結果

問題 No.93 ペガサス
コンテスト
ユーザー maroon_kuri
提出日時 2019-06-07 00:55:41
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 56 ms / 5,000 ms
コード長 8,434 bytes
コンパイル時間 2,071 ms
コンパイル使用メモリ 183,036 KB
実行使用メモリ 44,288 KB
最終ジャッジ日時 2024-10-02 06:56:11
合計ジャッジ時間 3,911 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge5
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 4
other AC * 16
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>
using namespace std;

using uint=unsigned;
using ll=long long;
using ull=unsigned long long;
#define int ll

#define FOR(i,a,b) for(int i=int(a);i<int(b);i++)
#define rep(i,b) FOR(i,0,b)
#define ROF(i,a,b) for(int i=int(b)-1;i>=a;i--)
#define per(i,b) ROF(i,0,b)
#define mp make_pair
#define mt make_tuple
#define pb push_back
#define eb emplace_back
#define all(x) x.begin(),x.end()
auto& errStream=cerr;
#ifdef LOCAL
#define cerr (cerr<<"-- line "<<__LINE__<<" -- ")
#else
class CerrDummy{}cerrDummy;
template<class T>
CerrDummy& operator<<(CerrDummy&cd,const T&){
	return cd;
}
using charTDummy=char;
using traitsDummy=char_traits<charTDummy>;
CerrDummy& operator<<(CerrDummy&cd,basic_ostream<charTDummy,traitsDummy>&(basic_ostream<charTDummy,traitsDummy>&)){
	return cd;
}
#define cerr cerrDummy
#endif
#define reach cerr<<"reached"<<endl
void dmpr(decltype(cerr)&os){os<<endl;}
template<class T,class... Args>
void dmpr(decltype(cerr)&os,const T&t,const Args&... args){
	os<<t<<" ";
	dmpr(os,args...);
}
#define dmp(...) dmpr(cerr,##__VA_ARGS__)
#define zero(x) memset(x,0,sizeof(x))
#define one(x) memset(x,-1,sizeof(x))
#define fs first
#define sc second
#define bg begin()
#define ed end()

template<class T> using V=vector<T>;
template<class T> using VV=V<V<T>>;

using pi=pair<int,int>;
using vi=vector<int>;
using ld=long double;

template<class T,class U>
ostream& operator<<(ostream& os,const pair<T,U>& p){
	os<<"("<<p.first<<","<<p.second<<")";
	return os;
}

template<class T>
ostream& operator <<(ostream& os,const vector<T>& v){
	os<<"{";
	rep(i,(int)v.size()){
		if(i)os<<",";
		os<<v[i];
	}
	os<<"}";
	return os;
}

template<int i,class T>
void print_tuple(ostream&,const T&){
}

template<int i,class T,class H,class ...Args>
void print_tuple(ostream&os,const T&t){
	if(i)os<<",";
	os<<get<i>(t);
	print_tuple<i+1,T,Args...>(os,t);
}

template<class ...Args>
ostream& operator<<(ostream&os,const tuple<Args...>&t){
	os<<"(";
	print_tuple<0,tuple<Args...>,Args...>(os,t);
	return os<<")";
}

ll read(){
	ll i;
	scanf("%lld",&i);
	return i;
}

void printSpace(){
	printf(" ");
}

void printEoln(){
	printf("\n");
}

void print(ll x,int suc=1){
	printf("%lld",x);
	if(suc==1)
		printEoln();
	if(suc==2)
		printSpace();
}

vi readvi(int n,int off=0){
	vi v(n);
	rep(i,n)v[i]=read()+off;
	return v;
}

template<class T>
void print(const vector<T>&v,int suc=1){
	rep(i,v.size())
		print(v[i],i==int(v.size())-1?suc:2);
}

string readString(){
	static char buf[3341000];
	scanf("%s",buf);
	return string(buf);
}

char* readCharArray(){
	static char buf[3341000];
	static int bufUsed=0;
	char* ret=buf+bufUsed;
	scanf("%s",ret);
	bufUsed+=strlen(ret)+1;
	return ret;
}

template<class T,class U>
void chmax(T& a,U b){
	if(a<b)
		a=b;
}

template<class T,class U>
void chmin(T& a,U b){
	if(b<a)
		a=b;
}

template<class T>
T Sq(const T& t){
	return t*t;
}

//#define CAPITAL
void Yes(bool ex=true){
	#ifdef CAPITAL
	cout<<"YES"<<endl;
	#else
	cout<<"Yes"<<endl;
	#endif
	if(ex)exit(0);
}
void No(bool ex=true){
	#ifdef CAPITAL
	cout<<"NO"<<endl;
	#else
	cout<<"No"<<endl;
	#endif
	if(ex)exit(0);
}

const ll infLL=LLONG_MAX/3;

#ifdef int
const int inf=infLL;
#else
const int inf=INT_MAX/2-100;
#endif

constexpr ll TEN(int n){
	return n==0?1:TEN(n-1)*10;
}

template<class T>
vector<T> uni(const vector<T>&vv){
	auto v(vv);
	sort(all(v));
	v.erase(unique(all(v)),v.end());
	return v;
}
template<class T>
void mkuni(vector<T>&v){
	sort(all(v));
	v.erase(unique(all(v)),v.end());
}

//ayasii
int topbit(signed t){
	return t==0?-1:31-__builtin_clz(t);
}
int topbit(ll t){
	return t==0?-1:63-__builtin_clzll(t);
}
int popcount(signed t){
	return __builtin_popcount(t);
}
int popcount(ll t){
	return __builtin_popcountll(t);
}
bool ispow2(int i){
	return i&&(i&-i)==i;
}

bool inc(int a,int b,int c){
	return a<=b&&b<=c;
}

#define SMOD

#ifdef SMOD
template<uint mod>
#else
uint mod;
#endif
struct ModInt{
	#ifdef SMOD
	static constexpr uint base=mod;
	#else
	static constexpr uint& base=mod;
	#endif
	uint v;
	ModInt():v(0){}
	ModInt(ll vv){
		s(vv%mod+mod);
	}
	ModInt& s(uint vv){
		v=vv<mod?vv:vv-mod;
		return *this;
	}
	explicit operator bool()const{
		return v;
	}
	explicit operator int()const{
		return v;
	}
	bool operator==(const ModInt&rhs)const{
		return v==rhs.v;
	}
	bool operator!=(const ModInt&rhs)const{
		return v!=rhs.v;
	}
	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*=rhs.inv();
	}
	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 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;
	}
	ModInt pow(int n)const{
		ModInt res(1),x(*this);
		while(n){
			if(n&1)res*=x;
			x*=x;
			n>>=1;
		}
		return res;
	}
	ModInt inv()const{
		return pow(mod-2);
	}
};

#ifdef SMOD
template<uint mod>
ostream& operator<<(ostream&os,const ModInt<mod>&m){
	return os<<m.v;
}
template<uint mod>
void print(const ModInt<mod>&m,int suc=1){
	print(m.v,suc);
}
#else
ostream& operator<<(ostream&os,const ModInt&m){
	return os<<m.v;
}
void print(const ModInt&m,int suc=1){
	print(m.v,suc);
}
#endif

#ifdef SMOD
using mint=ModInt<1000000007>;
//using mint=ModInt<998244353>;
#else
using mint=ModInt;
#endif

const int Vmax=(1<<21)+10;
mint fact[Vmax],factInv[Vmax],invs[Vmax];
void InitFact(){
	fact[0]=1;
	FOR(i,1,Vmax){
		fact[i]=fact[i-1]*i;
	}
	factInv[Vmax-1]=fact[Vmax-1].inv();
	for(int i=Vmax-2;i>=0;i--){
		factInv[i]=factInv[i+1]*(i+1);
	}
	for(int i=Vmax-1;i>=1;i--){
		invs[i]=factInv[i]*fact[i-1];
	}
}
#ifdef SMOD
struct InitFactDummy{
	InitFactDummy(){
		InitFact();
	}
} initFactDummy;
#endif
mint Choose(int n,int k){
	return fact[n]*factInv[n-k]*factInv[k];
}
mint Binom(int a,int b){
	return fact[a+b]*factInv[a]*factInv[b];
}
mint Catalan(int n){
	return Binom(n,n)-(n-1>=0?Binom(n-1,n+1):0);
}

//res: k by d table
//for all n sum_{0<=i<k} f_i(n)*a_{n+i} = 0
//f_i(n)=sum_{0<=j<d} res[i][j]*(n+i)^j
VV<mint> p_recursive(const V<mint>&a,int d){
	int n=a.size();
	int k=(n+2)/(d+1);
	int m=k*d;
	VV<mint> x(m,V<mint>(m+m-1));
	rep(p,m-1)rep(i,k){
		mint w=a[p+i];
		rep(j,d){
			x[i*d+j][p]=w;
			w*=(p+i);
		}
	}
	rep(i,m)
		x[i][m-1+i]=1;
	V<mint> v;
	rep(i,m){
		int j=0;
		while(j<m-1&&x[i][j]==0)
			j++;
		if(j==m-1){
			rep(h,i+1)
				v.pb(x[i][m-1+h]);
			break;
		}else{
			FOR(h,i+1,m){
				mint w=x[h][j]/x[i][j];
				rep(l,m+m-1)
					x[h][l]-=x[i][l]*w;
			}
		}
	}
	assert(v.size());
	VV<mint> res=VV<mint>(int(v.size()+d-1)/d,V<mint>(d));
	rep(i,v.size())
		res[i/d][i%d]=v[i];
	return res;
}

V<mint> extend_sequence(const V<mint>&a,const VV<mint>& f,int n){
	int k=f.size(),d=f[0].size();
	assert(int(a.size())>=k-1);
	V<mint> res(n),w(k);
	rep(i,n){
		if(i<k-1)
			res[i]=a[i];
		else{
			rep(j,k){
				w[j]=0;
				mint z=1;
				rep(h,d){
					w[j]+=f[j][h]*z;
					z*=i-k+1+j;
				}
			}
			assert(w[k-1]);
			mint s=0;
			rep(j,k-1)
				s+=w[j]*res[i-k+1+j];
			res[i]=-s/w[k-1];
		}
	}
	return res;
}

const int Nmax=1010;

mint dp[Nmax][Nmax][2][2];

V<mint> calc(int n){
	V<mint> res(n+1);
	res[1]=1;
	dp[2][0][0][0]=2;
	FOR(i,2,n+1){
		res[i]=dp[i][0][0][0];
		rep(j,i){
			rep(p,2)rep(q,2){
				mint a=p==0?j:j-1;
				mint b=p==0?2:1;
				mint c=p==0?0:1;
				mint d=i+1-a-b-c;
				if(j){
					if(q==0){
						dp[i+1][j-1][q][0]+=dp[i][j][p][q]*a;
					}else{
						dp[i+1][j-1][q][0]+=dp[i][j][p][q]*(a-1);
						dp[i+1][j-1][0][0]+=dp[i][j][p][q];
					}
				}
				dp[i+1][j+1][q][1]+=dp[i][j][p][q]*b;
				dp[i+1][j][q][1]+=dp[i][j][p][q]*c;
				dp[i+1][j][q][0]+=dp[i][j][p][q]*d;
			}
		}
	}
	return res;
}

signed main(){
	auto a=calc(100);
	a.erase(a.bg);
	
	auto f=p_recursive(a,5);
	errStream<<f.size()<<endl;
	dmp(f);
	
	auto ans=extend_sequence(a,f,1000);
	
	int n=read();
	print(ans[n-1]);
}
0