Submission #1068711

#	Time	Username	Problem	Language	Result	Execution time	Memory
1068711		LittleOrange	Rectangles (IOI19_rect)	C++17	72 / 100	2832 ms	1048576 KiB

rect

#include "rect.h"
#include<bits/stdc++.h>
using namespace std;
using ll = int;
using lll = long long;
const ll maxn = 2500;
const ll big = 1e9;
struct BIT{
	ll n;
	vector<ll> a;
	BIT(ll N):n(N),a(N+1,0){}
	void add(ll i, ll v){
		for(;i<=n;i+=i&-i) a[i] += v;
	}
	ll get(ll i){
		ll x = 0;
		for(;i>0;i-=i&-i) x += a[i];
		return x;
	}
};
struct dsu{
	vector<ll> p;
	dsu(ll N):p(N,-1){}
	ll g(ll i){
		return p[i]<0?i:p[i] = g(p[i]);
	}
	bool m(ll a,ll b){
		a = g(a),b = g(b);
		if (a==b) return false;
		if (p[a]>p[b]) swap(a,b);
		p[a] += p[b];
		p[b] = a;
		return true;
	}
};
struct node{
	ll l,r,m,v;
	node *L,*R;
	node(ll a, ll b):l(a),r(b),m(a+b>>1),v(0),L(nullptr),R(nullptr){
		if (l<r){
			L = new node(l,m);
			R = new node(m+1,r);
		}
	}
	void add(ll i, ll x){
		if(l<r){
			if(i<=m) (L=new node(*L))->add(i,x);
			else (R=new node(*R))->add(i,x);
		}else v+=x;
	}
	ll qry(ll i){
		if(l<r){
			if(i<=m) return L->qry(i);
			else return R->qry(i);
		}else return v;
	}
};
struct segtree{
	vector<node*> rt;
	segtree(ll l, ll r){
		rt.push_back(new node(l,r));
	}
	void nw(){
		//cerr << "nw\n";
		rt.push_back(new node(*rt.back()));
	}
	void add(ll t, ll i, ll x){
		//cerr << "add " << t << " " << i << " " << x << "\n";
		rt[t]->add(i,x);
	}
	ll qry(ll t, ll i){
		ll ret = rt[t]->qry(i);
		//cerr << "qry " << t << " " << i << " -> " << ret << "\n";
		return ret;
	}
};
struct segtree_n{
	ll l0,r0;
	vector<ll> rt,v,L,R;
	segtree_n(ll l, ll r):l0(l),r0(r){
		rt.push_back(build(l,r));
	}
	ll newnode(){
		ll ret = v.size();
		v.emplace_back();
		L.push_back(-1);
		R.push_back(-1);
		return ret;
	}
	ll copy(ll i){
		ll ret = v.size();
		v.push_back(v[i]);
		L.push_back(L[i]);
		R.push_back(R[i]);
		return ret;
	}
	ll build(ll l, ll r){
		ll ret = newnode();
		if (l<r){
			ll m = l+r>>1;
			ll tmp = build(l,m);
			L[ret] = tmp;
			tmp = build(m+1,r);
			R[ret] = tmp;
		}
		return ret;
	}
	void nw(){
		//cerr << "nw\n";
		rt.push_back(copy(rt.back()));
	}
	void add(ll i, ll l, ll r, ll p, ll x){
		if (l==r) v[i] += x;
		else{
			ll m = l+r>>1;
			if (p<=m) {
				ll tmp = copy(L[i]);
				add(L[i]=tmp,l,m,p,x);
			}else{
				ll tmp = copy(R[i]);
 				add(R[i]=tmp,m+1,r,p,x);
			}
		}
	}
	void add(ll t, ll i, ll x){
		//cerr << "add " << t << " " << i << " " << x << "\n";
		add(rt[t],l0,r0,i,x);
	}
	ll qry(ll i, ll l, ll r, ll p){
		if (l==r) return v[i];
		else{
			ll m = l+r>>1;
			if (p<=m) return qry(L[i],l,m,p);
			else return qry(R[i],m+1,r,p);
		}
	}
	ll qry(ll t, ll i){
		ll ret = qry(rt[t],l0,r0,i);
		//cerr << "qry " << t << " " << i << " -> " << ret << "\n";
		return ret;
	}
};
struct mxt{
	ll n;
	vector<ll> a;
	mxt(ll N):n(N),a(N<<2,0){}
	void mod(ll i, ll l, ll r, ll x, ll v){
		if (l==r) a[i] = v;
		else{
			ll m = l+r>>1;
			if (x<=m) mod(i<<1,l,m,x,v);
			else mod(i<<1|1,m+1,r,x,v);
			a[i] = max(a[i<<1],a[i<<1|1]);
		}
	}
	ll qry(ll i, ll l, ll r, ll ql, ll qr){
		if (ql<=l&&r<=qr) return a[i];
		else{
			ll m = l+r>>1;
			ll ret = -big;
			if (ql<=m)ret = max(ret,qry(i<<1,l,m,ql,qr));
			if(qr>m)ret = max(ret,qry(i<<1|1,m+1,r,ql,qr));
			return ret;
		}
	}
};

long long count_rectangles(std::vector<std::vector<int> > a) {
	ll n = a.size(), m = a[0].size();
	if (n<3||m<3) return 0;
	ll sub6 = 1;
	for(auto &o : a) for(ll &i : o) if (i>1) sub6 = 0;
	if (0&&sub6){
		dsu d(n*m);
		for(ll i = 1;i<n-1;i++){
			for(ll j = 1;j<m-1;j++){
				if(i>1&&!a[i][j]&&!a[i-1][j]){
					d.m((i)*m+(j),(i-1)*m+(j));
				}
				if(j>1&&!a[i][j]&&!a[i][j-1]){
					d.m((i)*m+(j),(i)*m+(j-1));
				}
			}
		}
		vector<ll> gs;
		for(ll i = 1;i<n-1;i++){
			for(ll j = 1;j<m-1;j++){
				if(!a[i][j]){
					gs.push_back(d.g((i)*m+(j)));
				}
			}
		}
		sort(gs.begin(),gs.end());
		gs.erase(unique(gs.begin(),gs.end()),gs.end());
		ll gc = gs.size();
		vector<vector<pair<ll,ll>>> ps(gc);
		for(ll i = 1;i<n-1;i++){
			for(ll j = 1;j<m-1;j++){
				if(!a[i][j]){
					ll p = d.g((i)*m+(j));
					ll idx = lower_bound(gs.begin(),gs.end(),p)-gs.begin();
					ps[idx].push_back({i,j});
				}
			}
		}
		ll ans = 0;
		for(auto &o : ps){
			ll x1 = o[0].first, x2=o[0].first, y1=o[0].second, y2=o[0].second;
			for(auto [x,y] : o){
				x1 = min(x,x1);
				x2 = max(x,x2);
				y1 = min(y,y1);
				y2 = max(y,y2);
			}
			ll req = (x2-x1+1)*(y2-y1+1);
			if (req==o.size()) ans++;
		}
		return ans;
	}
	vector<vector<pair<ll,ll>>> row(n),col(m);
	for(ll i = 0;i<n;i++){
		vector<pair<ll,ll>> st;
		for(ll j = 0;j<m;j++){
			while(st.size()&&st.back().first<a[i][j]){
				if(j>st.back().second+1)row[i].push_back({st.back().second,j});
				st.pop_back();
			}
			if(st.size()){
				if(j>st.back().second+1)row[i].push_back({st.back().second,j});
			}
			if (st.size()&&st.back().first==a[i][j]) st.pop_back();
			st.push_back({a[i][j],j});
		}
	}
	for(ll j = 0;j<m;j++){
		vector<pair<ll,ll>> st;
		for(ll i = 0;i<n;i++){
			while(st.size()&&st.back().first<a[i][j]){
				if(i>st.back().second+1)col[j].push_back({st.back().second,i});
				st.pop_back();
			}
			if(st.size()){
				if(i>st.back().second+1)col[j].push_back({st.back().second,i});
			}
			if (st.size()&&st.back().first==a[i][j]) st.pop_back();
			st.push_back({a[i][j],i});
		}
	}
	for(auto &o : row) sort(o.begin(),o.end());
	for(auto &o : col) sort(o.begin(),o.end());
	vector<vector<ll>> down(n,vector<ll>(m,0)),up(n,vector<ll>(m,n));
	for(ll i = 0;i<m;i++){
		for(auto [l,r] : col[i]){
			down[l][i] = r;
			up[l][i] = min(up[l][i],r);
		}
	}
	segtree_n tree(0,m*m);
	for(ll i = 0;i<n;i++){
		tree.nw();
		for(auto [l,r] : row[i]){
			ll idx = l*m+r;
			tree.add(i+1,idx,1);
		}
	}
	lll ans = 0;
	for(ll r1 = 1;r1<n-1;r1++){
		vector<pair<ll,ll>> cur;
		vector<pair<ll,ll>> nw;
		BIT t(m);
		vector<vector<pair<ll,ll>>> ops(n);
		BIT t0(m);
		vector<vector<pair<ll,ll>>> ops0(n);
		BIT t1(m);
		vector<vector<pair<ll,ll>>> ops1(n);
		vector<vector<pair<ll,ll>>> nws(n);
		mxt mt(m);
		if (1||sub6) for(ll i = 0;i<m;i++) {
			mt.mod(1,0,m-1,i,max(up[r1-1][i]-1,r1));
			ops[max(up[r1-1][i]-1,r1)].push_back({i+1,1});
			ops[down[r1-1][i]].push_back({i+1,-1});
			ops1[r1].push_back({i+1,1});
			ops1[down[r1-1][i]].push_back({i+1,-1});
			auto itl = lower_bound(col[i].begin(),col[i].end(),make_pair(r1-1,r1+1));
			auto itr = lower_bound(col[i].begin(),col[i].end(),make_pair(r1,0));
			for(auto it = itl;it!=itr;it++){
				ll r = (*it).second;
				ops0[r-1].push_back({i+1,1});
				ops0[r].push_back({i+1,-1});
			}
		}
		for(auto &o : row[r1]){
			ll g = mt.qry(1,0,m-1,o.first+1,o.second-1);
			nws[g].push_back(o);
			////cerr << r1 << " " << g << " " << o.first << " " << o.second << "\n";
		}
		for(ll r2 = r1;r2<n-1;r2++){
			if (1||sub6) for(auto [i,v] : ops[r2]){
				t.add(i,v);
			}
			if (1||sub6) for(auto [i,v] : ops0[r2]){
				t0.add(i,v);
			}
			if (1||sub6) for(auto [i,v] : ops1[r2]){
				t1.add(i,v);
			}
			////cerr << "r2=" << r2 << " has " << nws[r2].size() <<"\n";
			if (1||sub6) for(auto o: nws[r2]){
				ll idx = o.first*m+o.second;
				ll cnt = tree.qry(r2,idx)-tree.qry(r1,idx);
				if(cnt>=r2-r1)cur.push_back(o);
				////cerr << "add " << o.first << " " << o.second << "\n";
			}
			if(r2>r1){
				for(auto &o : cur){
					if (t1.get(o.second)-t1.get(o.first+1)==(o.second-o.first-1)&&binary_search(row[r2].begin(),row[r2].end(),o)){
						nw.push_back(o);
					}
				}
				nw.swap(cur);
				nw.clear();
			}
			if (1||sub6){
				for(auto &o : cur){
					if (t.get(o.second)-t.get(o.first+1)==(o.second-o.first-1)&&
					t0.get(o.second)-t0.get(o.first+1)==(o.second-o.first-1)) ans++;
				}
			}else{
				pair<ll,ll> t = {r1-1,r2+1};
				vector<ll> ok(m,0);
				for(ll i = 0;i<m;i++) ok[i] = down[r1-1][i]>r2&&up[r1-1][i]-1<=r2&&binary_search(col[i].begin(),col[i].end(),t);
				vector<ll> p(m+1,0);
				for(ll i = 0;i<m;i++) p[i+1] = p[i]+ok[i];
				for(auto &o : cur){
					if (p[o.second]-p[o.first+1]==(o.second-o.first-1)) ans++;
				}
			}
		}
	}
	return ans;
}

Compilation message (stderr)

rect.cpp: In constructor 'node::node(ll, ll)':
rect.cpp:39:32: warning: suggest parentheses around '+' inside '>>' [-Wparentheses]
   39 |  node(ll a, ll b):l(a),r(b),m(a+b>>1),v(0),L(nullptr),R(nullptr){
      |                               ~^~
rect.cpp: In member function 'll segtree_n::build(ll, ll)':
rect.cpp:100:12: warning: suggest parentheses around '+' inside '>>' [-Wparentheses]
  100 |    ll m = l+r>>1;
      |           ~^~
rect.cpp: In member function 'void segtree_n::add(ll, ll, ll, ll, ll)':
rect.cpp:115:12: warning: suggest parentheses around '+' inside '>>' [-Wparentheses]
  115 |    ll m = l+r>>1;
      |           ~^~
rect.cpp: In member function 'll segtree_n::qry(ll, ll, ll, ll)':
rect.cpp:132:12: warning: suggest parentheses around '+' inside '>>' [-Wparentheses]
  132 |    ll m = l+r>>1;
      |           ~^~
rect.cpp: In member function 'void mxt::mod(ll, ll, ll, ll, ll)':
rect.cpp:150:12: warning: suggest parentheses around '+' inside '>>' [-Wparentheses]
  150 |    ll m = l+r>>1;
      |           ~^~
rect.cpp: In member function 'll mxt::qry(ll, ll, ll, ll, ll)':
rect.cpp:159:12: warning: suggest parentheses around '+' inside '>>' [-Wparentheses]
  159 |    ll m = l+r>>1;
      |           ~^~
rect.cpp: In function 'long long int count_rectangles(std::vector<std::vector<int> >)':
rect.cpp:216:11: warning: comparison of integer expressions of different signedness: 'll' {aka 'int'} and 'std::vector<std::pair<int, int> >::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  216 |    if (req==o.size()) ans++;
      |        ~~~^~~~~~~~~~

• Subtask 1: 8 / 8
• Subtask 2: 7 / 7
• Subtask 3: 12 / 12
• Subtask 4: 22 / 22
• Subtask 5: 10 / 10
• Subtask 6: 13 / 13
• Subtask 7: 0 / 28