結果

問題 No.2149 Vanitas Vanitatum
ユーザー sigma425sigma425
提出日時 2022-12-07 02:28:25
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 62 ms / 2,000 ms
コード長 7,352 bytes
コンパイル時間 2,537 ms
コンパイル使用メモリ 212,484 KB
実行使用メモリ 38,400 KB
最終ジャッジ日時 2024-10-13 12:50:15
合計ジャッジ時間 4,721 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge3
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 56 ms
38,272 KB
testcase_01 AC 62 ms
38,272 KB
testcase_02 AC 60 ms
38,400 KB
testcase_03 AC 57 ms
38,400 KB
testcase_04 AC 58 ms
38,272 KB
testcase_05 AC 59 ms
38,400 KB
testcase_06 AC 58 ms
38,272 KB
testcase_07 AC 56 ms
38,272 KB
testcase_08 AC 56 ms
38,400 KB
testcase_09 AC 57 ms
38,272 KB
testcase_10 AC 56 ms
38,400 KB
testcase_11 AC 56 ms
38,272 KB
testcase_12 AC 56 ms
38,400 KB
testcase_13 AC 56 ms
38,400 KB
testcase_14 AC 56 ms
38,272 KB
testcase_15 AC 57 ms
38,272 KB
testcase_16 AC 55 ms
38,400 KB
testcase_17 AC 55 ms
38,272 KB
testcase_18 AC 56 ms
38,400 KB
testcase_19 AC 59 ms
38,400 KB
testcase_20 AC 59 ms
38,400 KB
testcase_21 AC 56 ms
38,272 KB
testcase_22 AC 57 ms
38,272 KB
testcase_23 AC 59 ms
38,272 KB
testcase_24 AC 57 ms
38,272 KB
testcase_25 AC 56 ms
38,400 KB
testcase_26 AC 59 ms
38,400 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>
using namespace std;
using ll = long long;
using uint = unsigned int;
using ull = unsigned long long;
#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 per(i,n) for(int i=int(n)-1;i>=0;i--)
#define per1(i,n) for(int i=int(n);i>0;i--)
#define all(c) c.begin(),c.end()
#define si(x) int(x.size())
#define pb push_back
#define eb emplace_back
#define fs first
#define sc second
template<class T> using V = vector<T>;
template<class T> using VV = vector<vector<T>>;
template<class T,class U> bool chmax(T& x, U y){
	if(x<y){ x=y; return true; }
	return false;
}
template<class T,class U> bool chmin(T& x, U y){
	if(y<x){ x=y; return true; }
	return false;
}
template<class T> void mkuni(V<T>& v){sort(all(v));v.erase(unique(all(v)),v.end());}
template<class T> int lwb(const V<T>& v, const T& a){return lower_bound(all(v),a) - v.begin();}
template<class T>
V<T> Vec(size_t a) {
    return V<T>(a);
}
template<class T, class... Ts>
auto Vec(size_t a, Ts... ts) {
  return V<decltype(Vec<T>(ts...))>(a, Vec<T>(ts...));
}
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;
}
constexpr ll TEN(int n) { return (n == 0) ? 1 : 10 * TEN(n-1); }

#ifdef LOCAL
#define show(x) cerr << "LINE" << __LINE__ << " : " << #x << " = " << (x) << endl
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 shows(...) cerr << "LINE" << __LINE__ << " : ";dmpr(cerr,##__VA_ARGS__)
#define dump(x) cerr << "LINE" << __LINE__ << " : " << #x << " = {";  \
	for(auto v: x) cerr << v << ","; cerr << "}" << endl;
#else
#define show(x) void(0)
#define dump(x) void(0)
#define shows(...) void(0)
#endif

template<class D> D divFloor(D a, D b){
	return a / b - (((a ^ b) < 0 && a % b != 0) ? 1 : 0);
}
template<class D> D divCeil(D a, D b) {
	return a / b + (((a ^ b) > 0 && a % b != 0) ? 1 : 0);
}
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;}
	template<class T> friend ModInt operator+(T a, const ModInt& b){ return (ModInt(a) += b);}
	template<class T> friend ModInt operator-(T a, const ModInt& b){ return (ModInt(a) -= b);}
	template<class T> friend ModInt operator*(T a, const ModInt& b){ return (ModInt(a) *= b);}
	template<class T> friend ModInt operator/(T a, const ModInt& b){ return (ModInt(a) /= b);}
	ModInt pow(ll p) const {
		if(p<0) return inv().pow(-p);
		ModInt a = 1;
		ModInt x = *this;
		while(p){
			if(p&1) a *= x;
			x *= x;
			p >>= 1;
		}
		return a;
	}
	ModInt inv() const {		// should be prime
		return pow(mod-2);
	}
	// 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));
	// }

	bool operator==(const ModInt& b) const { return v==b.v;}
	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<998244353>;
//using mint = ModInt<1000000007>;

V<mint> fact,ifact,invs;
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){	//[0,N]
	N++;
	fact.resize(N);
	ifact.resize(N);
	invs.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);
	rep1(i,N-1) invs[i] = fact[i-1] * ifact[i];
}
struct UnionFind{
	vector<int> par,sz;
	UnionFind(int N){
		par.assign(N,0);
		sz.assign(N,1);
		rep(i,N) par[i]=i;
	}
	int find(int x){
		if(par[x]==x) return x;
		return par[x]=find(par[x]);
	}
	bool same(int x,int y){
		return find(x)==find(y);
	}
	void unite(int x,int y){
		x=find(x),y=find(y);
		if(x==y) return;
		par[y]=x;
		sz[x] += sz[y];
	}
};
int sgn(V<int> o){
	int N = si(o);
	UnionFind UF(N);
	rep(i,N) UF.unite(i,o[i]);
	int s = 1;
	rep(i,N) if(UF.find(i) == i){
		if(UF.sz[i]%2 == 0) s = -s;
	}
	return s;
}

mint brute(V<int> A){
	int N = si(A);
	V<int> o(N); iota(all(o),0);
	mint res = 0;
	do{
		mint tmp = sgn(o);
		rep(i,N){
			int v = A[i] - o[i];
			if(v < 0) tmp = 0;
			else tmp *= ifact[v];
		}
		res += tmp;
	}while(next_permutation(all(o)));
	return res;
}
// decreasing -> decreasing
V<int> ConjugateYoung(V<int> a){
	if(a.empty()) return a;
	int w = a[0];
	V<int> b(w);
	int h = si(a);
	rep(j,w){
		while(h>0 && a[h-1] <= j) h--;
		b[j] = h;
	}
	return b;
}
// hook length formula
mint Hook(V<int> a){
	int n = accumulate(all(a),0);
	auto b = ConjugateYoung(a);
	mint res = fact[n];
	rep(i,si(a)){
		rep(j,a[i]){
			res *= invs[a[i]+b[j]-i-j-1];
		}
	}
	return res;
}
mint solve(V<int> A){
	// res = det ( 1 / (A_i-j)! )_{i,j}
	// f^λ = N! det ( 1 / (λ_i-i+j)! )_{i,j}
	int N = si(A);
	// mint god = brute(A);
	V<int> lam(N); rep(i,N) lam[i] = A[i]-i;
	reverse(all(lam));
	int S = accumulate(all(lam),0);
	mint res = Hook(lam) * ifact[S];
	show("---------------");
	show(A);
	show(res);
	// show(god);
	show(lam);
	return res;
}

int main(){
	cin.tie(0);
	ios::sync_with_stdio(false);		//DON'T USE scanf/printf/puts !!
	cout << fixed << setprecision(20);
	InitFact(TEN(6)*3);
	/*
		res = (-1)^縦の個数 χ^λ(2^m)
		χ^λ(2^m) = [x^(λ+δ)] p_{2^m}a_δ
		= [x^(λ+δ)] (x1^2+..+xn^2)^m * det (x1^{n-1} x1 1)
										   (x2^{n-1} x2 2)
										   :

	*/
	
	int N; cin >> N;
	V<int> A(N); rep(i,N) cin >> A[i];
	int m = accumulate(all(A),0);
	if(m&1){
		cout << 0 << endl;
		return 0;
	}
	m /= 2;
	rep(i,N) A[i] += i;
	mint ans = 1;
	{
		V<int> B;
		rep(i,N) if(A[i]%2 == 0){
			B.pb(A[i]/2);
		}
		if(si(B) != (N+1)/2){
			cout << 0 << endl;
			return 0;
		}
		ans *= solve(B);
	}
	{
		V<int> B;
		rep(i,N) if(A[i]%2 == 1){
			B.pb(A[i]/2);
		}
		ans *= solve(B);
	}
	cout << ans * fact[m] << endl;
}
0