Submission #771338

#	Time	Username	Problem	Language	Result	Execution time	Memory
771338		TimDee	Rectangles (IOI19_rect)	C++17	50 / 100	5055 ms	385856 KiB

rect

#include "rect.h"
#include <bits/stdc++.h>
using namespace std;
#define forn(i,n) for(int i=0; i<n; ++i)
#define pi pair<int,int>
#define f first
#define s second
#define ll long long
#define pb push_back
#define all(x) x.begin(),x.end()
struct DSU {
	vector<int> p, sz, l, r, t, d;
	int m;
	DSU(int n, int _m) {
		m=_m;
		forn(i,n*m) {
			p.pb(i);
			sz.pb(1);
			l.pb(i%m);
			r.pb(i%m);
			t.pb(i/m);
			d.pb(i/m);
		}
	}
	int get(int u) {
		return p[u]==u?u:get(p[u]);
	}
	void uni(int u, int v) {
		u=get(u), v=get(v);
		if (u==v) return;
		if (sz[u]<sz[v]) swap(u,v);
		p[v]=u;
		sz[u]+=sz[v];
		l[u]=min(l[u],l[v]);
		r[u]=max(r[u],r[v]);
		t[u]=min(t[u],t[v]);
		d[u]=max(d[u],d[v]);
	}
	void uni(int a, int b, int c, int d) {
		uni(a*m+b,c*m+d);
	}
};
ll wrong(vector<vector<int>> b) {
	int n=b.size(), m=b[0].size();
	vector<vector<int>> a(n+2,vector<int>(m+2,-1));
	forn(i,n) forn(j,m) a[i+1][j+1]=b[i][j];
	vector<pi> v;
	n+=2, m+=2;
	DSU dsu(n,m);
	forn(i,n) forn(j,m) if (a[i][j]!=-1) v.pb({a[i][j],i*m+j});
	sort(all(v));
 
	vector<vector<int>> ok(n,vector<int>(m,0));
	forn(i,n) forn(j,m) {
		if (i==0 || i==n-1) ok[i][j]=1;
		if (j==0 || j==m-1) ok[i][j]=1;
	}
	forn(i,n) forn(j,m) if (ok[i][j]) dsu.uni(i,j,0,0);
 
	ll ans=0;
	int N=v.size();
	for(int i=0; i<N; ) {
		vector<int> z;
		int x=v[i].f;
		while (i<N && v[i].f==x) {
			z.pb(v[i].s);
			++i;
		}
		for(auto&it:z) {
			int x=it/m, y=it%m;
			if (ok[x-1][y]) dsu.uni(x-1,y,x,y);
			if (ok[x+1][y]) dsu.uni(x+1,y,x,y);
			if (ok[x][y-1]) dsu.uni(x,y-1,x,y);
			if (ok[x][y+1]) dsu.uni(x,y+1,x,y);
			ok[x][y]=1;
		}
		map<int,int> was;
		for(auto&it:z) {
			int x=it/m, y=it%m; 
 
			int u=dsu.get(it);
			if (was[u]) continue;
			was[u]=1;
			int b=dsu.l[u];
			int a=dsu.t[u];
			int d=dsu.r[u];
			int c=dsu.d[u];
			int k=(c-a+1)*(d-b+1);
			if (k==dsu.sz[u]) ++ans;
		}
	}
	return ans-1;
}

const int N=700;
bitset<N> dp1[N][N], dp2[N][N];

struct BIT {
	int n,m;
	vector<vector<int>> t;
	BIT(int n, int m) {
		this->n=n, this->m=m;
		t.assign(n,vector<int>(m,0));
	}
	void addi(int i, int j, int x) {
		for(;j<m;j=j|(j+1)) t[i][j]+=x;
	}
	void add(int i, int j, int x) {
		for(;i<n;i=i|(i+1)) addi(i,j,x);
	}
	int sumi(int i, int j) {
		int q=0;
		for(;j>=0;j=(j&(j+1))-1) q+=t[i][j];
		return q;
	}
	int sum(int a, int b) {
		int q=0;
		for(;a>=0;a=(a&(a+1))-1) q+=sumi(a,b);
		return q;
	}
	int sum(int a, int b, int c, int d) {
		return sum(c,d)-sum(a-1,d)-sum(c,b-1)+sum(a-1,b-1);
	}
};

struct dsu {
	vector<int> p,sz,l,r;
	dsu(int n) {
		forn(i,n) p.pb(i), sz.pb(1);
		l=r=p;
	}
	int get(int u) {
		return p[u]==u?u:get(p[u]);
	}
	void uni(int u, int v) {
		u=get(u),v=get(v);
		if (u==v) return;
		if (sz[u]<sz[v]) swap(u,v);
		p[v]=u;
		sz[u]+=sz[v];
		l[u]=min(l[u],l[v]);
		r[u]=max(r[u],r[v]);
	}
};
vector<dsu> dsu1(N,dsu(N)), dsu2(N,dsu(N));
int ok[N][N];
BIT ft(N,N);
int a[N][N];
int pre[N+1];

const int K=11;
int st1[N][N][K], st2[N][N][K];
void init() {
	int p=0;
	forn(i,N+1) {
		while (2*(1<<p) < i) ++p;
		pre[i]=p;
	}
}
void build(int k, vector<int>&a) {
	int n=a.size();
	forn(i,n) st1[k][i][0]=a[i];
	for(int j=1; j<K; ++j) {
		forn(i,n) st1[k][i][j]=max(st1[k][i][j-1], (i+(1<<(j-1)))<n ? st1[k][i+(1<<(j-1))][j-1] : 0 );
	}
}
inline int query1(int k, int l, int r) {
	int p=pre[r-l+1];
	return max( st1[k][l][p] , st1[k][r-(1<<p)+1][p] );
}
inline int query2(int k, int l, int r) {
	int p=pre[r-l+1];
	return max( st2[k][l][p] , st2[k][r-(1<<p)+1][p] );
}

int it=0;
int check(int l, int u, int r, int d) {
	int ok=1;
	for (int i=l; i<=r; ++i) {
		int x=query1(i,u,d);
		ok&=a[i][u-1]>x && x<a[i][d+1];
	}
	for (int i=u; i<=d; ++i) {
		int x=query2(i,l,r);
		ok&=a[l-1][i]>x && x<a[r+1][i];
	}
	return ok;
} 

ll count_rectangles(vector<vector<int>> b) {

	int n=b.size(), m=b[0].size();
	if (min(n,m)<3) return 0;
	int mx=0; for(auto&x:b) for(auto&y:x) mx=max(mx,y);
	if (mx==1) return wrong(b);

	if (n==3) {
		ll ans=0;
		for (int i=0; i<m; ++i) {
			int mx=0;
			for (int j=i+1; j<m-1; ++j) {
				if (b[0][j]<=b[1][j] || b[1][j]>=b[2][j]) break;
				mx=max(mx,b[1][j]);
				ans += b[1][i]>mx && mx<b[1][j+1];
			}
		}
		return ans;
	}
	if (max(n,m)>N) exit(0);

	init();
	forn(i,n) forn(j,m) a[i][j]=b[i][j];
	forn(i,n) build(i,b[i]);
	swap(st1,st2);
	forn(j,m) {
		vector<int> v; forn(i,n) v.pb(a[i][j]);
		build(j,v);
	}
	swap(st1,st2);

	vector<pi> v;
	forn(i,n) forn(j,m) v.pb({a[i][j],i*m+j});
	sort(all(v));

	ll ans=0;
	int N=v.size();
	map<ll,ll> was;
	for(int i=0; i<N; ) {
		vector<int> z;
		int x=v[i].f;
		while (i<N && v[i].f==x) {
			z.pb(v[i].s);
			++i;
		}
		for(auto&it:z) {
			int x=it/m, y=it%m;
			if (x) if (ok[x-1][y]) dsu1[y].uni(x-1,x); 
			if (x<n-1) if (ok[x+1][y]) dsu1[y].uni(x+1,x);
			if (y) if (ok[x][y-1]) dsu2[x].uni(y-1,y);
			if (y<m-1) if (ok[x][y+1]) dsu2[x].uni(y+1,y);
			ok[x][y]=1;
			ft.add(x,y,1);
		}
		for(auto&it:z) {
			int x=it/m, y=it%m;
			int u=dsu1[y].get(x);
			int a=dsu1[y].l[u], c=dsu1[y].r[u];
			int v=dsu2[x].get(y);
			int b=dsu2[x].l[v], d=dsu2[x].r[v];
			if (a==0 || b==0 || c==n-1 || d==m-1) continue;
			if (was[1ll*a*m+b+1ll*n*m*(1ll*c*m+d)]) continue;
			was[1ll*a*m+b+1ll*n*m*(1ll*c*m+d)]=1;
			if (it<=0.5e8) {
				int q = check(a,b,c,d);
				ans+=q;
				it+=(c-a+1)+(d-b+1);
			} else {
				exit(0);
			}
		}
	}
	assert(it<=2e8);
	return ans;
}

Compilation message (stderr)

rect.cpp: In function 'long long int wrong(std::vector<std::vector<int> >)':
rect.cpp:79:8: warning: unused variable 'x' [-Wunused-variable]
   79 |    int x=it/m, y=it%m;
      |        ^
rect.cpp:79:16: warning: unused variable 'y' [-Wunused-variable]
   79 |    int x=it/m, y=it%m;
      |                ^

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