#867048 (C++17) No.1774 Love Triangle (Hard)

• 問題: No.1774 Love Triangle (Hard)
• ユーザー: maroon_kuri
• 提出日時: 2023-05-06 21:29:09
• 言語: C++17 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 4,241 ms / 8,000 ms
• コード長: 16,377 bytes
• コンパイル時間: 4,234 ms
• コンパイル使用メモリ: 263,424 KB
• 最終ジャッジ日時: 2025-02-12 20:46:55
• ジャッジサーバーID （参考情報）: judge5 / judge4

ファイルパターン	結果
sample	AC * 3
other	AC * 90

ソースコード

#ifndef LOCAL
#pragma GCC optimize ("Ofast")
#pragma GCC optimize ("unroll-loops")
#endif

#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> bool chmax(t&a,u b){if(a<b){a=b;return true;}else return false;}
template<class t,class u> bool chmin(t&a,u b){if(b<a){a=b;return true;}else return false;}

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<<"}";
}

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_single(t x,int suc=1){
	cout<<x;
	if(suc==1)
		cout<<"\n";
	if(suc==2)
		cout<<" ";
}

template<class t,class u>
void print_single(const pair<t,u>&p,int suc=1){
	print_single(p.a,2);
	print_single(p.b,suc);
}

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

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

template<class T,size_t N>
void print_single(const array<T,N>&v,int suc=1){
	rep(i,N)
		print_single(v[i],i==int(N)-1?suc:2);
}

template<class T>
void print(const T&t){
	print_single(t);
}

template<class T,class ...Args>
void print(const T&t,const Args&...args){
	print_single(t,2);
	print(args...);
}

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

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

void YES(bool ex=true){
	cout<<"YES\n";
	if(ex)exit(0);
	#ifdef LOCAL
	cout.flush();
	#endif
}
void NO(bool ex=true){
	cout<<"NO\n";
	if(ex)exit(0);
	#ifdef LOCAL
	cout.flush();
	#endif
}
void Yes(bool ex=true){
	cout<<"Yes\n";
	if(ex)exit(0);
	#ifdef LOCAL
	cout.flush();
	#endif
}
void No(bool ex=true){
	cout<<"No\n";
	if(ex)exit(0);
	#ifdef LOCAL
	cout.flush();
	#endif
}
//#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 topbit(ull 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 botbit(ull a){
	return a==0?64:__builtin_ctzll(a);
}
int popcount(signed t){
	return __builtin_popcount(t);
}
int popcount(ll t){
	return __builtin_popcountll(t);
}
int popcount(ull t){
	return __builtin_popcountll(t);
}
int bitparity(ll t){
	return __builtin_parityll(t);
}
bool ispow2(int i){
	return i&&(i&-i)==i;
}
ll mask(int i){
	return (ll(1)<<i)-1;
}
ull umask(int i){
	return (ull(1)<<i)-1;
}
ll minp2(ll n){
	if(n<=1)return 1;
	else return ll(1)<<(topbit(n-1)+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);
}

ll rand_int(ll k){ //[0,k)
	return rand_int(0,k-1);
}

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;
}
template<class t>
bool bis(const vc<t>&v,const t&a){
	return binary_search(all(v),a);
}

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);
}

vc<ll> presum(const vi&a){
	vc<ll> s(si(a)+1);
	rep(i,si(a))s[i+1]=s[i]+a[i];
	return s;
}
//BIT で数列を管理するときに使う (CF850C)
template<class t>
vc<t> predif(vc<t> a){
	gnr(i,1,si(a))a[i]-=a[i-1];
	return a;
}
template<class t>
vvc<ll> imos(const vvc<t>&a){
	int n=si(a),m=si(a[0]);
	vvc<ll> b(n+1,vc<ll>(m+1));
	rep(i,n)rep(j,m)
		b[i+1][j+1]=b[i+1][j]+b[i][j+1]-b[i][j]+a[i][j];
	return b;
}

//verify してないや
void transvvc(int&n,int&m){
	swap(n,m);
}
template<class t,class... Args>
void transvvc(int&n,int&m,vvc<t>&a,Args&...args){
	assert(si(a)==n);
	vvc<t> b(m,vi(n));
	rep(i,n){
		assert(si(a[i])==m);
		rep(j,m)b[j][i]=a[i][j];
	}
	a.swap(b);
	transvvc(n,m,args...);
}
//CF854E
void rotvvc(int&n,int&m){
	swap(n,m);
}
template<class t,class... Args>
void rotvvc(int&n,int&m,vvc<t>&a,Args&...args){
	assert(si(a)==n);
	vvc<t> b(m,vi(n));
	rep(i,n){
		assert(si(a[i])==m);
		rep(j,m)b[m-1-j][i]=a[i][j];
	}
	a.swap(b);
	rotvvc(n,m,args...);
}

//ソートして i 番目が idx[i]
//CF850C
template<class t>
vi sortidx(const vc<t>&a){
	int n=si(a);
	vi idx(n);iota(all(idx),0);
	sort(all(idx),[&](int i,int j){return a[i]<a[j];});
	return idx;
}
//vs[i]=a[idx[i]]
//例えば sortidx で得た idx を使えば単にソート列になって返ってくる
//CF850C
template<class t>
vc<t> a_idx(const vc<t>&a,const vi&idx){
	int n=si(a);
	assert(si(idx)==n);
	vc<t> vs(n);
	rep(i,n)vs[i]=a[idx[i]];
	return vs;
}
//CF850C
vi invperm(const vi&p){
	int n=si(p);
	vi q(n);
	rep(i,n)q[p[i]]=i;
	return q;
}

template<class t,class s=t>
s SUM(const vc<t>&a){
	return accumulate(all(a),s(0));
}

template<class t>
t MAX(const vc<t>&a){
	return *max_element(all(a));
}

template<class t>
t MIN(const vc<t>&a){
	return *min_element(all(a));
}

template<class t,class u>
pair<t,u> operator+(const pair<t,u>&a,const pair<t,u>&b){
	return mp(a.a+b.a,a.b+b.b);
}

vi vid(int n){
	vi res(n);iota(all(res),0);
	return res;
}

template<class S>
S getrev(S s){
	reverse(all(s));
	return s;
}

pi operator+(pi a,pi b){return pi(a.a+b.a,a.b+b.b);}

template<class t>
t gpp(vc<t>&vs){
	assert(si(vs));
	t res=move(vs.back());
	vs.pop_back();
	return res;
}

//mint107 は verify してねえ
//#define DYNAMIC_MOD

struct modinfo{uint mod,root;
#ifdef DYNAMIC_MOD
constexpr modinfo(uint m,uint r):mod(m),root(r),im(0){set_mod(m);}
ull im;
constexpr void set_mod(uint m){
	mod=m;
	im=ull(-1)/m+1;
}
uint product(uint a,uint b)const{
	ull z=ull(a)*b;
	uint x=((unsigned __int128)z*im)>>64;
	uint v=uint(z)-x*mod;
	return v<mod?v:v+mod;
}
#endif
};
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){
		#ifndef DYNAMIC_MOD
		v=ull(v)*rhs.v%mod;
		#else
		v=ref.product(v,rhs.v);
		#endif
		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(ll n)const{
		if(n<0)return inv().pow(-n);
		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+(ll x,const modular&y){
		return modular(x)+y;
	}
	friend modular operator-(ll x,const modular&y){
		return modular(x)-y;
	}
	friend modular operator*(ll x,const modular&y){
		return modular(x)*y;
	}
	friend modular operator/(ll 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;
	}
};

#ifndef DYNAMIC_MOD
//extern constexpr modinfo base{998244353,3};
//extern constexpr modinfo base{1000000007,0};
extern constexpr modinfo base{2147483579,0};//2^31 未満の最大の安全素数
//modinfo base{1,0};
#ifdef USE_GOOD_MOD
static_assert(base.mod==998244353);
#endif
#else
modinfo base(1,0);
extern constexpr modinfo base107(1000000007,0);
using mint107=modular<base107>;
#endif
using mint=modular<base>;

mint parity(int i){
	return i%2==0?1:-1;
}

#ifdef LOCAL
const int vmax=10010;
#else
const int vmax=(1<<21)+10;
#endif
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];
	}
}
*/

mint p2[vmax],p2inv[vmax];
void initp2(){
	p2[0]=1;
	rep(i,vmax-1)p2[i+1]=p2[i]*2;
	p2inv[vmax-1]=p2[vmax-1].inv();
	per(i,vmax-1)p2inv[i]=p2inv[i+1]*2;
}

template<class t>
void mat0(vvc<t>&a,int n,int m){
	static vvc<t> pool;
	while(si(a)<n){
		if(pool.empty())a.resize(n);
		else a.pb(gpp(pool));
	}
	while(si(a)>n)pool.pb(gpp(a));
	rep(i,n){
		a[i].resize(m);
		fill(all(a[i]),0);
	}
}

//VERIFY: yosupo
mint det(vvc<mint>&a){
	const int n=a.size();
	mint ans(1);
	rep(i,n){
		rng(j,i+1,n)if(a[j][i]){
			ans=-ans;
			swap(a[j],a[i]);
			break;
		}
		if(a[i][i]==0)return 0;
		ans*=a[i][i];
		mint z=a[i][i].inv();
		rng(j,i+1,n){
			mint w=-a[j][i]*z;
			rng(k,i,n)
				a[j][k]+=a[i][k]*w;
		}
	}
	return ans;
}

//inplace
//左c列をsweepしする
//aの先頭rank行に要素が入っている感じ
//Yuhao Du Contest 11 (Ucup1-10 G)
//https://uoj.ac/problem/785
int sweep(vvc<mint>&a,vi*col=nullptr,int c=-1){
	if(a.empty())return 0;
	if(c==-1)c=a[0].size();
	int h=a.size(),w=a[0].size(),r=0;
	rep(i,c){
		if(r==h)break;
		rng(j,r,h)if(a[j][i]){
			swap(a[r],a[j]);
			break;
		}
		if(a[r][i]==0)continue;
		mint u=a[r][i].inv();
		rep(j,h)if(j!=r){
		//rng(j,r+1,h){ //for speed up (sweep に使った列に複数の non-zero があっても良い場合)
			mint z=-a[j][i]*u;
			rng(k,i,w)
				a[j][k]+=a[r][k]*z;
		}
		if(col)col->pb(i);
		r++;
	}
	return r;
}

//https://uoj.ac/problem/785
bool inverse(vvc<mint>&a){
	int n=si(a);
	rep(i,n){
		assert(si(a[i])==n);
		a[i].resize(2*n);
	}
	static vi row;
	row.resize(n);rep(i,n)row[i]=i;
	rep(i,n){
		rng(j,i,n)if(a[j][i]){
			swap(a[i],a[j]);
			swap(row[i],row[j]);
			break;
		}
		if(a[i][i]==0)return false;
		mint u=a[i][i].inv();
		a[i][n+i]=1;
		rng(k,i,n+i+1)a[i][k]*=u;
		rep(j,n)if(j!=i){
			mint z=-a[j][i];
			rng(k,i,n+i+1)a[j][k]+=a[i][k]*z;
		}
	}
	rep(i,n){
		rep(j,n)a[i][row[j]]=a[i][n+j];
		a[i].resize(n);
	}
	return true;
}

//https://uoj.ac/problem/785
//mod を減らして定数倍を，改善…
void mmm(vvc<mint>&c,const vvc<mint>&a,const vvc<mint>&b){
	int n=si(a),m=si(a[0]),l=si(b[0]);
	assert(m==si(b));
	mat0(c,n,l);
	static vvc<uint> d;mat0(d,l,m);
	static vvc<uint> e;mat0(e,l,m);
	static const int L=15;
	rep(j,m)rep(k,l)d[k][j]=b[j][k].v&mask(L);
	rep(j,m)rep(k,l)e[k][j]=b[j][k].v>>L;
	rep(i,n)rep(k,l){
		ull sum=0;
		rep(j,m)sum+=(ull)a[i][j].v*e[k][j];
		sum=(sum%mint::mod)<<L;
		rep(j,m)sum+=(ull)a[i][j].v*d[k][j];
		c[i][k]=sum;
	}
}

//メモリを全部vectorからarrayに変えたけど速くならない…
//modintの計算がボトルネックだとあんま変わらないのかな
//inverseはullに変えても速くない，なぜ？

//Yukicoder No.1774
struct Harvey{
	const int n;
	vvc<mint> a,inv;
	Harvey(const vvc<mint>&ini):n(si(ini)),a(ini),inv(ini){
		bool tmp=inverse(inv);
		assert(tmp);
	}
	using T=tuple<int,int,mint>;
	vc<T> buf;
	void add(int i,int j,mint v){
		buf.eb(i,j,v);
	}
	vi pos;
	vvc<mint> dif,invss,invst,invts,w,z;
	//add の結果を使って inv を更新しようとする
	//正則なら更新に成功し，true が返る
	//非正則なら a/inv はもとのまま false が返る
	bool upd(){
		pos.clear();
		for(auto [i,j,v]:buf){
			pos.pb(i);
			pos.pb(j);
		}
		mkuni(pos);
		int s=si(pos);
		
		mat0(dif,s,s);
		for(auto [i,j,v]:buf)
			dif[lwb(pos,i)][lwb(pos,j)]+=v;
		mat0(invss,s,s);
		rep(i,s)rep(j,s)invss[i][j]=inv[pos[i]][pos[j]];
		
		mmm(w,dif,invss);
		rep(i,s)w[i][i]+=1;
		if(!inverse(w)){
			buf.clear();
			return false;
		}
		
		mat0(invst,s,n);
		rep(i,s)rep(j,n)invst[i][j]=inv[pos[i]][j];
		mat0(invts,n,s);
		rep(i,n)rep(j,s)invts[i][j]=inv[i][pos[j]];
		
		mmm(z,w,dif);
		mmm(w,invts,z);
		mmm(z,w,invst);
		
		rep(i,n)rep(j,n)
			inv[i][j]-=z[i][j];
		
		for(auto [i,j,v]:buf)
			a[i][j]+=v;
		
		buf.clear();
		return true;
	}
};

void slv(){
	int n,m;cin>>n>>m;
	vc<mint> diag(n);
	rep(i,n)diag[i]=rand_int(1,mint::mod-1);
	vvc<mint> ini(n,vc<mint>(n));
	rep(i,n)ini[i][i]=diag[i];
	Harvey h(ini);
	int ans=0;
	rep(_,m){
		int a,b,c;cin>>a>>b>>c;
		a--;b--;c--;
		mint v=rand_int(1,mint::mod-1);
		h.add(a,a,v);
		h.add(a,c,-v);
		h.add(b,a,-v);
		h.add(b,c,v);
		h.add(a,a,-v);
		h.add(c,a,v);
		h.add(a,b,v);
		h.add(c,b,-v);
		bool tmp=h.upd();
		assert(tmp);
		rep(i,n)if(diag[i]){
			h.add(i,i,-diag[i]);
			if(h.upd()){
				ans++;
				diag[i]=0;
			}
		}
		assert(ans%2==0);
		print(ans/2);
	}
}

signed main(){
	cin.tie(0);
	ios::sync_with_stdio(0);
	cout<<fixed<<setprecision(20);
	
	//int t;cin>>t;rep(_,t)
	slv();
}