0; for(int i : rep(pm, int(s.size()))) x = x * 10 + (s[i] - '0'); if(pm) x *= -1; return is; } ostream& operator<<(ostream& os, const i128& x) { if(x == 0) return os << '0'; i128 y = x; if(y < 0) { os << '-'; y *= -1; } std::vector<int> ny; while(y > 0) { ny.push_back(y % 10); y /= 10; } for(int i : revrep(ny.size())) os << ny[i]; return os; } template < class S, class T > istream& operator>>(istream& is, std::pair< S, T >& x) { is >> x.first >> x.second; return is; } template < class S, class T > ostream& operator<<(ostream& os, const std::pair< S, T >& x) { os << x.first << " " << x.second; return os; } namespace scanner { struct sca { template < class T > operator T() { T s; std::cin >> s; return s; } }; struct vec { int n; vec(int n) : n(n) {} template < class T > operator std::vector< T >() { std::vector< T > v(n); for(T& x : v) std::cin >> x; return v; } }; struct mat { int h, w; mat(int h, int w) : h(h), w(w) {} template < class T > operator std::vector< std::vector< T > >() { std::vector m(h, std::vector< T >(w)); for(std::vector< T >& v : m) for(T& x : v) std::cin >> x; return m; } }; struct speedup { speedup() { std::cin.tie(0); std::ios::sync_with_stdio(0); } } speedup_instance; } scanner::sca in() { return scanner::sca(); } scanner::vec in(int n) { return scanner::vec(n); } scanner::mat in(int h, int w) { return scanner::mat(h, w); } namespace printer { void precision(int d) { std::cout << std::fixed << std::setprecision(d); } void flush() { std::cout.flush(); } } template < class T > ostream& operator<<(ostream& os, const std::vector< T > a) { int n = a.size(); for(int i : rep(n)) { os << a[i]; if(i != n - 1) os << ' '; } return os; } int print() { std::cout << '\n'; return 0; } template < class head, class... tail > int print(head&& h, tail&&... t) { std::cout << h; if(sizeof...(tail)) std::cout << ' '; return print(std::forward<tail>(t)...); } template < class T > int print_n(const std::vector< T > a) { int n = a.size(); for(int i : rep(n)) std::cout << a[i] << "\n"; return 0; } #line 2 "cp-library/src/utility/key_val.hpp" template < class K, class V > struct key_val { K key; V val; key_val() {} key_val(K key, V val) : key(key), val(val) {} template < std::size_t Index > std::tuple_element_t< Index, key_val >& get() { if constexpr (Index == 0) return key; if constexpr (Index == 1) return val; } }; namespace std { template < class K, class V > struct tuple_size < key_val< K, V > > : integral_constant< size_t, 2 > {}; template < class K, class V > struct tuple_element < 0, key_val< K, V > > { using type = K; }; template < class K, class V > struct tuple_element < 1, key_val< K, V > > { using type = V; }; } #line 2 "cp-library/src/utility/vec_op.hpp" template < class T > key_val< int, T > max_of(const vector< T >& a) { int i = std::max_element(a.begin(), a.end()) - a.begin(); return {i, a[i]}; } template < class T > key_val< int, T > min_of(const vector< T >& a) { int i = std::min_element(a.begin(), a.end()) - a.begin(); return {i, a[i]}; } template < class S, class T > S sum_of(const vector< T >& a) { S sum = 0; for(const T x : a) sum += x; return sum; } template < class S, class T > vector< S > freq_of(const vector< T >& a, T L, T R) { vector< S > res(R - L, S(0)); for(const T x : a) res[x - L] += 1; return res; } template < class S, class T > struct prefix_sum { vector< S > s; prefix_sum(const vector< T >& a) : s(a) { s.insert(s.begin(), S(0)); for(int i : rep(a.size())) s[i + 1] += s[i]; } // [L, R) S sum(int L, int R) { return s[R] - s[L]; } }; #line 3 "cp-library/src/utility/heap.hpp" template < class T > using heap_min = std::priority_queue< T, std::vector< T >, std::greater< T > >; template < class T > using heap_max = std::priority_queue< T, std::vector< T >, std::less< T > >; #line 27 "cp-library/src/cp-template.hpp" #line 1 "cp-library/src/algorithm/bin_search.hpp" template < class T, class F > T bin_search(T ok, T ng, F f) { while(abs(ng - ok) > 1) { T mid = (ok + ng) / 2; (f(mid) ? ok : ng) = mid; } return ok; } template < class T, class F > T bin_search_real(T ok, T ng, F f, int step = 80) { while(step--) { T mid = (ok + ng) / 2; (f(mid) ? ok : ng) = mid; } return ok; } #line 2 "cp-library/src/algorithm/argsort.hpp" template < class T > std::vector< int > argsort(const std::vector< T > &a) { std::vector< int > ids((int)a.size()); std::iota(ids.begin(), ids.end(), 0); std::sort(ids.begin(), ids.end(), [&](int i, int j) { return a[i] < a[j] || (a[i] == a[j] && i < j); }); return ids; } #line 1 "macro.hpp" namespace macro { using size_type = int; template < class container > void sort(container& a) { std::sort(std:: begin(a), std:: end(a)); } template < class container > void rsort(container& a) { std::sort(std::rbegin(a), std::rend(a)); } template < class container > void reverse(container& a) { std::reverse(std::begin(a), std::end(a)); } template < class container > void unique(container& a) { std::sort(std::begin(a), std::end(a)); a.erase(std::unique(std::begin(a), std::end(a)), std::end(a)); } template < class container > container sorted(const container& a) { container b = a; sort(b); return std::move(b); } template < class container > container rsorted(const container& a) { container b = a; rsort(b); return std::move(b); } template < class container, class compare > void sort(container& a, const compare& cmp) { std::sort(std::begin(a), std::end(a), cmp); } template < class container, class compare > container sorted(const container& a, const compare& cmp) { container b = a; sort(b, cmp); return std::move(b); } template < class container, class value > size_type lower_bound(const container& a, const value& x) { return std::lower_bound(std::begin(a), std::end(a), x) - std::begin(a); } template < class container, class value > size_type upper_bound(const container& a, const value& x) { return std::upper_bound(std::begin(a), std::end(a), x) - std::begin(a); } const std::vector<std::pair<size_type, size_type>> dir4 = { {+1, 0}, {-1, 0}, { 0, +1}, { 0, -1} }; const std::vector<std::pair<size_type, size_type>> dir8 = { {-1, -1}, {-1, 0}, {-1, +1}, { 0, -1}, { 0, +1}, {+1, -1}, {+1, 0}, {+1, +1} }; #ifdef _DEBUG #define debug(x) std::cout << "[" << __LINE__ << "] " << #x << ": " << x << std::endl #else #define debug(x) #endif template < class container > void concat(container& a, const container& b) { a.insert(std::end(a), std::begin(b), std::end(b)); } std::vector<size_type> iota(const size_type n) { std::vector<size_type> I(n); std::iota(std::begin(I), std::end(I), 0); return I; } template < class container > std::vector<size_type> sort_idx(const container& a) { const size_type n = a.size(); std::vector<size_type> I = iota(n); std::sort(std::begin(I), std::end(I), [&](size_type i, size_type j) { return a[i] < a[j] or (a[i] == a[j] and i < j); }); return I; } template < class container, class compare > std::vector<size_type> sort_idx(const container& a, const compare& cmp) { const size_type n = a.size(); std::vector<size_type> I = iota(n); std::sort(std::begin(I), std::end(I), [&](size_type i, size_type j) { return cmp(a[i], a[j]) or (a[i] == a[j] and i < j); }); return std::move(I); } struct grid { using size_type = int; size_type H, W; grid(const size_type H, const size_type W) : H(H), W(W) {} bool contains(const size_type i, const size_type j) { return 0 <= i and i < H and 0 <= j and j < W; } }; using f64 = long double; template < class T > vector< T >& operator++(vector< T >& a) { for(T& x : a) x++; return a; } template < class T > vector< T >& operator--(vector< T >& a) { for(T& x : a) x--; return a; } template < class T > vector< T > operator++(vector< T >& a, signed) { vector< T > res = a; for(T& x : a) x++; return res; } template < class T > vector< T > operator--(vector< T >& a, signed) { vector< T > res = a; for(T& x : a) x--; return res; } } // namespace macro using namespace macro; #line 2 "cp-library/src/number/modint.hpp" struct modinfo { uint mod, root, isprime; }; template < modinfo const &ref > struct modint { static constexpr uint const &mod = ref.mod; static constexpr uint const &root = ref.root; static constexpr uint const &isprime = ref.isprime; uint v = 0; constexpr modint& s(uint v) { this->v = v < mod ? v : v - mod; return *this; } constexpr modint(ll v = 0) { s(v % mod + mod); } modint operator-() const { return modint() - *this; } modint& operator+=(const modint& rhs) { return s(v + rhs.v); } modint& operator-=(const modint& rhs) { return s(v + mod - rhs.v); } modint& operator*=(const modint& rhs) { v = ull(v) * rhs.v % mod; return *this; } modint& operator/=(const modint& rhs) { return *this *= inv(rhs); } modint operator+(const modint& rhs) const { return modint(*this) += rhs; } modint operator-(const modint& rhs) const { return modint(*this) -= rhs; } modint operator*(const modint& rhs) const { return modint(*this) *= rhs; } modint operator/(const modint& rhs) const { return modint(*this) /= rhs; } friend modint pow(modint x, ll n) { modint res(1); while(n > 0) { if(n & 1) res *= x; x *= x; n >>= 1; } return res; } friend modint inv(modint v) { if(isprime) { return pow(v, mod - 2); } else { ll a = v.v, b = modint::mod, x = 1, y = 0, t; while(b > 0) { t = a / b; swap(a -= t * b, b); swap(x -= t * y, y); } return modint(x); } } friend modint operator+(int x, const modint& y) { return modint(x) + y; } friend modint operator-(int x, const modint& y) { return modint(x) - y; } friend modint operator*(int x, const modint& y) { return modint(x) * y; } friend modint operator/(int x, const modint& y) { return modint(x) / y; } friend istream& operator>>(istream& is, modint& m) { ll x; is >> x; m = modint(x); return is; } friend ostream& operator<<(ostream& os, const modint& m) { return os << m.v; } bool operator==(const modint& r) const { return v == r.v; } bool operator!=(const modint& r) const { return v != r.v; } static uint get_mod() { return mod; } static int is_prime() { return isprime; } }; constexpr modinfo base998244353 { 998244353, 3, 1 }; constexpr modinfo base1000000007 { 1000000007, 0, 1 }; using mint998244353 = modint< base998244353 >; using mint1000000007 = modint< base1000000007 >; #line 3 "cp-library/src/number/binom_mod.hpp" template < class mint > mint fact(int n) { assert(0 <= n); assert(mint::is_prime()); static const uint mod = mint::get_mod(); static std::vector<mint> data = {1, 1}; while(int(data.size()) <= n) { int i = data.size(); data.push_back(data.back() * i); } return data[n]; } template < class mint > mint inv(int n) { assert(0 <= n); assert(mint::is_prime()); static const uint mod = mint::get_mod(); static std::vector<mint> data = {1, 1}; while(int(data.size()) <= n) { int i = data.size(); data.push_back(- data[mod % i] * (mod / i)); } return data[n]; } template < class mint > mint fact_inv(int n) { assert(0 <= n); assert(mint::is_prime()); static const uint mod = mint::get_mod(); static std::vector<mint> data = {1, 1}; while(int(data.size()) <= n) { int i = data.size(); data.push_back(data.back() * inv<mint>(i)); } return data[n]; } template < class mint > mint comb(int n, int k) { if(k < 0 or n < k) return 0; return fact<mint>(n) * fact_inv<mint>(k) * fact_inv<mint>(n - k); } template < class mint > mint perm(int n, int k) { return fact<mint>(n) * fact_inv<mint>(n - k); } template < class mint > mint homo(int n, int k) { return comb<mint>(n + k - 1, k); } template < class mint > struct power { mint a; std::vector<mint> data = {1}; power() {} power(const mint a) : a(a) {} // a^n mint get(const int n) { assert(0 <= n); while(int(data.size()) <= n) data.push_back(data.back() * a); return data[n]; } }; #line 5 "C.cpp" #line 7 "C.cpp" #define rep(i,n) for(int i = 0; i < (n); i++) using namespace std; using ll = long long; using ld = long double; template< int mod > struct Fp { ll x; Fp() : x(0) {} Fp(int64_t y) : x(y >= 0 ? y % mod : (mod + y % mod) % mod) {} Fp &operator+=(const Fp &p) { if((x += p.x) >= mod) x -= mod; return *this; } Fp &operator-=(const Fp &p) { if((x += mod - p.x) >= mod) x -= mod; return *this; } Fp &operator*=(const Fp &p) { x = (int)(1LL * x * p.x % mod); return *this; } Fp &operator/=(const Fp &p) { *this *= p.inv(); return *this; } Fp operator-() const { return Fp(-x); } Fp operator+(const Fp &p) const { return Fp(*this) += p; } Fp operator-(const Fp &p) const { return Fp(*this) -= p; } Fp operator*(const Fp &p) const { return Fp(*this) *= p; } Fp operator/(const Fp &p) const { return Fp(*this) /= p; } bool operator==(const Fp &p) const { return x == p.x; } bool operator!=(const Fp &p) const { return x != p.x; } Fp inv() const { int a = x, b = mod, u = 1, v = 0, t; while(b > 0) { t = a / b; swap(a -= t * b, b); swap(u -= t * v, v); } return Fp(u); } Fp pow(int64_t n) const { Fp ret(1), mul(x); while(n > 0) { if(n & 1) ret *= mul; mul *= mul; n >>= 1; } return ret; } friend ostream &operator<<(ostream &os, const Fp &p) { return os << p.x; } friend istream &operator>>(istream &is, Fp &a) { int64_t t; is >> t; a = Fp< mod > (t); return (is); } static long long getmod() { return mod; } }; using mint = Fp<998244353>; // Binomial coefficient template<class T> struct BiCoef { vector<T> fact_, inv_, finv_; constexpr BiCoef() {} constexpr BiCoef(int n) noexcept : fact_(n, 1), inv_(n, 1), finv_(n, 1) { init(n); } constexpr void init(int n) noexcept { fact_.assign(n, 1), inv_.assign(n, 1), finv_.assign(n, 1); int MOD = fact_[0].getmod(); for(int i = 2; i < n; i++){ fact_[i] = fact_[i-1] * i; inv_[i] = -inv_[MOD%i] * (MOD/i); finv_[i] = finv_[i-1] * inv_[i]; } } constexpr T com(int n, int k) const noexcept { if (n < k || n < 0 || k < 0) return 0; return fact_[n] * finv_[k] * finv_[n-k]; } constexpr T fact(int n) const noexcept { if (n < 0) return 0; return fact_[n]; } constexpr T inv(int n) const noexcept { if (n < 0) return 0; return inv_[n]; } constexpr T finv(int n) const noexcept { if (n < 0) return 0; return finv_[n]; } }; const int MOD = 998244353; using mint = Fp<MOD>; template < class S > S lagrange_interpolation(vector< S > x, vector< S > y, S T) { int n = x.size() - 1u; S res(0); for(int i = 0; i <= n; i++) { S ft(1), fx(1); for(int j = 0; j <= n; j++) if(i != j) { ft *= T - x[j]; fx *= x[i] - x[j]; } res += y[i] * ft / fx; } return res; } template < class S > S lagrange_interpolation_arithmetic(S a, S d, vector< S > y, S T) { int n = y.size() - 1u; vector< S > fx(n + 1); fx[0] = 1; for(int j = 1; j <= n; j++) fx[0] *= mint(-j) * d; for(int i = 0; i <= n - 1; i++) fx[i + 1] = fx[i] * (i + 1) / (i - n); vector< S > ft(n + 1), L(n + 1), R(n + 1); L[0] = R[n] = 1; for(int i = 0; i < n; i++) L[i + 1] = L[i] * (T - (a + S(i) * d)); for(int i = n; i > 0; i--) R[i - 1] = R[i] * (T - (a + S(i) * d)); for(int i = 0; i <= n; i++) ft[i] = L[i] * R[i]; S res(0); for(int i = 0; i <= n; i++) { res += y[i] * ft[i] / fx[i]; } return res; } template < class S > vector< S > lagrange_interpolation(vector< S > x, vector< S > y) { int n = x.size() - 1u; vector< S > c(n + 1); for(int i = 0; i <= n; i++) { S fx(1); for(int j = 0; j <= n; j++) if(i != j) fx *= x[i] - x[j]; c[i] = y[i] / fx; } // g = prod (x - x[i]) vector< S > g(n + 2); g[0] = 1; for(int i = 0; i <= n; i++) { vector< S > g2(n + 2, 0), a = {-x[i], 1}; for(int j = 0; j <= n; j++) { for(int k = 0; k <= 1; k++) { g2[j + k] += g[j] * a[k]; } } swap(g, g2); } vector< S > xinv(n + 1); for(int i = 0; i <= n; i++) xinv[i] = S(1) / x[i]; vector< S > f(n + 1); for(int i = 0; i <= n; i++) { vector< S > g2 = g, h(n + 1), a = {-x[i], 1}; for(int j = n; j >= 0; j--) { h[j] = g2[j + 1]; f[j] += h[j] * c[i]; for(int k = 0; k <= 1; k++) g2[k + j] -= a[k] * h[j]; } } return f; } BiCoef<mint> bc(10001000); mint lagrange_interpolation_0n(vector< mint > y, mint T) { int n = y.size() - 1u; if(0 <= T.x && T.x <= n) return y[T.x]; /* vector< mint > fact(n + 1, 1), inv(n + 1, 1), finv(n + 1, 1); int MOD = fact[0].getmod(); for(int i = 2; i <= n; i++) { fact[i] = fact[i - 1] * i; inv[i] = -inv[MOD % i] * (MOD / i); finv[i] = finv[i - 1] * inv[i]; } */ vector< mint > L(n + 1), R(n + 1); L[0] = R[n] = 1; for(int i = 0; i < n; i++) L[i + 1] = L[i] * mint(T - i); for(int i = n; i > 0; i--) R[i - 1] = R[i] * mint(T - i); mint res(0); for(int i = 0; i <= n; i++) { res += y[i] * L[i] * R[i] * bc.finv(i) * bc.finv(n - i) * ((n - i) % 2 ? -1 : +1); } return res; } mint solve(i64 r, i64 d, i64 n) { if(n == 0) { return 0; } n--; vector<mint> sum(d + 2); rep(i,d+2) sum[i] = mint(r).pow(i) * mint(i).pow(d); rep(i,d+1) sum[i + 1] += sum[i]; if(r == 1) { return lagrange_interpolation_0n(sum, n); } else { mint c = 0; rep(i,d+1) c += bc.com(d + 1, i + 1) * mint(-r).pow(d - i) * sum[i]; c /= mint(1 - r).pow(d + 1); vector<mint> y(d + 1); mint div = 1, rinv = mint(r).inv(); rep(i,d+1) { y[i] = (sum[i] - c) * div; div *= rinv; } return mint(r).pow(n) * lagrange_interpolation_0n(y, n) + c; } } int main() { int N = in(), K = in(); mint ans = 0; ans += solve(1, K, N) * N - solve(1, K + 1, N); print(ans * bc.fact(N - 1) * 2); }