結果

問題 No.940 ワープ ε=ε=ε=ε=ε=│;p>д<│
ユーザー sigma425sigma425
提出日時 2019-12-03 14:57:32
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 2,375 ms / 5,000 ms
コード長 15,657 bytes
コンパイル時間 2,756 ms
コンパイル使用メモリ 225,248 KB
実行使用メモリ 198,288 KB
最終ジャッジ日時 2024-05-06 08:18:23
合計ジャッジ時間 18,835 ms
ジャッジサーバーID
(参考情報)
judge5 / judge1
このコードへのチャレンジ
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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 76 ms
42,752 KB
testcase_01 AC 76 ms
42,752 KB
testcase_02 AC 74 ms
42,752 KB
testcase_03 AC 94 ms
44,856 KB
testcase_04 AC 73 ms
42,496 KB
testcase_05 AC 82 ms
43,824 KB
testcase_06 AC 76 ms
43,136 KB
testcase_07 AC 77 ms
43,264 KB
testcase_08 AC 77 ms
43,264 KB
testcase_09 AC 77 ms
43,264 KB
testcase_10 AC 77 ms
43,264 KB
testcase_11 AC 77 ms
43,008 KB
testcase_12 AC 81 ms
43,740 KB
testcase_13 AC 76 ms
43,264 KB
testcase_14 AC 73 ms
42,752 KB
testcase_15 AC 477 ms
81,548 KB
testcase_16 AC 2,045 ms
198,288 KB
testcase_17 AC 659 ms
81,548 KB
testcase_18 AC 722 ms
81,548 KB
testcase_19 AC 651 ms
81,420 KB
testcase_20 AC 795 ms
81,548 KB
testcase_21 AC 601 ms
81,548 KB
testcase_22 AC 1,240 ms
120,332 KB
testcase_23 AC 979 ms
120,336 KB
testcase_24 AC 1,223 ms
120,332 KB
testcase_25 AC 2,318 ms
198,288 KB
testcase_26 AC 2,375 ms
198,164 KB
権限があれば一括ダウンロードができます

ソースコード

diff #

#include <bits/stdc++.h>
#define rep(i,n) for(int i=0;i<(int)(n);i++)
#define rep1(i,n) for(int i=1;i<=(int)(n);i++)
#define all(c) c.begin(),c.end()
#define pb push_back
#define fs first
#define sc second
#define chmin(x,y) x=min(x,y)
#define chmax(x,y) x=max(x,y)
using namespace std;
template<class S,class T> ostream& operator<<(ostream& o,const pair<S,T> &p){
	return o<<"("<<p.fs<<","<<p.sc<<")";
}
template<class T> ostream& operator<<(ostream& o,const vector<T> &vc){
	o<<"{";
	for(const T& v:vc) o<<v<<",";
	o<<"}";
	return o;
}
using ll = long long;
template<class T> using V = vector<T>;
template<class T> using VV = vector<vector<T>>;
constexpr ll TEN(int n) { return (n == 0) ? 1 : 10 * TEN(n-1); }

#ifdef LOCAL
#define show(x) cerr << "LINE" << __LINE__ << " : " << #x << " = " << (x) << endl
#else
#define show(x) true
#endif

template<unsigned int mod_>
struct ModInt{
	using uint = unsigned int;
	using ll = long long;
	using ull = unsigned long long;

	constexpr static uint mod = mod_;

	uint v;
	ModInt():v(0){}
	ModInt(ll _v):v(normS(_v%mod+mod)){}
	explicit operator bool() const {return v!=0;}
	static uint normS(const uint &x){return (x<mod)?x:x-mod;}		// [0 , 2*mod-1] -> [0 , mod-1]
	static ModInt make(const uint &x){ModInt m; m.v=x; return m;}
	ModInt operator+(const ModInt& b) const { return make(normS(v+b.v));}
	ModInt operator-(const ModInt& b) const { return make(normS(v+mod-b.v));}
	ModInt operator-() const { return make(normS(mod-v)); }
	ModInt operator*(const ModInt& b) const { return make((ull)v*b.v%mod);}
	ModInt operator/(const ModInt& b) const { return *this*b.inv();}
	ModInt& operator+=(const ModInt& b){ return *this=*this+b;}
	ModInt& operator-=(const ModInt& b){ return *this=*this-b;}
	ModInt& operator*=(const ModInt& b){ return *this=*this*b;}
	ModInt& operator/=(const ModInt& b){ return *this=*this/b;}
	ModInt& operator++(int){ return *this=*this+1;}
	ModInt& operator--(int){ return *this=*this-1;}
	ll extgcd(ll a,ll b,ll &x,ll &y) const{
		ll p[]={a,1,0},q[]={b,0,1};
		while(*q){
			ll t=*p/ *q;
			rep(i,3) swap(p[i]-=t*q[i],q[i]);
		}
		if(p[0]<0) rep(i,3) p[i]=-p[i];
		x=p[1],y=p[2];
		return p[0];
	}
	ModInt inv() const {
		ll x,y;
		extgcd(v,mod,x,y);
		return make(normS(x+mod));
	}
	ModInt pow(ll p) const {
		ModInt a = 1;
		ModInt x = *this;
		while(p){
			if(p&1) a *= x;
			x *= x;
			p >>= 1;
		}
		return a;
	}
	bool operator==(const ModInt& b) const { return v==b.v;}
	bool operator!=(const ModInt& b) const { return v!=b.v;}
	friend istream& operator>>(istream &o,ModInt& x){
		ll tmp;
		o>>tmp;
		x=ModInt(tmp);
		return o;
	}
	friend ostream& operator<<(ostream &o,const ModInt& x){ return o<<x.v;}
};
using mint = ModInt<1000000007>;


int bsr(int x) { return 31 - __builtin_clz(x); }
using D = double;
const D pi = acos(-1);
using Pc = complex<D>;

void fft(bool type, vector<Pc> &c){	//multiply : false -> mult -> true
	static vector<Pc> buf[30];
	int N = c.size();
	int s = bsr(N);
	assert(1<<s == N);
	if(buf[s].empty()){
		buf[s]=vector<Pc>(N);
		rep(i,N) buf[s][i] = polar<D>(1,i*2*pi/N);
	}
	vector<Pc> a(N),b(N);
	copy(begin(c),end(c),begin(a));
	rep1(i,s){
		int W = 1<<(s-i);
		for(int y=0;y<N/2;y+=W){
			Pc now = buf[s][y];
			if(type) now = conj(now);
			rep(x,W){
				auto l =       a[y<<1 | x];
				auto r = now * a[y<<1 | x | W];
				b[y | x]        = l+r;
				b[y | x | N>>1] = l-r;
			}
		}
		swap(a,b);
	}
	copy(begin(a),end(a),begin(c));
}
template<class Mint>
vector<Mint> multiply_fft(const vector<Mint>& x,const vector<Mint>& y){
	if(x.empty() || y.empty()) return {};
	const int B = 15;
	const int K = 2;
	int S = x.size()+y.size()-1;
	int N = 1; while(N<S) N*=2;
	vector<Pc> a[K],b[K];
	rep(t,K){
		a[t] = vector<Pc>(N);
		b[t] = vector<Pc>(N);
		rep(i,x.size()) a[t][i] = Pc( (x[i].v >> (t*B)) & ((1<<B)-1) , 0 );
		rep(i,y.size()) b[t][i] = Pc( (y[i].v >> (t*B)) & ((1<<B)-1) , 0 );
		fft(false,a[t]);
		fft(false,b[t]);
	}
	vector<Mint> z(S);
	vector<Pc> c(N);
	Mint base = 1;
	rep(t,K+K-1){
		fill_n(begin(c),N,Pc(0,0));
		rep(xt,K){
			int yt = t-xt;
			if(0<=yt && yt<K){
				rep(i,N) c[i] += a[xt][i] * b[yt][i];
			}
		}
		fft(true,c);
		rep(i,S){
			c[i] *= 1.0/N;
			z[i] += Mint(ll(round(c[i].real()))) * base;
		}
		base *= 1<<B;
	}
	return z;
}
template<class D>
struct Poly{
	vector<D> v;
	int size() const{ return v.size();}	//deg+1
	Poly(){}
	Poly(vector<D> _v) : v(_v){shrink();}

	Poly& shrink(){
		while(!v.empty()&&v.back()==D(0)) v.pop_back();
		return *this;
	}
	D at(int i) const{
		return (i<size())?v[i]:D(0);
	}
	void set(int i,const D& x){		//v[i] := x
		if(i>=size() && !x) return;
		while(i>=size()) v.push_back(D(0));
		v[i]=x;
		shrink();
		return;
	}
	D operator()(D x) const {
		D res = 0;
		int n = size();
		D a = 1;
		rep(i,n){
			res += a*v[i];
			a *= x;
		}
		return res;
	}

	Poly operator+(const Poly &r) const{
		int N=max(size(),r.size());
		vector<D> ret(N);
		rep(i,N) ret[i]=at(i)+r.at(i);
		return Poly(ret);
	}
	Poly operator-(const Poly &r) const{
		int N=max(size(),r.size());
		vector<D> ret(N);
		rep(i,N) ret[i]=at(i)-r.at(i);
		return Poly(ret);
	}
	Poly operator-() const{
		int N=size();
		vector<D> ret(N);
		rep(i,N) ret[i] = -at(i);
		return Poly(ret);
	}
	Poly operator*(const Poly &r) const{
		if(size()==0||r.size()==0) return Poly();
		return mul_fft(r);									// FFT or NTT ?
	}
	Poly operator*(const D &r) const{
		int N=size();
		vector<D> ret(N);
		rep(i,N) ret[i]=v[i]*r;
		return Poly(ret);
	}
	Poly operator/(const D &r) const{
		return *this * r.inv();
	}
	Poly operator/(const Poly &y) const{
		return div_fast(y);
	}
	Poly operator%(const Poly &y) const{
		return rem_fast(y);
//		return rem_naive(y);
	}
	Poly operator<<(const int &n) const{	// *=x^n
		assert(n>=0);
		int N=size();
		vector<D> ret(N+n);
		rep(i,N) ret[i+n]=v[i];
		return Poly(ret);
	}
	Poly operator>>(const int &n) const{	// /=x^n
		assert(n>=0);
		int N=size();
		if(N<=n) return Poly();
		vector<D> ret(N-n);
		rep(i,N-n) ret[i]=v[i+n];
		return Poly(ret);
	}
	bool operator==(const Poly &y) const{
		return v==y.v;
	}
	bool operator!=(const Poly &y) const{
		return v!=y.v;
	}

	Poly& operator+=(const Poly &r) {return *this = *this+r;}
	Poly& operator-=(const Poly &r) {return *this = *this-r;}
	Poly& operator*=(const Poly &r) {return *this = *this*r;}
	Poly& operator*=(const D &r) {return *this = *this*r;}
	Poly& operator/=(const Poly &r) {return *this = *this/r;}
	Poly& operator/=(const D &r) {return *this = *this/r;}
	Poly& operator%=(const Poly &y) {return *this = *this%y;}
	Poly& operator<<=(const int &n) {return *this = *this<<n;}
	Poly& operator>>=(const int &n) {return *this = *this>>n;}

	Poly diff() const {
		int n = size();
		if(n == 0) return Poly();
		V<D> u(n-1);
		rep(i,n-1) u[i] = at(i+1) * (i+1);
		return Poly(u);
	}
	Poly intg() const {
		int n = size();
		V<D> u(n+1);
		rep(i,n) u[i+1] = at(i) / (i+1);
		return Poly(u);
	}

	Poly pow(long long n, int L) const {		// f^n, ignoring x^L,x^{L+1},..
		Poly a({1});
		Poly x = *this;
		while(n){
			if(n&1){
				a *= x;
				a = a.strip(L);
			}
			x *= x;
			x = x.strip(L);
			n /= 2;
		}
		return a;
	}

	/*
		[x^0~n] exp(f) = 1 + f + f^2 / 2 + f^3 / 6 + ..
		f(0) should be 0

		O((N+n) log n)	(N = size())
		NTT, -O3
		- N = n = 100000 : 200 [ms]
		- N = n = 200000 : 400 [ms]
		- N = n = 500000 : 1000 [ms]
	*/
	Poly exp(int n) const {
		assert(at(0) == 0);
		Poly f({1}), g({1});
		for(int i=1;i<=n;i*=2){
			g = (g*2 - f*g*g).strip(i);
			Poly q = (this->diff()).strip(i-1);
			Poly w = (q + g * (f.diff() - f*q)) .strip(2*i-1);
			f = (f + f * (*this - w.intg()).strip(2*i)) .strip(2*i);
		}
		return f.strip(n+1);
	}

	/*
		[x^0~n] log(f) = log(1-(1-f)) = - (1-f) - (1-f)^2 / 2 - (1-f)^3 / 3 - ...
		f(0) should be 1
		O(n log n)

		NTT, -O3
		1e5 : 140 [ms]
		2e5 : 296 [ms]
		5e5 : 640 [ms]
		1e6 : 1343 [ms]
	*/
	Poly log(int n) const {
		assert(at(0) == 1);
		auto f = strip(n+1);
		return (f.diff() * f.inv(n)).strip(n).intg();
	}

	/*
		[x^0~n] sqrt(f)
		f(0) should be 1
		いや平方剰余なら何でもいいと思うけど探すのがめんどくさいので
		+- 2通りだけど 定数項が 1 の方
		O(n log n)

		NTT, -O3
		1e5 : 234 [ms]
		2e5 : 484 [ms]
		5e5 : 1000 [ms]
		1e6 : 2109 [ms]
	*/
	Poly sqrt(int n) const {
		assert(at(0) == 1);
		Poly f = strip(n+1);
		Poly g({1});
		for(int i=1; i<=n; i*=2){
			g = (g + f.strip(2*i)*g.inv(2*i-1)) / 2;
		}
		return g.strip(n+1);
	}

	/*
		[x^0~n] f^-1 = (1-(1-f))^-1 = (1-f) + (1-f)^2 + ...
		f * f.inv(n) = 1 + x^n * poly
		f(0) should be non0
		O(n log n)
	*/
	Poly inv(int n) const {
		assert(at(0) != 0);
		Poly f = strip(n+1);
		Poly g({at(0).inv()});
		for(int i=1; i<=n; i*=2){		//need to strip!!
			g *= (Poly({2}) - f.strip(2*i)*g).strip(2*i);
		}
		return g.strip(n+1);
	}	

	Poly exp_naive(int n) const {
		assert(at(0) == 0);
		Poly res;
		Poly fk({1});
		rep(k,n+1){
			res += fk;
			fk *= *this;
			fk = fk.strip(n+1) / (k+1);
		}
		return res;
	}
	Poly log_naive(int n) const {
		assert(at(0) == 1);
		Poly res;
		Poly g({1});
		rep1(k,n){
			g *= (Poly({1}) - *this);
			g = g.strip(n+1);
			res -= g / k;
		}
		return res;
	}


	Poly mul_naive(const Poly &r) const{
		int N=size(),M=r.size();
		vector<D> ret(N+M-1);
		rep(i,N) rep(j,M) ret[i+j]+=at(i)*r.at(j);
		return Poly(ret);
	}
	Poly mul_ntt(const Poly &r) const{
		return Poly(multiply_ntt(v,r.v));
	}
	Poly mul_fft(const Poly &r) const{
		return Poly(multiply_fft(v,r.v));
	}

	Poly div_fast_with_inv(const Poly &inv, int B) const {
		return (*this * inv)>>(B-1);
	}
	Poly div_fast(const Poly &y) const{
		if(size()<y.size()) return Poly();
		int n = size();
		return div_fast_with_inv(y.inv_div(n-1),n);
	}
	Poly rem_naive(const Poly &y) const{
		Poly x = *this;
		while(y.size()<=x.size()){
			int N=x.size(),M=y.size();
			D coef = x.v[N-1]/y.v[M-1];
			x -= (y<<(N-M))*coef;
		}
		return x;
	}
	Poly rem_fast(const Poly &y) const{
		return *this - y * div_fast(y);
	}
	Poly strip(int n) const {	//ignore x^n , x^n+1,...
		vector<D> res = v;
		res.resize(min(n,size()));
		return Poly(res);
	}
	Poly rev(int n = -1) const {	//ignore x^n ~  ->  return x^(n-1) * f(1/x)
		vector<D> res = v;
		if(n!=-1) res.resize(n);
		reverse(all(res));
		return Poly(res);
	}

	/*
		f.inv_div(n) = x^n / f
		f should be non0
		O((N+n) log n)

		for division
	*/
	Poly inv_div(int n) const {
		n++;
		int d = size() - 1;
		assert(d != -1);
		if(n < d) return Poly();
		Poly a = rev();
		Poly g({at(d).inv()});
		for(int i=1; i+d<=n; i*=2){		//need to strip!!
			g *= (Poly({2})-a.strip(2*i)*g).strip(2*i);
		}
		return g.rev(n-d);
	}


	friend ostream& operator<<(ostream &o,const Poly& x){
		if(x.size()==0) return o<<0;
		rep(i,x.size()) if(x.v[i]!=D(0)){
			o<<x.v[i]<<"x^"<<i;
			if(i!=x.size()-1) o<<" + ";
		}
		return o;
	}
};

V<mint> fact,ifact;
mint Choose(int a,int b){
	if(b<0 || a<b) return 0;
	return fact[a] * ifact[b] * ifact[a-b];
}
void InitFact(int N){
	fact.resize(N);
	ifact.resize(N);
	fact[0] = 1;
	rep1(i,N-1) fact[i] = fact[i-1] * i;
	ifact[N-1] = fact[N-1].inv();
	for(int i=N-2;i>=0;i--) ifact[i] = ifact[i+1] * (i+1);
}

vector<mint> extended(int n, const vector< vector<mint> >& coeffs, const vector<mint>& terms) {

	vector<mint> ret(max<int>(n + 1, terms.size()));
	copy(terms.begin(), terms.end(), ret.begin());
	const int order = coeffs.size() - 1;
	const int deg = coeffs[0].size() - 1;
	assert((int) terms.size() >= order);
	for (int m = terms.size(); m <= n; ++m) {
		mint s = 0;
		for (int i = 1; i <= order; ++i) {
			int k = m - i;
			mint t = ret[k];
			for (int d = 0; d <= deg; ++d) {
				s += t * coeffs[i][d];
				t *= k;
			}
		}
		mint denom = 0, mpow = 1;
		for (int d = 0; d <= deg; ++d) {
			denom += mpow * coeffs[0][d];
			mpow *= m;
		}
		ret[m] = -s/denom;
	}
	return ret;
}

vector< vector<mint> > find_recurrence_relation(vector<mint> terms, int deg, int ord = -1, bool verify=true) {

	if(ord != -1){		//given order
		int n = (deg+1)*(ord+1)+ord-1;
		while((int)terms.size()>n) terms.pop_back();
	}

	const int n = terms.size();
	const int B = (n + 2) / (deg + 2); // number of blocks
	const int C = B * (deg + 1); // number of columns
	const int R = n - (B - 1); // number of rows
	assert(B >= 2); assert(R >= C - 1);

	auto error = [] (int order, int deg) {
		fprintf(stderr, 
			"Error: Could not find a recurrence relation "
			"of order <= %d and degree <= %d.\n\n", 
			order, deg);
		assert(0);
	};

	vector< vector<mint> > mat(R, vector<mint>(C));
	for (int y = 0; y < R; ++y) {
		for (int b = 0; b < B; ++b) {
			mint v = terms[y+b];
			for (int d = 0; d <= deg; ++d) {
				mat[y][b * (deg + 1) + d] = v;
				v *= y+b;
			}
		}
	}

	int rank = 0;
	for (int x = 0; x < C; ++x) {
		int pivot = -1;
		for (int y = rank; y < R; ++y) if (mat[y][x] != 0) {
			pivot = y; break;
		}
		if (pivot < 0) break;
		if (pivot != rank) swap(mat[rank], mat[pivot]);
		mint inv = mat[rank][x].inv();
		for (int x2 = x; x2 < C; ++x2) mat[rank][x2] *= inv;
		for (int y = rank + 1; y < R; ++y) if (mat[y][x]) {
			mint c = -mat[y][x];
			for (int x2 = x; x2 < C; ++x2) {
				mat[y][x2] += c * mat[rank][x2];
			}
		}
		++rank;
	}

	if (rank == C) error(B - 1, deg);

	for (int y = rank - 1; y >= 0; --y) if (mat[y][rank]) {
		assert(mat[y][y] == 1);
		mint c = -mat[y][rank];
		for (int y2 = 0; y2 < y; ++y2) {
			mat[y2][rank] += c * mat[y2][y];
		}
	}

	int order = rank / (deg + 1);

	vector< vector<mint> > ret(order + 1, vector<mint>(deg + 1));
	ret[0][rank % (deg + 1)] = 1;
	for (int y = rank - 1; y >= 0; --y) {
		int k = order - y / (deg + 1), d = y % (deg + 1);
		ret[k][d] = -mat[y][rank];
	}

	if (verify) {
		auto extended_terms = extended(n - 1, ret, 
				vector<mint>(terms.begin(), terms.begin() + order));
		for (int i = 0; i < (int) terms.size(); ++i) {
			if (terms[i] != extended_terms[i]) error(B - 1, deg);
		}
	}

	auto verbose = [&] {
		int last = verify ? n - 1 : order + R - 1;
		fprintf(stderr, 
			"[ Found a recurrence relation ]\n"
			"- order %d\n"
			"- degree %d\n"
			"- verified up to a(%d) (number of non-trivial terms: %d)\n",
			order, deg, last, (last + 1) - ((deg + 2) * (order + 1) - 2)
		);
		fprintf(stderr, "{\n");
		for (int k = 0; k <= order; ++k) {
			fprintf(stderr, "  {");
			for (int d = 0; d <= deg; ++d) {
				if (d) fprintf(stderr, ", ");
				fprintf(stderr, "%d", ret[k][d].v);
			}
			fprintf(stderr, "}%s\n", k == order ? "" : ",");
		}
		fprintf(stderr, "}\n\n");
	};
	verbose();

	return ret;
}

void show_extended_sequence(int n, const vector<mint>& terms, int degree, int order = -1) {
	auto coeffs = find_recurrence_relation(terms, degree, order);
	auto extended_terms = extended(n, coeffs, terms);
	for (int i = 0; i < (int) extended_terms.size(); ++i) {
		printf("%d %d\n", i, extended_terms[i].v);
	}
	puts("");
}
V<mint> get_extended_sequence(int n, const vector<mint>& terms, int degree, int order = -1) {
	auto coeffs = find_recurrence_relation(terms, degree, order);
	return extended(n, coeffs, terms);
}
int main(){
	cin.tie(0);
	ios::sync_with_stdio(false);		//DON'T USE scanf/printf/puts !!
	cout << fixed << setprecision(20);
	InitFact(5000010);
	int X,Y,Z; cin >> X >> Y >> Z;
	int ZZ = Z;
	chmin(Z,100000);
	Poly<mint> y({1,-2,1});
	Poly<mint> f({1});
	while((int)f.size() < X+Y+Z+100){
		f *= (y + Poly<mint>({1}));
		y *= y;
	}
	show(f.size());

	mint ans = 0;
	if(X+Y+Z == 0){
		cout << 1 << endl;
		return 0;
	}
	
	V<mint> vals;
	rep(d,20){
		mint ans = 0;
		rep1(k,f.size()){
			ans += Choose(X+k-1,k-1) * Choose(Y+k-1,k-1) * Choose(Z+d+k-1,k-1) * f.at(k-1);
		}
		vals.pb(ans);
	}
	auto v = get_extended_sequence(ZZ-Z,vals,2,3);
	cout << v[ZZ-Z] << endl;
}
0