結果
問題 | No.2243 Coaching Schedule |
ユーザー | 👑 Nachia |
提出日時 | 2023-03-09 03:56:52 |
言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
結果 |
AC
|
実行時間 | 495 ms / 4,000 ms |
コード長 | 19,307 bytes |
コンパイル時間 | 1,259 ms |
コンパイル使用メモリ | 101,332 KB |
実行使用メモリ | 40,152 KB |
最終ジャッジ日時 | 2024-09-18 02:45:13 |
合計ジャッジ時間 | 11,513 ms |
ジャッジサーバーID (参考情報) |
judge3 / judge5 |
(要ログイン)
テストケース
テストケース表示入力 | 結果 | 実行時間 実行使用メモリ |
---|---|---|
testcase_00 | AC | 1 ms
6,816 KB |
testcase_01 | AC | 2 ms
6,940 KB |
testcase_02 | AC | 1 ms
6,940 KB |
testcase_03 | AC | 2 ms
6,940 KB |
testcase_04 | AC | 4 ms
6,944 KB |
testcase_05 | AC | 495 ms
40,152 KB |
testcase_06 | AC | 448 ms
29,488 KB |
testcase_07 | AC | 451 ms
29,772 KB |
testcase_08 | AC | 451 ms
29,588 KB |
testcase_09 | AC | 438 ms
29,824 KB |
testcase_10 | AC | 429 ms
30,012 KB |
testcase_11 | AC | 426 ms
29,884 KB |
testcase_12 | AC | 310 ms
21,152 KB |
testcase_13 | AC | 308 ms
19,584 KB |
testcase_14 | AC | 313 ms
19,388 KB |
testcase_15 | AC | 310 ms
19,552 KB |
testcase_16 | AC | 15 ms
6,940 KB |
testcase_17 | AC | 101 ms
9,940 KB |
testcase_18 | AC | 335 ms
23,396 KB |
testcase_19 | AC | 351 ms
22,204 KB |
testcase_20 | AC | 224 ms
16,612 KB |
testcase_21 | AC | 195 ms
15,444 KB |
testcase_22 | AC | 155 ms
13,604 KB |
testcase_23 | AC | 23 ms
6,944 KB |
testcase_24 | AC | 242 ms
19,188 KB |
testcase_25 | AC | 30 ms
6,940 KB |
testcase_26 | AC | 87 ms
10,808 KB |
testcase_27 | AC | 250 ms
20,200 KB |
testcase_28 | AC | 39 ms
6,944 KB |
testcase_29 | AC | 296 ms
20,976 KB |
testcase_30 | AC | 367 ms
25,512 KB |
testcase_31 | AC | 412 ms
28,240 KB |
testcase_32 | AC | 124 ms
11,516 KB |
testcase_33 | AC | 99 ms
12,292 KB |
testcase_34 | AC | 281 ms
21,420 KB |
testcase_35 | AC | 327 ms
25,948 KB |
testcase_36 | AC | 378 ms
26,468 KB |
ソースコード
#line 1 "Main.cpp" #include <iostream> #include <string> #include <vector> #include <algorithm> #include <atcoder/modint> #line 5 "nachia\\fps\\fps-struct.hpp" #include <cassert> #line 3 "nachia\\math-modulo\\modulo-primitive-root.hpp" #include <utility> namespace nachia{ template<unsigned int MOD> struct PrimitiveRoot{ using u64 = unsigned long long; static constexpr u64 powm(u64 a, u64 i) { u64 res = 1, aa = a; while(i){ if(i & 1) res = res * aa % MOD; aa = aa * aa % MOD; i /= 2; } return res; } static constexpr bool ExamineVal(unsigned int g){ unsigned int t = MOD - 1; for(u64 d=2; d*d<=t; d++) if(t % d == 0){ if(powm(g, (MOD - 1) / d) == 1) return false; while(t % d == 0) t /= d; } if(t != 1) if(powm(g, (MOD - 1) / t) == 1) return false; return true; } static constexpr unsigned int GetVal(){ for(unsigned int x=2; x<MOD; x++) if(ExamineVal(x)) return x; return 0; } static const unsigned int val = GetVal(); }; } // namespace nachia #line 3 "nachia\\math\\combination.hpp" namespace nachia{ template<class Modint> class Comb{ private: std::vector<Modint> F; std::vector<Modint> iF; public: void extend(int newN){ int prevN = (int)F.size() - 1; if(prevN >= newN) return; F.resize(newN+1); iF.resize(newN+1); for(int i=prevN+1; i<=newN; i++) F[i] = F[i-1] * Modint::raw(i); iF[newN] = F[newN].inv(); for(int i=newN; i>prevN; i--) iF[i-1] = iF[i] * Modint::raw(i); } Comb(int n = 1){ F.assign(2, Modint(1)); iF.assign(2, Modint(1)); extend(n); } Modint factorial(int n) const { return F[n]; } Modint invFactorial(int n) const { return iF[n]; } Modint invOf(int n) const { return iF[n] * F[n-1]; } Modint comb(int n, int r) const { if(n < 0 || n < r || r < 0) return Modint(0); return F[n] * iF[r] * iF[n-r]; } Modint invComb(int n, int r) const { if(n < 0 || n < r || r < 0) return Modint(0); return iF[n] * F[r] * F[n-r]; } Modint perm(int n, int r) const { if(n < 0 || n < r || r < 0) return Modint(0); return F[n] * iF[n-r]; } Modint invPerm(int n, int r) const { if(n < 0 || n < r || r < 0) return Modint(0); return iF[n] * F[n-r]; } Modint operator()(int n, int r) const { return comb(n,r); } }; } // namespace nachia #line 4 "nachia\\misc\\bit-operations.hpp" namespace nachia{ int Popcount(unsigned long long c) noexcept { #ifdef __GNUC__ return __builtin_popcountll(c); #else c = (c & (~0ull/3)) + ((c >> 1) & (~0ull/3)); c = (c & (~0ull/5)) + ((c >> 2) & (~0ull/5)); c = (c & (~0ull/17)) + ((c >> 4) & (~0ull/17)); c = (c * (~0ull/257)) >> 56; return c; #endif } // please ensure x != 0 int MsbIndex(unsigned long long x) noexcept { #ifdef __GNUC__ return 63 - __builtin_clzll(x); #else int res = 0; for(int d=32; d>0; d>>=1) if(x >> d){ res |= d; x >>= d; } return res; #endif } // please ensure x != 0 int LsbIndex(unsigned long long x) noexcept { #ifdef __GNUC__ return __builtin_ctzll(x); #else return MsbIndex(x & -x); #endif } } #line 2 "nachia\\fps\\ntt-interface.hpp" namespace nachia { template<class mint> struct NttInterface{ template<class Iter> void Butterfly(Iter, int) const {} template<class Iter> void IButterfly(Iter, int) const {} template<class Iter> void BitReversal(Iter a, int N) const { for(int i=0, j=0; j<N; j++){ if(i < j) std::swap(a[i], a[j]); for(int k = N>>1; k > (i^=k); k>>=1); } } }; } // namespace nachia #line 5 "nachia\\fps\\ntt-acl.hpp" #include <iterator> #line 8 "nachia\\fps\\ntt-acl.hpp" #include <array> namespace nachia{ constexpr int bsf_constexpr(unsigned int n) { int x = 0; while (!(n & (1 << x))) x++; return x; } template <class mint> struct NttFromAcl : NttInterface<mint> { using u32 = unsigned int; using u64 = unsigned long long; static int ceil_pow2(int n) { int x = 0; while ((1U << x) < (u32)(n)) x++; return x; } struct fft_info { static constexpr u32 g = nachia::PrimitiveRoot<mint::mod()>::val; static constexpr int rank2 = bsf_constexpr(mint::mod()-1); std::array<mint, rank2+1> root; std::array<mint, rank2+1> iroot; std::array<mint, std::max(0, rank2-1)> rate2; std::array<mint, std::max(0, rank2-1)> irate2; std::array<mint, std::max(0, rank2-2)> rate3; std::array<mint, std::max(0, rank2-2)> irate3; fft_info(){ root[rank2] = mint(g).pow((mint::mod() - 1) >> rank2); iroot[rank2] = root[rank2].inv(); for(int i=rank2-1; i>=0; i--){ root[i] = root[i+1] * root[i+1]; iroot[i] = iroot[i+1] * iroot[i+1]; } mint prod = 1, iprod = 1; for(int i=0; i<=rank2-2; i++){ rate2[i] = root[i+2] * prod; irate2[i] = iroot[i+2] * iprod; prod *= iroot[i+2]; iprod *= root[i+2]; } prod = 1; iprod = 1; for(int i=0; i<=rank2-3; i++){ rate3[i] = root[i+3] * prod; irate3[i] = iroot[i+3] * iprod; prod *= iroot[i+3]; iprod *= root[i+3]; } } }; template<class RandomAccessIterator> void Butterfly(RandomAccessIterator a, int n) const { int h = ceil_pow2(n); static const fft_info info; int len = 0; while(len < h){ if(h-len == 1){ int p = 1 << (h-len-1); mint rot = 1; for(int s=0; s<(1<<len); s++){ int offset = s << (h-len); for(int i=0; i<p; i++){ auto l = a[i+offset]; auto r = a[i+offset+p] * rot; a[i+offset] = l+r; a[i+offset+p] = l-r; } if(s+1 != (1<<len)) rot *= info.rate2[LsbIndex(~(u32)(s))]; } len++; } else { int p = 1 << (h-len-2); mint rot = 1, imag = info.root[2]; for(int s=0; s<(1<<len); s++){ mint rot2 = rot * rot; mint rot3 = rot2 * rot; int offset = s << (h-len); for(int i=0; i<p; i++){ auto mod2 = 1ULL * mint::mod() * mint::mod(); auto a0 = 1ULL * a[i+offset].val(); auto a1 = 1ULL * a[i+offset+p].val() * rot.val(); auto a2 = 1ULL * a[i+offset+2*p].val() * rot2.val(); auto a3 = 1ULL * a[i+offset+3*p].val() * rot3.val(); auto a1na3imag = 1ULL * mint(a1 + mod2 - a3).val() * imag.val(); auto na2 = mod2 - a2; a[i+offset] = a0 + a2 + a1 + a3; a[i+offset+1*p] = a0 + a2 + (2 * mod2 - (a1 + a3)); a[i+offset+2*p] = a0 + na2 + a1na3imag; a[i+offset+3*p] = a0 + na2 + (mod2 - a1na3imag); } if(s+1 != (1<<len)) rot *= info.rate3[LsbIndex(~(u32)(s))]; } len += 2; } } } template<class RandomAccessIterator> void IButterfly(RandomAccessIterator a, int n) const { int h = ceil_pow2(n); static const fft_info info; constexpr int MOD = mint::mod(); int len = h; while(len){ if(len == 1){ int p = 1 << (h-len); mint irot = 1; for(int s=0; s<(1<<(len-1)); s++){ int offset = s << (h-len+1); for(int i=0; i<p; i++){ auto l = a[i+offset]; auto r = a[i+offset+p]; a[i+offset] = l+r; a[i+offset+p] = (u64)(MOD + l.val() - r.val()) * irot.val(); } if(s+1 != (1<<(len-1))) irot *= info.irate2[LsbIndex(~(u32)(s))]; } len--; } else { int p = 1 << (h-len); mint irot = 1, iimag = info.iroot[2]; for(int s=0; s<(1<<(len-2)); s++){ mint irot2 = irot * irot; mint irot3 = irot2 * irot; int offset = s << (h-len+2); for(int i=0; i<p; i++){ auto a0 = 1ULL * a[i+offset+0*p].val(); auto a1 = 1ULL * a[i+offset+1*p].val(); auto a2 = 1ULL * a[i+offset+2*p].val(); auto a3 = 1ULL * a[i+offset+3*p].val(); auto a2na3iimag = 1ULL * mint((MOD + a2 - a3) * iimag.val()).val(); a[i+offset] = a0 + a1 + a2 + a3; a[i+offset+1*p] = (a0 + (MOD - a1) + a2na3iimag) * irot.val(); a[i+offset+2*p] = (a0 + a1 + (MOD - a2) + (MOD - a3)) * irot2.val(); a[i+offset+3*p] = (a0 + (MOD - a1) + (MOD - a2na3iimag)) * irot3.val(); } if(s+1 != (1<<(len-2))) irot *= info.irate3[LsbIndex(~(u32)(s))]; } len -= 2; } } } }; } // namespace nachia #line 11 "nachia\\fps\\fps-struct.hpp" namespace nachia { template<class Elem, class NttInst = NttFromAcl<Elem>> struct FpsNtt { public: using Fps = FpsNtt; using ElemTy = Elem; static constexpr unsigned int MOD = Elem::mod(); static constexpr int CONV_THRES = 30; static const NttInst nttInst; static const unsigned int zeta = nachia::PrimitiveRoot<MOD>::GetVal(); private: using u32 = unsigned int; static Elem ZeroElem() noexcept { return Elem(0); } static Elem OneElem() noexcept { return Elem(1); } static Comb<Elem> comb; std::vector<Elem> a; int RSZ(int& sz) const { return sz = (sz < 0 ? size() : sz); } public: int size() const noexcept { return a.size(); } Elem& operator[](int x) noexcept { return a[x]; } const Elem& operator[](int x) const noexcept { return a[x]; } Elem getCoeff(int x) const noexcept { return (0 <= x && x < size()) ? a[x] : ZeroElem(); } static Comb<Elem>& GetComb() { return comb; } static int BestNttSize(int x) noexcept { assert(x); return 1 << MsbIndex(x*2-1); } Fps move(){ return std::move(*this); } Fps& set(int i, Elem c){ a[i] = c; return *this; } Fps& removeLeadingZeros(){ int newsz = size(); while(newsz && a[newsz-1].val() == 0) newsz--; a.resize(newsz); if((int)a.capacity() / 4 > newsz) a.shrink_to_fit(); return *this; } FpsNtt(){} FpsNtt(int sz) : a(sz, ZeroElem()) {} FpsNtt(std::vector<Elem>&& src) : a(std::move(src)) {} FpsNtt(const std::vector<Elem>& src) : a(src) {} Fps& ntt() { capSize(BestNttSize(size())); nttInst.Butterfly(a.begin(), size()); return *this; } Fps& intt() { nttInst.IButterfly(a.begin(), a.size()); return times(Elem::raw(size()).inv()); } Fps nttDouble(Fps vanilla) const { int n = size(); assert(n == (n&-n)); // n is a power of 2 Elem q = Elem::raw(zeta).pow((Elem::mod() - 1) / (n*2)); Elem qq = OneElem(); for(int i=0; i<n; i++){ vanilla[i] *= qq; qq *= q; } vanilla.ntt(); Fps res = clip(0, n*2); for(int i=0; i<n; i++) res[n+i] = vanilla[i]; return res; } Fps nttDouble() const { return nttDouble(clip().intt().move()); } // Fps res(resSz); // for(int j=0; j<resSz-destL && j+srcL < srcR; j++) res[j+destL] = a.getCoeff(j+srcL) // if srcR is unspecified -> srcR = max(srcL, size()); // if resSz is unspecified -> resSz = destL + srcR - srcL Fps clip(int srcL, int srcR = -1, int destL = 0, int resSz = -1) const { srcR = RSZ(srcR); if(resSz < 0) resSz = destL + srcR - srcL; int rj = std::min(std::min(srcR, size()) - srcL, resSz - destL); Fps res(resSz); for(int j=std::max(0, -srcL); j<rj; j++) res[j+destL] = a[j+srcL]; return res; } Fps clip() const { return *this; } Fps& capSize(int l, int r) { if(r <= (int)size()) a.resize(r); if(size() <= l) a.resize(l, ZeroElem()); return *this; } Fps& capSize(int z){ a.resize(RSZ(z), ZeroElem()); return *this; } Fps& times(Elem x){ for(int i=0; i<size(); i++){ a[i] *= x; } return *this; } Fps& timesFactorial(int z = -1){ comb.extend(RSZ(z)); for(int i=0; i<z; i++){ a[i] *= comb.factorial(i); } return *this; } Fps& timesInvFactorial(int z = -1){ comb.extend(RSZ(z)); for(int i=0; i<z; i++){ a[i] *= comb.invFactorial(i); } return *this; } Fps& clrRange(int l, int r){ for(int i=l; i<r; i++){ a[i] = ZeroElem(); } return *this; } Fps& negate(){ for(auto& e : a){ e = -e; } return *this; } Fps& mulEach(const Fps& other, int maxi = -1){ maxi = std::min(RSZ(maxi), std::min(size(), other.size())); for(int i=0; i<maxi; i++) a[i] *= other[i]; return *this; } Fps& reverse(int sz = -1){ RSZ(sz); std::reverse(a.begin(), a.begin() + sz); return *this; } static Fps convolution(const Fps& a, const Fps& b, int sz = -1){ if(std::min(a.size(), b.size()) <= CONV_THRES){ if(a.size() > b.size()) return convolution(b, a, sz); if(sz < 0) sz = std::max(0, a.size() + b.size() - 1); std::vector<Elem> res(sz); for(int i=0; i<a.size(); i++) for(int j=0; j<b.size() && i+j<sz; j++) res[i+j] += a[i] * b[j]; return res; } int Z = BestNttSize(a.size() + b.size() - 1); return a.clip(0, Z).ntt().mulEach(b.clip(0, Z).ntt()).intt().capSize(sz).move(); } Fps convolve(const Fps& r, int sz = -1) const { return convolution(*this, r, sz); } // 1 // ----- = 1 + f + f^2 + f^3 + ... // 1-f Fps powerSum(int sz) const { RSZ(sz); if(sz == 0) return {}; int q = std::min(sz, 32); Fps x = Fps(q).set(0, OneElem()).move(); for(int i=1; i<q; i++) for(int j=1; j<=std::min(i,(int)a.size()-1); j++) x[i] += x[i-j] * a[j]; while(x.size() < sz){ int hN = x.size(), N = hN*2; Fps a = x.clip(0, N).ntt().move(); Fps b = clip(0, N).ntt().mulEach(a).intt().clrRange(0,hN).ntt().mulEach(a).intt().move(); for(int i=0; i<hN; i++) b[i] = x[i]; std::swap(b, x); } return x.capSize(sz).move(); } Fps inv(int sz = -1) const { RSZ(sz); Elem iA0 = a[0].inv(); return clip(0, std::min(sz, size())).times(-iA0).set(0, ZeroElem()).powerSum(sz).times(iA0).move(); } Fps& difference(){ if(size() == 0) return *this; for(int i=0; i+1<size(); i++) a[i] = a[i+1] * Elem::raw(i+1); return capSize(size()-1); } Fps& integral(){ if(size() == 0) return capSize(1); capSize(size()+1); comb.extend(size()); for(int i=size()-1; i>=1; i--) a[i] = a[i-1] * comb.invOf(i); return set(0, ZeroElem()); } Fps log(int sz = -1){ RSZ(sz); assert(sz != 0); assert(a[0].val() == 1); return convolution(inv(sz), clip().difference(), sz-1).integral(); } Fps exp(int sz = -1){ RSZ(sz); Fps res = Fps(1).set(0, OneElem()); while(res.size() < sz){ auto z = res.size(); auto tmp = res.capSize(z*2).log().set(0, -OneElem()).move(); for(int i=0; i<z*2 && i<size(); i++) tmp[i] -= a[i]; auto resntt = res.clip().ntt().mulEach(tmp.ntt()).intt().move(); for(int i=z; i<z*2; i++) res[i] = -resntt[i]; } return res.capSize(0, sz).move(); } Fps pow(unsigned long long k, int sz = -1){ int n = RSZ(sz); if(k == 0) return Fps(n).set(0, OneElem()).move(); int ctz = 0; while(ctz<n && a[ctz].val() == 0) ctz++; if((unsigned long long)ctz >= (n-1) / k + 1) return Fps(n); Elem a0 = a[ctz]; return clip(ctz, ctz+n-ctz*k).times(a0.inv()).log().times(Elem(k)).exp().times(a0.pow(k)).clip(0, -1, ctz*k); } auto begin(){ return a.begin(); } auto end(){ return a.end(); } auto begin() const { return a.begin(); } auto end() const { return a.end(); } std::string toString(std::string beg = "[ ", std::string delim = " ", std::string en = " ]") const { std::string res = beg; bool f = false; for(auto x : a){ if(f){ res += delim; } f = true; res += std::to_string(x.val()); } res += en; return res; } std::vector<Elem> getVectorMoved(){ return std::move(a); } Fps& operator+=(const Fps& r){ capSize(std::max(size(), r.size())); for(int i=0; i<r.size(); i++) a[i] += r[i]; return *this; } Fps& operator-=(const Fps& r){ capSize(std::max(size(), r.size())); for(int i=0; i<r.size(); i++) a[i] -= r[i]; return *this; } Fps operator+(const Fps& r) const { return (clip(0, std::max(size(), r.size())) += r).move(); } Fps operator-(const Fps& r) const { return (clip(0, std::max(size(), r.size())) -= r).move(); } Fps operator-() const { return (clip().negate()).move(); } Fps operator*(const Fps& r) const { return convolve(r).removeLeadingZeros().move(); } Fps& operator*=(const Fps& r){ return (*this) = operator*(r); } Fps& operator*=(Elem m){ return times(m); } Fps operator*(Elem m) const { return (clip() *= m).move(); } Elem eval(Elem x) const { Elem res = 0; for(int i=size()-1; i>=0; i--) res = res * x + a[i]; return res; } }; template<class Elem, class NttInst> Comb<Elem> FpsNtt<Elem, NttInst>::comb; template<class Elem, class NttInst> const NttInst FpsNtt<Elem, NttInst>::nttInst; } // namespace nachia #line 8 "Main.cpp" using namespace std; using i32 = int; using u32 = unsigned int; using i64 = long long; using u64 = unsigned long long; #define rep(i,n) for(int i=0; i<(int)(n); i++) const i64 INF = 1001001001001001001; using Modint = atcoder::static_modint<998244353>; int main(){ using Fps = nachia::FpsNtt<Modint>; auto comb = Fps::GetComb(); int M, N; cin >> M >> N; comb.extend(N+M); vector<int> Cnt(M); rep(i,N){ int a; cin >> a; a--; Cnt[a]++; } rep(i,Cnt.size()) if(Cnt[i] == 0){ swap(Cnt[i], Cnt.back()); i--; Cnt.pop_back(); } M = Cnt.size(); vector<Fps> fps(M); Fps invF = Fps(N+1); rep(i,N+1) invF[i] = comb.invFactorial(i); Fps invF2 = invF; rep(i,N+1) if(i%2 == 1) invF2[i] = -invF2[i]; rep(i,M) fps[i] = Fps(Cnt[i]+1).set(Cnt[i], 1); for(int i=0; i+1<(int)fps.size(); i+=2){ int z = fps[i].size() + fps[i+1].size() - 1; auto t = fps[i].convolve(invF.clip(0, z), z).mulEach(fps[i+1].convolve(invF.clip(0, z)), z); rep(i,z) t[i] *= comb.factorial(i); fps.push_back(t.convolve(invF2.clip(0, z), z)); } Modint res = 0; auto q = fps.back().move(); for(int i=0; i<q.size(); i++) res += q[i] * comb.factorial(i); cout << res.val() << '\n'; return 0; } struct ios_do_not_sync{ ios_do_not_sync(){ ios::sync_with_stdio(false); cin.tie(nullptr); } } ios_do_not_sync_instance;