#544045 (C++17) No.1204 お菓子配り-FINAL

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問題	No.1204 お菓子配り-FINAL
コンテスト
ユーザー	maroon_kuri
提出日時	2020-08-30 14:51:10
言語	C++17 (gcc 13.3.0 + boost 1.87.0)
結果	AC
実行時間	5 ms / 8,000 ms
コード長	10,622 bytes
コンパイル時間	4,320 ms
コンパイル使用メモリ	212,208 KB
最終ジャッジ日時	2025-01-13 22:02:46
ジャッジサーバーID （参考情報）	judge3 / judge4
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ファイルパターン	結果
other	AC * 130
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ソースコード

raw source code
#include <bits/stdc++.h>
using namespace std;

using ll=long long;
#define int ll

#define rng(i,a,b) for(int i=int(a);i<int(b);i++)
#define rep(i,b) rng(i,0,b)
#define gnr(i,a,b) for(int i=int(b)-1;i>=int(a);i--)
#define per(i,b) gnr(i,0,b)
#define pb push_back
#define eb emplace_back
#define a first
#define b second
#define bg begin()
#define ed end()
#define all(x) x.bg,x.ed
#define si(x) int(x.size())
#ifdef LOCAL
#define dmp(x) cerr<<__LINE__<<" "<<#x<<" "<<x<<endl
#else
#define dmp(x) void(0)
#endif

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> using vc=vector<t>;
template<class t> using vvc=vc<vc<t>>;

using pi=pair<int,int>;
using vi=vc<int>;

template<class t,class u>
ostream& operator<<(ostream& os,const pair<t,u>& p){
	return os<<"{"<<p.a<<","<<p.b<<"}";
}

template<class t> ostream& operator<<(ostream& os,const vc<t>& v){
	os<<"{";
	for(auto e:v)os<<e<<",";
	return os<<"}";
}

#define mp make_pair
#define mt make_tuple
#define one(x) memset(x,-1,sizeof(x))
#define zero(x) memset(x,0,sizeof(x))
#ifdef LOCAL
void dmpr(ostream&os){os<<endl;}
template<class T,class... Args>
void dmpr(ostream&os,const T&t,const Args&... args){
	os<<t<<" ";
	dmpr(os,args...);
}
#define dmp2(...) dmpr(cerr,__LINE__,##__VA_ARGS__)
#else
#define dmp2(...) void(0)
#endif

using uint=unsigned;
using ull=unsigned long long;

template<class t,size_t n>
ostream& operator<<(ostream&os,const array<t,n>&a){
	return os<<vc<t>(all(a));
}

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<<"}";
}

template<class t>
void print(t x,int suc=1){
	cout<<x;
	if(suc==1)
		cout<<"\n";
	if(suc==2)
		cout<<" ";
}

ll read(){
	ll i;
	cin>>i;
	return i;
}

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

pi readpi(int off=0){
	int a,b;cin>>a>>b;
	return pi(a+off,b+off);
}

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(){
	string s;
	cin>>s;
	return s;
}

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

//#define CAPITAL
void yes(bool ex=true){
	#ifdef CAPITAL
	cout<<"YES"<<"\n";
	#else
	cout<<"Yes"<<"\n";
	#endif
	if(ex)exit(0);
	#ifdef LOCAL
	cout.flush();
	#endif
}
void no(bool ex=true){
	#ifdef CAPITAL
	cout<<"NO"<<"\n";
	#else
	cout<<"No"<<"\n";
	#endif
	if(ex)exit(0);
	#ifdef LOCAL
	cout.flush();
	#endif
}
void possible(bool ex=true){
	#ifdef CAPITAL
	cout<<"POSSIBLE"<<"\n";
	#else
	cout<<"Possible"<<"\n";
	#endif
	if(ex)exit(0);
	#ifdef LOCAL
	cout.flush();
	#endif
}
void impossible(bool ex=true){
	#ifdef CAPITAL
	cout<<"IMPOSSIBLE"<<"\n";
	#else
	cout<<"Impossible"<<"\n";
	#endif
	if(ex)exit(0);
	#ifdef LOCAL
	cout.flush();
	#endif
}

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

const ll infLL=LLONG_MAX/3;

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

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 botbit(signed a){
	return a==0?32:__builtin_ctz(a);
}
int botbit(ll a){
	return a==0?64:__builtin_ctzll(a);
}
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;
}
ll mask(int i){
	return (ll(1)<<i)-1;
}

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

template<class t> void mkuni(vc<t>&v){
	sort(all(v));
	v.erase(unique(all(v)),v.ed);
}

ll rand_int(ll l, ll r) { //[l, r]
	#ifdef LOCAL
	static mt19937_64 gen;
	#else
	static mt19937_64 gen(chrono::steady_clock::now().time_since_epoch().count());
	#endif
	return uniform_int_distribution<ll>(l, r)(gen);
}

template<class t>
void myshuffle(vc<t>&a){
	rep(i,si(a))swap(a[i],a[rand_int(0,i)]);
}

template<class t>
int lwb(const vc<t>&v,const t&a){
	return lower_bound(all(v),a)-v.bg;
}

vvc<int> readGraph(int n,int m){
	vvc<int> g(n);
	rep(i,m){
		int a,b;
		cin>>a>>b;
		//sc.read(a,b);
		a--;b--;
		g[a].pb(b);
		g[b].pb(a);
	}
	return g;
}

vvc<int> readTree(int n){
	return readGraph(n,n-1);
}

struct modinfo{uint mod,root;};
template<modinfo const&ref>
struct modular{
	static constexpr uint const &mod=ref.mod;
	static modular root(){return modular(ref.root);}
	uint v;
	//modular(initializer_list<uint>ls):v(*ls.bg){}
	modular(ll vv=0){s(vv%mod+mod);}
	modular& s(uint vv){
		v=vv<mod?vv:vv-mod;
		return *this;
	}
	modular operator-()const{return modular()-*this;}
	modular& operator+=(const modular&rhs){return s(v+rhs.v);}
	modular&operator-=(const modular&rhs){return s(v+mod-rhs.v);}
	modular&operator*=(const modular&rhs){
		v=ull(v)*rhs.v%mod;
		return *this;
	}
	modular&operator/=(const modular&rhs){return *this*=rhs.inv();}
	modular operator+(const modular&rhs)const{return modular(*this)+=rhs;}
	modular operator-(const modular&rhs)const{return modular(*this)-=rhs;}
	modular operator*(const modular&rhs)const{return modular(*this)*=rhs;}
	modular operator/(const modular&rhs)const{return modular(*this)/=rhs;}
	modular pow(int n)const{
		modular res(1),x(*this);
		while(n){
			if(n&1)res*=x;
			x*=x;
			n>>=1;
		}
		return res;
	}
	modular inv()const{return pow(mod-2);}
	/*modular inv()const{
		int x,y;
		int g=extgcd<ll>(v,mod,x,y);
		assert(g==1);
		if(x<0)x+=mod;
		return modular(x);
	}*/
	friend modular operator+(int x,const modular&y){
		return modular(x)+y;
	}
	friend modular operator-(int x,const modular&y){
		return modular(x)-y;
	}
	friend modular operator*(int x,const modular&y){
		return modular(x)*y;
	}
	friend modular operator/(int x,const modular&y){
		return modular(x)/y;
	}
	friend ostream& operator<<(ostream&os,const modular&m){
		return os<<m.v;
	}
	friend istream& operator>>(istream&is,modular&m){
		ll x;is>>x;
		m=modular(x);
		return is;
	}
	bool operator<(const modular&r)const{return v<r.v;}
	bool operator==(const modular&r)const{return v==r.v;}
	bool operator!=(const modular&r)const{return v!=r.v;}
	explicit operator bool()const{
		return v;
	}
};

//extern constexpr modinfo base{998244353,3};
extern constexpr modinfo base{1000000007,0};
//modinfo base{1,0};
using mint=modular<base>;

const int vmax=1000;
mint fact[vmax],finv[vmax],invs[vmax];
void initfact(){
	fact[0]=1;
	rng(i,1,vmax){
		fact[i]=fact[i-1]*i;
	}
	finv[vmax-1]=fact[vmax-1].inv();
	for(int i=vmax-2;i>=0;i--){
		finv[i]=finv[i+1]*(i+1);
	}
	for(int i=vmax-1;i>=1;i--){
		invs[i]=finv[i]*fact[i-1];
	}
}
mint choose(int n,int k){
	return fact[n]*finv[n-k]*finv[k];
}
mint binom(int a,int b){
	return fact[a+b]*finv[a]*finv[b];
}
mint catalan(int n){
	return binom(n,n)-(n-1>=0?binom(n-1,n+1):0);
}

/*
const int vmax=110;
mint binbuf[vmax][vmax];
mint choose(int n,int k){
	return binbuf[n-k][k];
}
mint binom(int a,int b){
	return binbuf[a][b];
}
void initfact(){
	binbuf[0][0]=1;
	rep(i,vmax)rep(j,vmax){
		if(i)binbuf[i][j]+=binbuf[i-1][j];
		if(j)binbuf[i][j]+=binbuf[i][j-1];
	}
}
*/

//initfact
mint interpolate(const vc<mint>&a,mint x){
	int n=si(a);
	if(inc(0,x.v,n-1))return a[x.v];
	vc<mint> z(n+1);
	z[n]=1;
	per(i,n)z[i]=z[i+1]*(x-i);
	mint res,w=1;
	rep(i,n){
		res+=w*z[i+1]*a[i]*finv[i]*finv[n-1-i]*((n-1-i)%2?-1:1);
		w*=x-i;
	}
	return res;
}

//VERIFTY:yosupo
// f は k 次多項式を 0 から k で評価した値が入る
//sum {0<=i<=n-1} a^i f[i]
mint exp_poly_sum(const mint a,const vc<mint>&f,const int n){
	if(n==0)return 0;
	int k=si(f)-1;
	if(a==0){
		return f[0];
	}else if(a==1){
		vc<mint> g(k+2);
		rep(i,k+1)g[i+1]=g[i]+f[i];
		return interpolate(g,n);
	}else{
		vc<mint> g(k+1);
		{
			mint r=1;
			rep(i,k+1){
				g[i]=f[i]*r;
				r*=a;
			}
		}
		mint c;
		{
			mint w,r=1;
			rep(i,k+1){
				w+=choose(k+1,i)*r;
				r*=-a;
				c+=g[k-i]*w;
			}
			c/=mint(1-a).pow(k+1);
		}
		rep(i,k)g[i+1]+=g[i];
		mint ainv=a.inv(),w=1;
		rep(i,k+1){
			g[i]=(g[i]-c)*w;
			w*=ainv;
		}
		return interpolate(g,n-1)*a.pow(n-1)+c;
	}
}

const int mmax=105;
mint small[mmax];

mint getpowsum(int n,int k,int s,vc<mint> vs,mint r){
	assert(s>=0);
	mint w=mint(n).pow(k);
	r*=n;
	return exp_poly_sum(r,vs,s)*w;
}

mint subsum(int n,int k,int s,vc<mint> vs,mint r){
	assert(s>=0);
	mint w=k==0?mint(n).inv():mint(n).pow(k-1);
	r*=n;
	rep(i,si(vs))
		vs[i]*=n-k-i;
	return exp_poly_sum(r,vs,s)*w;
}

mint slv5(int a,int n,int k,int s,vc<mint> vs,mint r){
	assert(a>=0);
	assert(inc(a,k,n));
	mint res=getpowsum(n,k,s,vs,r);
	res-=subsum(n,k,s,vs,r)*a;
	if(a>=2){
		chmin(s,n-1-k);
		if(s>=0){
			rep(i,a-1){
				res+=subsum(n-(i+1),k-i,s,vs,r)*(a-1-i)*small[i+1];
				rep(j,si(vs)){
					vs[j]*=k+j-i;
					vs[j]*=invs[i+1];
				}
			}
		}
	}
	return res;
}

mint conv[mmax];

mint slv4(int a,int b,int n,int k,int s,vc<mint> vs,mint r){
	assert(a>=0);
	assert(b>=0);
	assert(a+b+1<=n);
	assert(inc(a+b,k,n-1));
	mint res=subsum(n,k,s,vs,r);
	chmin(s,n-1-k);
	if(s>=0){
		rep(_,2){
			rng(i,1,a+1){
				vc<mint> tmp=vs;
				rep(j,si(tmp))tmp[j]*=choose(k+j,i-1);
				//res-=choose(k,i-1)*small[i]*sub(n-i,k-(i-1));
				res-=subsum(n-i,k-(i-1),s,tmp,r)*small[i];
			}
			swap(a,b);
		}
	}
	chmin(s,n-2-k);
	if(s>=0){
		rep(sum,a+b-1){
			vc<mint> tmp=vs;
			rep(j,si(tmp))tmp[j]*=choose(k+j,sum);
			res+=subsum(n-(sum+2),k-sum,s,tmp,r)*conv[sum];
			//res+=choose(k,sum)*conv[sum]*sub(n-(sum+2),k-sum);
		}
	}
	return res;
}

signed main(){
	cin.tie(0);
	ios::sync_with_stdio(0);
	cout<<fixed<<setprecision(20);
	
	initfact();
	
	int n,m;cin>>n>>m;
	small[1]=1;
	rng(i,2,m+2){
		small[i]=mint(i).pow(i-2);
	}
	
	vi ls;
	int cur=0;
	string str;cin>>str;
	int cnt=0;
	for(auto c:str){
		if(c=='o'){
			ls.pb(cur);
			cur=0;
		}else{
			cnt++;
			cur++;
		}
	}
	ls.pb(cur);
	mint ans;
	const int d=m+5;
	if(si(ls)==1){
		int k=cnt,s=n-cnt+1;
		ans+=slv5(ls[0],n,k,s,vc<mint>(d,1),mint(n).inv())*mint(n).pow(n-k);
	}else{
		int a=ls[0],b=ls.back();
		rep(i,a)rep(j,b){
			conv[i+j]+=small[i+1]*small[j+1]*binom(i,j);
		}
		mint w=1;
		int u=0;
		rng(i,1,si(ls)-1){
			w*=small[ls[i]+1];
			w*=finv[ls[i]];
			u+=ls[i];
		}
		w*=fact[u];
		int k=cnt,s=n-(si(ls)-1)+1-k;
		w*=mint(n).pow(n-k);
		vc<mint> vs(d);
		rep(i,d)vs[i]=choose(k+i,u);
		ans+=slv4(a,b,n-(si(ls)-2)-u,k-u,s,vs,mint(n).inv());
		/*rng(k,cnt,n-(si(ls)-1)+1){
			mint ad=slv4(a,b,n-(si(ls)-2)-u,k-u)*choose(k,u)*getpow(n,n-k);
			ans+=ad;
		}*/
		ans*=w;
	}
	print(ans*(n-m+1));
}
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結果

ソースコード
