結果
問題 | No.1011 Infinite Stairs |
ユーザー | masayoshi361 |
提出日時 | 2020-05-13 22:16:47 |
言語 | C++11 (gcc 11.4.0) |
結果 |
AC
|
実行時間 | 577 ms / 2,000 ms |
コード長 | 16,110 bytes |
コンパイル時間 | 3,728 ms |
コンパイル使用メモリ | 197,992 KB |
実行使用メモリ | 22,780 KB |
最終ジャッジ日時 | 2024-07-17 12:07:49 |
合計ジャッジ時間 | 6,108 ms |
ジャッジサーバーID (参考情報) |
judge2 / judge3 |
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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 | 2 ms
6,816 KB |
testcase_01 | AC | 2 ms
6,812 KB |
testcase_02 | AC | 7 ms
6,944 KB |
testcase_03 | AC | 276 ms
13,376 KB |
testcase_04 | AC | 61 ms
6,944 KB |
testcase_05 | AC | 577 ms
22,780 KB |
testcase_06 | AC | 2 ms
6,944 KB |
testcase_07 | AC | 8 ms
6,944 KB |
testcase_08 | AC | 2 ms
6,940 KB |
testcase_09 | AC | 3 ms
6,944 KB |
testcase_10 | AC | 8 ms
6,944 KB |
testcase_11 | AC | 62 ms
6,944 KB |
testcase_12 | AC | 8 ms
6,940 KB |
testcase_13 | AC | 64 ms
6,944 KB |
testcase_14 | AC | 3 ms
6,944 KB |
testcase_15 | AC | 62 ms
6,940 KB |
testcase_16 | AC | 276 ms
13,112 KB |
testcase_17 | AC | 15 ms
6,940 KB |
testcase_18 | AC | 271 ms
12,548 KB |
testcase_19 | AC | 8 ms
6,940 KB |
testcase_20 | AC | 4 ms
6,940 KB |
testcase_21 | AC | 130 ms
8,168 KB |
testcase_22 | AC | 131 ms
8,200 KB |
testcase_23 | AC | 131 ms
8,380 KB |
testcase_24 | AC | 129 ms
8,232 KB |
testcase_25 | AC | 130 ms
8,288 KB |
testcase_26 | AC | 63 ms
6,940 KB |
ソースコード
//header #ifdef LOCAL #include "cxx-prettyprint-master/prettyprint.hpp" #define debug(x) cout << x << endl #else #define debug(...) 42 #endif #pragma GCC optimize("Ofast") #include <bits/stdc++.h> //types using namespace std; using ll = long long; using ul = unsigned long long; using ld = long double; typedef pair < ll , ll > Pl; typedef pair < int, int > Pi; typedef vector<ll> vl; typedef vector<int> vi; template< typename T > using mat = vector< vector< T > >; template< int mod > struct modint { int x; modint() : x(0) {} modint(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {} modint &operator+=(const modint &p) { if((x += p.x) >= mod) x -= mod; return *this; } modint &operator-=(const modint &p) { if((x += mod - p.x) >= mod) x -= mod; return *this; } modint &operator*=(const modint &p) { x = (int) (1LL * x * p.x % mod); return *this; } modint &operator/=(const modint &p) { *this *= p.inverse(); return *this; } modint operator-() const { return modint(-x); } modint operator+(const modint &p) const { return modint(*this) += p; } modint operator-(const modint &p) const { return modint(*this) -= p; } modint operator*(const modint &p) const { return modint(*this) *= p; } modint operator/(const modint &p) const { return modint(*this) /= p; } bool operator==(const modint &p) const { return x == p.x; } bool operator!=(const modint &p) const { return x != p.x; } modint inverse() 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 modint(u); } modint pow(int64_t n) const { modint ret(1), mul(x); while(n > 0) { if(n & 1) ret *= mul; mul *= mul; n >>= 1; } return ret; } friend ostream &operator<<(ostream &os, const modint &p) { return os << p.x; } friend istream &operator>>(istream &is, modint &a) { int64_t t; is >> t; a = modint< mod >(t); return (is); } static int get_mod() { return mod; } }; //abreviations #define all(x) (x).begin(), (x).end() #define rall(x) (x).rbegin(), (x).rend() #define rep_(i, a_, b_, a, b, ...) for (int i = (a), max_i = (b); i < max_i; i++) #define rep(i, ...) rep_(i, __VA_ARGS__, __VA_ARGS__, 0, __VA_ARGS__) #define SZ(x) ((int)(x).size()) #define pb(x) push_back(x) #define eb(x) emplace_back(x) #define mp make_pair #define print(x) cout << x << endl #define vsum(x) accumulate(x, 0LL) #define vmax(a) *max_element(all(a)) #define vmin(a) *min_element(all(a)) //functions ll gcd(ll a, ll b) { return b ? gcd(b, a%b) : a; } ll lcm(ll a, ll b) { return a/gcd(a, b)*b;} template<class T>bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; } template<class T>bool chmin(T &a, const T &b) { if (b<a) { a=b; return 1; } return 0; } template< typename T > T mypow(T x, ll n) { T ret = 1; while(n > 0) { if(n & 1) (ret *= x); (x *= x); n >>= 1; } return ret; } ll modpow(ll x, ll n, const ll mod) { ll ret = 1; while(n > 0) { if(n & 1) (ret *= x); (x *= x); n >>= 1; x%=mod; ret%=mod; } return ret; } uint64_t my_rand(void) { static uint64_t x = 88172645463325252ULL; x = x ^ (x << 13); x = x ^ (x >> 7); return x = x ^ (x << 17); } //graph template template< typename T > struct edge { int src, to; T cost; edge(int to, T cost) : src(-1), to(to), cost(cost) {} edge(int src, int to, T cost) : src(src), to(to), cost(cost) {} edge &operator=(const int &x) { to = x; return *this; } operator int() const { return to; } }; template< typename T > using Edges = vector< edge< T > >; template< typename T > using WeightedGraph = vector< Edges< T > >; using UnWeightedGraph = vector< vector< int > >; //constant #define INF 4001002003004005006LL #define inf 1000000005 #define mod 1000000007LL //#define endl '\n' typedef modint<mod> mint; const long double eps = 0.001; const long double PI = 3.141592653589793; //library template< typename T > struct FormalPowerSeries : vector< T > { using vector< T >::vector; using P = FormalPowerSeries; using MULT = function< P(P, P) >; static MULT &get_mult() { static MULT mult = nullptr; return mult; } static void set_fft(MULT f) { get_mult() = f; } void shrink() { while(this->size() && this->back() == T(0)) this->pop_back(); } P operator+(const P &r) const { return P(*this) += r; } P operator+(const T &v) const { return P(*this) += v; } P operator-(const P &r) const { return P(*this) -= r; } P operator-(const T &v) const { return P(*this) -= v; } P operator*(const P &r) const { return P(*this) *= r; } P operator*(const T &v) const { return P(*this) *= v; } P operator/(const P &r) const { return P(*this) /= r; } P operator%(const P &r) const { return P(*this) %= r; } P &operator+=(const P &r) { if(r.size() > this->size()) this->resize(r.size()); for(int i = 0; i < r.size(); i++) (*this)[i] += r[i]; return *this; } P &operator+=(const T &r) { if(this->empty()) this->resize(1); (*this)[0] += r; return *this; } P &operator-=(const P &r) { if(r.size() > this->size()) this->resize(r.size()); for(int i = 0; i < r.size(); i++) (*this)[i] -= r[i]; shrink(); return *this; } P &operator-=(const T &r) { if(this->empty()) this->resize(1); (*this)[0] -= r; shrink(); return *this; } P &operator*=(const T &v) { const int n = (int) this->size(); for(int k = 0; k < n; k++) (*this)[k] *= v; return *this; } P &operator*=(const P &r) { if(this->empty() || r.empty()) { this->clear(); return *this; } assert(get_mult() != nullptr); return *this = get_mult()(*this, r); } P &operator%=(const P &r) { return *this -= *this / r * r; } P operator-() const { P ret(this->size()); for(int i = 0; i < this->size(); i++) ret[i] = -(*this)[i]; return ret; } P &operator/=(const P &r) { if(this->size() < r.size()) { this->clear(); return *this; } int n = this->size() - r.size() + 1; return *this = (rev().pre(n) * r.rev().inv(n)).pre(n).rev(n); } P pre(int sz) const { return P(begin(*this), begin(*this) + min((int) this->size(), sz)); } P operator>>(int sz) const { if(this->size() <= sz) return {}; P ret(*this); ret.erase(ret.begin(), ret.begin() + sz); return ret; } P operator<<(int sz) const { P ret(*this); ret.insert(ret.begin(), sz, T(0)); return ret; } P rev(int deg = -1) const { P ret(*this); if(deg != -1) ret.resize(deg, T(0)); reverse(begin(ret), end(ret)); return ret; } P diff() const { const int n = (int) this->size(); P ret(max(0, n - 1)); for(int i = 1; i < n; i++) ret[i - 1] = (*this)[i] * T(i); return ret; } P integral() const { const int n = (int) this->size(); P ret(n + 1); ret[0] = T(0); for(int i = 0; i < n; i++) ret[i + 1] = (*this)[i] / T(i + 1); return ret; } // F(0) must not be 0 P inv(int deg = -1) const { assert(((*this)[0]) != T(0)); const int n = (int) this->size(); if(deg == -1) deg = n; P ret({T(1) / (*this)[0]}); for(int i = 1; i < deg; i <<= 1) { ret = (ret + ret - ret * ret * pre(i << 1)).pre(i << 1); } return ret.pre(deg); } // F(0) must be 1 P log(int deg = -1) const { assert((*this)[0] == 1); const int n = (int) this->size(); if(deg == -1) deg = n; return (this->diff() * this->inv(deg)).pre(deg - 1).integral(); } P sqrt(int deg = -1) const { const int n = (int) this->size(); if(deg == -1) deg = n; if((*this)[0] == T(0)) { for(int i = 1; i < n; i++) { if((*this)[i] != T(0)) { if(i & 1) return {}; if(deg - i / 2 <= 0) break; auto ret = (*this >> i).sqrt(deg - i / 2) << (i / 2); if(ret.size() < deg) ret.resize(deg, T(0)); return ret; } } return P(deg, 0); } P ret({T(1)}); T inv2 = T(1) / T(2); for(int i = 1; i < deg; i <<= 1) { ret = (ret + pre(i << 1) * ret.inv(i << 1)) * inv2; } return ret.pre(deg); } // F(0) must be 0 P exp(int deg = -1) const { assert((*this)[0] == T(0)); const int n = (int) this->size(); if(deg == -1) deg = n; P ret({T(1)}); for(int i = 1; i < deg; i <<= 1) { ret = (ret * (pre(i << 1) + T(1) - ret.log(i << 1))).pre(i << 1); } return ret.pre(deg); } P pow(int64_t k, int deg = -1) const { const int n = (int) this->size(); if(deg == -1) deg = n; for(int i = 0; i < n; i++) { if((*this)[i] != T(0)) { T rev = T(1) / (*this)[i]; P C(*this * rev); P D(n - i); for(int j = i; j < n; j++) D[j - i] = C[j]; D = (D.log() * k).exp() * (*this)[i].pow(k); P E(deg); if(i * k > deg) return E; auto S = i * k; for(int j = 0; j + S < deg && j < D.size(); j++) E[j + S] = D[j]; return E; } } return *this; } T eval(T x) const { T r = 0, w = 1; for(auto &v : *this) { r += w * v; w *= x; } return r; } }; /* how to use // you can use ntt instead. ArbitraryModConvolution<mint> arb; using FPS = FormalPowerSeries< mint >; auto mult = [&](const FPS::P &a, const FPS::P &b) { auto ret = arb.multiply(a, b); return FPS::P(ret.begin(), ret.end()); }; FPS::set_fft(mult); //example FormalPowerSeries< mint > X(K + 1); */ namespace FastFourierTransform { using real = double; struct C { real x, y; C() : x(0), y(0) {} C(real x, real y) : x(x), y(y) {} inline C operator+(const C &c) const { return C(x + c.x, y + c.y); } inline C operator-(const C &c) const { return C(x - c.x, y - c.y); } inline C operator*(const C &c) const { return C(x * c.x - y * c.y, x * c.y + y * c.x); } inline C conj() const { return C(x, -y); } }; const real PI = acosl(-1); int base = 1; vector< C > rts = { {0, 0}, {1, 0} }; vector< int > rev = {0, 1}; void ensure_base(int nbase) { if(nbase <= base) return; rev.resize(1 << nbase); rts.resize(1 << nbase); for(int i = 0; i < (1 << nbase); i++) { rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1)); } while(base < nbase) { real angle = PI * 2.0 / (1 << (base + 1)); for(int i = 1 << (base - 1); i < (1 << base); i++) { rts[i << 1] = rts[i]; real angle_i = angle * (2 * i + 1 - (1 << base)); rts[(i << 1) + 1] = C(cos(angle_i), sin(angle_i)); } ++base; } } void fft(vector< C > &a, int n) { assert((n & (n - 1)) == 0); int zeros = __builtin_ctz(n); ensure_base(zeros); int shift = base - zeros; for(int i = 0; i < n; i++) { if(i < (rev[i] >> shift)) { swap(a[i], a[rev[i] >> shift]); } } for(int k = 1; k < n; k <<= 1) { for(int i = 0; i < n; i += 2 * k) { for(int j = 0; j < k; j++) { C z = a[i + j + k] * rts[j + k]; a[i + j + k] = a[i + j] - z; a[i + j] = a[i + j] + z; } } } } vector< int64_t > multiply(const vector< int > &a, const vector< int > &b) { int need = (int) a.size() + (int) b.size() - 1; int nbase = 1; while((1 << nbase) < need) nbase++; ensure_base(nbase); int sz = 1 << nbase; vector< C > fa(sz); for(int i = 0; i < sz; i++) { int x = (i < (int) a.size() ? a[i] : 0); int y = (i < (int) b.size() ? b[i] : 0); fa[i] = C(x, y); } fft(fa, sz); C r(0, -0.25 / (sz >> 1)), s(0, 1), t(0.5, 0); for(int i = 0; i <= (sz >> 1); i++) { int j = (sz - i) & (sz - 1); C z = (fa[j] * fa[j] - (fa[i] * fa[i]).conj()) * r; fa[j] = (fa[i] * fa[i] - (fa[j] * fa[j]).conj()) * r; fa[i] = z; } for(int i = 0; i < (sz >> 1); i++) { C A0 = (fa[i] + fa[i + (sz >> 1)]) * t; C A1 = (fa[i] - fa[i + (sz >> 1)]) * t * rts[(sz >> 1) + i]; fa[i] = A0 + A1 * s; } fft(fa, sz >> 1); vector< int64_t > ret(need); for(int i = 0; i < need; i++) { ret[i] = llround(i & 1 ? fa[i >> 1].y : fa[i >> 1].x); } return ret; } }; template< typename T > struct ArbitraryModConvolution { using real = FastFourierTransform::real; using C = FastFourierTransform::C; ArbitraryModConvolution() = default; vector< T > multiply(const vector< T > &a, const vector< T > &b, int need = -1) { if(need == -1) need = a.size() + b.size() - 1; int nbase = 0; while((1 << nbase) < need) nbase++; FastFourierTransform::ensure_base(nbase); int sz = 1 << nbase; vector< C > fa(sz); for(int i = 0; i < a.size(); i++) { fa[i] = C(a[i].x & ((1 << 15) - 1), a[i].x >> 15); } fft(fa, sz); vector< C > fb(sz); if(a == b) { fb = fa; } else { for(int i = 0; i < b.size(); i++) { fb[i] = C(b[i].x & ((1 << 15) - 1), b[i].x >> 15); } fft(fb, sz); } real ratio = 0.25 / sz; C r2(0, -1), r3(ratio, 0), r4(0, -ratio), r5(0, 1); for(int i = 0; i <= (sz >> 1); i++) { int j = (sz - i) & (sz - 1); C a1 = (fa[i] + fa[j].conj()); C a2 = (fa[i] - fa[j].conj()) * r2; C b1 = (fb[i] + fb[j].conj()) * r3; C b2 = (fb[i] - fb[j].conj()) * r4; if(i != j) { C c1 = (fa[j] + fa[i].conj()); C c2 = (fa[j] - fa[i].conj()) * r2; C d1 = (fb[j] + fb[i].conj()) * r3; C d2 = (fb[j] - fb[i].conj()) * r4; fa[i] = c1 * d1 + c2 * d2 * r5; fb[i] = c1 * d2 + c2 * d1; } fa[j] = a1 * b1 + a2 * b2 * r5; fb[j] = a1 * b2 + a2 * b1; } fft(fa, sz); fft(fb, sz); vector< T > ret(need); for(int i = 0; i < need; i++) { int64_t aa = llround(fa[i].x); int64_t bb = llround(fb[i].x); int64_t cc = llround(fa[i].y); aa = T(aa).x, bb = T(bb).x, cc = T(cc).x; ret[i] = aa + (bb << 15) + (cc << 30); } return ret; } }; const int mx = 100000; int main(){ cin.tie(0); ios::sync_with_stdio(0); cout << setprecision(20); ArbitraryModConvolution<mint> arb; using FPS = FormalPowerSeries< mint >; auto mult = [&](const FPS::P &a, const FPS::P &b) { auto ret = arb.multiply(a, b); return FPS::P(ret.begin(), ret.end()); }; FPS::set_fft(mult); int n, d, k; cin>>n>>d>>k; FormalPowerSeries<mint> F(k+1); rep(i, 1, d+1){ if(i<=k)F[i] = 1; } cout << F.pow(n)[k] << endl; }