Submission #854229

#	Time	Username	Problem	Language	Result	Execution time	Memory
854229		maroonrk	Thousands Islands (IOI22_islands)	C++17	100 / 100	294 ms	86020 KiB

islands

#include "islands.h"
#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);
}

template<class t>
vc<t> presum(const vc<t>&a){
	vc<t> s(si(a)+1);
	rep(i,si(a))s[i+1]=s[i]+a[i];
	return s;
}
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>
pair<t,int> MAXi(const vc<t>&a){
	auto itr=max_element(all(a));
	return mp(*itr,itr-a.bg);
}

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

template<class t>
pair<t,int> MINi(const vc<t>&a){
	auto itr=min_element(all(a));
	return mp(*itr,itr-a.bg);
}

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

template<class S>
void soin(S&s){
	sort(all(s));
}

template<class S>
S soout(S s){
	soin(s);
	return s;
}

template<class S>
void rein(S&s){
	reverse(all(s));
}

template<class S>
S reout(S s){
	rein(s);
	return s;
}

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

template<class t>
void pb(vc<t>&a,const vc<t>&b){
	a.insert(a.ed,all(b));
}

template<class t>
vc<t> cat(vc<t> a,const vc<t>&b){
	pb(a,b);
	return a;
}

template<class t,class u>
vc<t>& operator+=(vc<t>&a,u x){
	for(auto&v:a)v+=x;
	return a;
}

template<class t,class u>
vc<t> operator+(vc<t> a,u x){
	return a+=x;
}

template<class t,class u>
vc<t>& operator-=(vc<t>&a,u x){
	for(auto&v:a)v-=x;
	return a;
}

template<class t,class u>
vc<t>& operator-(vc<t> a,u x){
	return a-=x;
}

//CCPC Finals 2021 H
//Multiuni2023-3 E
struct dominator_tree{
	int n;
	vvc<int> g,rG,bct;
	vi idom,semi,us,id,rId,par,mn,anc;
	dominator_tree(int nn):n(nn),
		g(n),rG(n),bct(n),
		idom(n,-1),semi(n),us(n),id(n,-1),rId(n),par(n,-1),mn(n),anc(n,-1){
		iota(all(semi),0);
		iota(all(mn),0);
	}
	void ae(int a,int b){
		if(a==b)return;
		g[a].pb(b);
		rG[b].pb(a);
	}
	int find(int v){
		if(anc[v]==-1)
			return v;
		int a=find(anc[v]);
		if(id[semi[mn[anc[v]]]]<id[semi[mn[v]]])
			mn[v]=mn[anc[v]];
		return anc[v]=a;
	}
	void link(int c,int p){
		anc[c]=p;
	}
	void dfs(int v,int p,int& i){
		if(id[v]!=-1)
			return;
		id[v]=i;
		rId[i++]=v;
		par[v]=p;
		for(int c:g[v])
			dfs(c,v,i);
	}
	//return idom or -1 if unreachable from the root
	vi calc(int root){
		int sz=0;
		dfs(root,-1,sz);
		for(int i=sz-1;i>0;i--){
			int w=rId[i];
			for(int v:rG[w])if(id[v]!=-1){
				find(v);
				if(id[semi[mn[v]]]<id[semi[w]])
					semi[w]=semi[mn[v]];
			}
			bct[semi[w]].pb(w);
			for(int v:bct[par[w]]){
				find(v);
				us[v]=mn[v];
			}
			bct[par[w]].clear();
			link(w,par[w]);
		}
		rng(i,1,sz){
			int w=rId[i];
			if(semi[w]==semi[us[w]])
				idom[w]=semi[w];
			else
				idom[w]=idom[us[w]];
		}
		return idom;
	}
};

//dep,par は not verified
//yukicoder no.1024
//https://www.codechef.com/LTIME110A/problems/TREEQUER
//IOI2022 Islands
template<class E>
struct treedfs{
	const vvc<E>&g;
	const int n;
	int cnt;
	vi par,dep,in,out,ni;
	void dfs(int v,int p,int d){
		par[v]=p;
		dep[v]=d;
		in[v]=cnt++;
		for(auto e:g[v])if(e!=p)
			dfs(e,v,d+1);
		out[v]=cnt;
	}
	treedfs(const vvc<E>&gg,int r):g(gg),n(si(g)),cnt(0),par(n),dep(n,-1),in(n,-1),out(n,-1){
		dfs(r,-1,0);
		//not necessarily connected
		ni.resize(cnt);
		rep(i,n)if(in[i]!=-1)ni[in[i]]=i;
	}
	bool asde(int a,int b){
		return in[a]<=in[b]&&out[b]<=out[a];
	}
};

//CF869B
//複数始点
template<class E>
tuple<vi,vi,vc<E>> bfs(const vvc<E>&g,vi rs){
	int n=si(g);
	vi dist(n,-1),from(n,-1);
	vc<E> use(n);
	vi q(n);
	int b=0,e=0;
	auto reach=[&](int v,int d,int f,E u){
		if(dist[v]!=-1)return;
		dist[v]=d;
		from[v]=f;
		use[v]=u;
		q[e++]=v;
	};
	for(auto r:rs)reach(r,0,-1,E());
	while(b<e){
		int v=q[b++];
		for(auto to:g[v])
			reach(to,dist[v]+1,v,to);
	}
	return mt(move(dist),move(from),move(use));
}

bool dbg=false;

struct E{
	int to,id;
	operator int()const{return to;}
};

std::variant<bool, std::vector<int>> find_journey(
	int n, int m, std::vector<int> U, std::vector<int> V) {
	vvc<E> g(n);
	rep(i,m)g[U[i]].pb({V[i],i});
	
	int twocyc[2]{-1,-1};
	
	vi pv(n,-1),pe(n,-1),dep(n,-1),ord;
	{
		vi vis(n,0),bw(n,-1);
		vi ls;
		auto dfs=[&](auto self,int v,int p,int e,int d)->void{
			assert(vis[v]==0);
			assert(dep[v]==-1);
			vis[v]=1;
			ls.pb(v);
			pv[v]=p;
			pe[v]=e;
			dep[v]=d;
			ord.pb(v);
			int x[2]{-1,-1};
			for(auto [to,id]:g[v]){
				if(dep[to]==-1){
					self(self,to,v,id,d+1);
					int y=bw[to];
					rep(k,2)if(x[k]<y)swap(x[k],y);
				}else if(vis[to]==1){
					bw[ls[dep[to]+1]]=id;
				}else{
					//do nothing
				}
			}
			ls.pop_back();
			rep(k,2)chmax(bw[v],x[k]);
			if(x[0]!=-1&&x[1]!=-1){
				rep(k,2)twocyc[k]=x[k];
			}
			vis[v]=2;
		};
		dfs(dfs,0,-1,-1,0);
	}
	
	auto getcycle=[&](int c){
		vi res{c};
		for(int i=U[c];i!=V[c];i=pv[i]){
			res.pb(pe[i]);
		}
		return reout(res);
	};
	
	vc<bool> avail(m,true);
	auto getwalk=[&](vi cyc){
		vi pos(n,-1);
		rep(i,si(cyc))pos[U[cyc[i]]]=i;
		vc<bool> vis(n);
		
		vi cur;
		auto dfs=[&](auto self,int v)->bool{
			assert(!vis[v]);
			vis[v]=true;
			int step=rand_int(0,si(g[v]));
			myshuffle(g[v]);
			rep(_,si(g[v])+1){
				if(_==step){
					if(pos[v]!=-1){
						rep(i,si(cyc))cur.pb(cyc[(pos[v]+i)%si(cyc)]);
						return true;
					}
				}
				if(_<si(g[v])){
					auto [to,id]=g[v][_];
					if(avail[id]){
						if(!vis[to]){
							cur.pb(id);
							if(self(self,to)){
								cur.pb(id);
								return true;
							}else{
								cur.pop_back();
							}
						}
					}
				}
			}
			return false;
		};
		bool res=dfs(dfs,0);
		assert(res);
		return cur;
	};
	
	auto mg=[&](vi a,vi b){
		assert(a!=b);
		for(auto v:b){
			if(si(a)&&a.back()==v)a.pop_back();
			else a.pb(v);
		}
		return a;
	};
	
	if(twocyc[0]!=-1&&twocyc[1]!=-1){
		vi cyc[2];
		rep(k,2)cyc[k]=getcycle(twocyc[k]);
		
		rep(k,2)for(auto i:cyc[k])avail[i]=false;
		vi x=getwalk(cyc[0]);
		vi y=getwalk(cyc[1]);
		
		return mg(mg(x,y),mg(reout(x),reout(y)));
	}
	
	dominator_tree dt(n*2);
	vi bef(n,-1);
	vc<pi> arc;
	int s=n;
	{
		vi vis(n);
		vi ls;
		auto dfs=[&](auto self,int v,int d)->void{
			assert(!vis[v]);
			vis[v]=1;
			for(auto [to,id]:g[v]){
				if(!vis[to]){
					int e=s++;
					dt.ae(v,e);
					dt.ae(e,to);
					ls.pb(e);
					bef[to]=e;
					self(self,to,d+1);
					ls.pop_back();
				}else{
					dt.ae(v,to);
					if(vis[to]==1){
						arc.eb(id,ls[dep[to]]);
					}
				}
			}
			vis[v]=2;
		};
		dfs(dfs,0,0);
	}
	
	vi idom=dt.calc(0);
	vvc<int> t(s);
	rep(i,s)if(idom[i]!=-1)t[idom[i]].pb(i);
	
	treedfs<int> w(t,0);
	
	int singlecyc=-1;
	
	vc<bool> uni(n,true);
	for(auto i:ord)if(i){
		uni[i]=uni[pv[i]];
		if(idom[i]!=bef[i])uni[i]=false;
	}
	
	for(auto [i,pre]:arc){
		if(!w.asde(pre,U[i]))singlecyc=i;
		if(!uni[V[i]])singlecyc=i;
	}
	
	if(singlecyc==-1){
		return false;
	}
	
	vi cyc=getcycle(singlecyc);
	for(auto i:cyc)avail[i]=false;
	vi x=getwalk(cyc);
	vi y;
	do{y=getwalk(cyc);}while(x==y);
	
	return mg(x,reout(y));
}

• Subtask 1: 5 / 5
• Subtask 2: 5 / 5
• Subtask 3: 21 / 21
• Subtask 4: 24 / 24
• Subtask 5: 45 / 45