結果
問題 | No.2513 Power Eraser |
ユーザー |
👑 ![]() |
提出日時 | 2023-10-20 23:52:56 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 990 ms / 6,000 ms |
コード長 | 21,630 bytes |
コンパイル時間 | 1,813 ms |
コンパイル使用メモリ | 100,092 KB |
最終ジャッジ日時 | 2025-02-17 11:29:40 |
ジャッジサーバーID (参考情報) |
judge4 / judge5 |
(要ログイン)
ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 39 |
ソースコード
#line 1 "..\\Main.cpp"#include <iostream>#include <string>#include <vector>#include <algorithm>#include <atcoder/modint>#line 5 "D:\\Programming\\VSCode\\competitive-cpp\\nachia\\fps\\fps-ntt.hpp"#include <cassert>#line 3 "D:\\Programming\\VSCode\\competitive-cpp\\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 "D:\\Programming\\VSCode\\competitive-cpp\\nachia\\math\\combination.hpp"namespace nachia{template<class Modint>class Comb{private:static constexpr int MOD = Modint::mod();std::vector<Modint> F;std::vector<Modint> iF;public:void extend(int newN){int prevN = (int)F.size() - 1;if(newN >= MOD) newN = MOD - 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 "D:\\Programming\\VSCode\\competitive-cpp\\nachia\\misc\\bit-operations.hpp"namespace nachia{int Popcount(unsigned long long c) noexcept {#ifdef __GNUC__return __builtin_popcountll(c);#elsec = (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 != 0int MsbIndex(unsigned long long x) noexcept {#ifdef __GNUC__return 63 - __builtin_clzll(x);#elseusing u64 = unsigned long long;int q = (n >> 32) ? 32 : 0;auto m = n >> q;constexpr u64 hi = 0x8888'8888;constexpr u64 mi = 0x1111'1111;m = (((m | ~(hi - (m & ~hi))) & hi) * mi) >> 35;m = (((m | ~(hi - (n & ~hi))) & hi) * mi) >> 31;q += (m & 0xf) << 2;q += 0x3333'3333'2222'1100 >> (((n >> q) & 0xF) << 2) & 0xfreturn q;#endif}// please ensure x != 0int LsbIndex(unsigned long long x) noexcept {#ifdef __GNUC__return __builtin_ctzll(x);#elsereturn MsbIndex(x & -x);#endif}}#line 2 "D:\\Programming\\VSCode\\competitive-cpp\\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 "D:\\Programming\\VSCode\\competitive-cpp\\nachia\\fps\\ntt-acl.hpp"#include <iterator>#line 8 "D:\\Programming\\VSCode\\competitive-cpp\\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 "D:\\Programming\\VSCode\\competitive-cpp\\nachia\\fps\\fps-ntt.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(int sz, Elem e) : a(sz, e) {}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 2Elem 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 - srcLFps 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-fFps 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& EgfToOgf(){comb.extend(size());for(int i=0; i<size(); i++) a[i] *= comb.factorial(i);return *this;}Fps& OgfToEgf(){comb.extend(size());for(int i=0; i<size(); i++) a[i] *= comb.invFactorial(i);return *this;}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 4 "D:\\Programming\\VSCode\\competitive-cpp\\nachia\\fps\\polynomial-division.hpp"namespace nachia{// return polynomials have no leading zerostemplate<class Fps>std::pair<Fps, Fps> PolynomialDivision(Fps A,Fps D,bool do_get_remainder = true){D.removeLeadingZeros();auto dsize = D.size();assert(dsize != 0);if(A.size() == 0){ return std::make_pair(Fps(), Fps()); }if(A.size() < dsize){ return std::make_pair(Fps(), A.move()); }int n = A.size();int divSize = n - dsize + 1;D.reverse();A.reverse();auto invD = D.inv(divSize);auto tmp = A.clip(0, divSize).convolve(invD, divSize);if(!do_get_remainder || dsize == 1) return std::make_pair(tmp.reverse().move(), Fps());Fps tmp2 = tmp.convolve(D);Fps ans2(dsize - 1);for(int i=0; i<dsize-1; i++) ans2[i] = A[n-1-i] - tmp2[n-1-i];return std::make_pair(tmp.reverse().move(), ans2.removeLeadingZeros().move());}} // namespace nachia#line 8 "..\\Main.cpp"using Modint = atcoder::static_modint<998244353>;using namespace std;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 Fps = nachia::FpsNtt<Modint>;void testcase(){int N; cin >> N;vector<Modint> A(N);rep(i,N){ int a; cin >> a; A[i] = a; }Modint ans = 1;vector<Fps> subproduct; {auto dfs = [&](auto& dfs, int l, int r, int i) -> void {if(l + 1 == r){subproduct[i] = Fps(2).set(0,-A[l]).set(1,1).move();return;}int m = (l + r) / 2;int i1 = (int)subproduct.size();subproduct.push_back(Fps());dfs(dfs, l, m, i1);int i2 = (int)subproduct.size();subproduct.push_back(Fps());dfs(dfs, m, r, i2);subproduct[i] = subproduct[i1] * subproduct[i2];};subproduct.push_back(Fps());dfs(dfs, 0, N, 0);}int spsize = 0;auto dfs = [&](auto& dfs, int l, int r, Fps f, int i) -> Fps {if(f.size() >= subproduct[i].size()) f = nachia::PolynomialDivision(f.move(), subproduct[i]).second;if(l + 1 == r){ans *= f.eval(A[l]);return Fps(2).set(0,A[l]).set(1,-1);}int m = (l + r) / 2;int i1 = spsize++;auto qute1 = dfs(dfs, l, m, f, i1);int i2 = spsize++;auto qute2 = dfs(dfs, m, r, f * qute1, i2);return qute1 * qute2;};dfs(dfs, 0, N, Fps(1).set(0,1), spsize++);cout << ans.val() << endl;}int main(){ios::sync_with_stdio(false);cin.tie(nullptr);testcase();return 0;}