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Submission #565186

# Submission time Handle Problem Language Result Execution time Memory
565186 2022-05-20T12:26:56 Z errorgorn Fences (JOI18_fences) C++17
51 / 100
 925 ms 2100 KB 
#include <bits/stdc++.h>
using namespace std;

#define int long long
#define ii pair<int,int>
#define fi first
#define se second

#define puf push_front
#define pof pop_front
#define pub push_back
#define pob pop_back
#define lb lower_bound
#define ub upper_bound

#define rep(x,s,e) for (int x=(s)-((s)>(e));x!=(e)-((s)>(e));((s)<(e))?x++:x--)
#define all(x) (x).begin(),(x).end()
#define sz(x) (int) (x).size()

mt19937 rng(chrono::system_clock::now().time_since_epoch().count());

const double EPS=1e-9;
const double TAU=acos(0)*4;

struct vec{
	double x,y;
};

vec add(vec i,vec j){
	return {i.x+j.x,i.y+j.y};
}

vec sub(vec i,vec j){
	return {i.x-j.x,i.y-j.y};
};

vec mul(double lambda,vec i){
	return {i.x*lambda,i.y*lambda};
};

double dist(vec i,vec j){
	double dx=i.x-j.x;
	double dy=i.y-j.y;
	return sqrt(dx*dx+dy*dy);
}

int n;
double k;
int arr[110][4];

vector<vec> p; //stores all points
vector<double> angle;

double diff(double i,double j){
	double res=i-j;
	while (res<-TAU/2) res+=TAU;
	while (res>TAU/2) res-=TAU;
	return res;
}

int count(double i){
	return floor(i/TAU+0.5);
}

#define id pair<int,double>
#define dii pair<double,ii>
double w[10005][5];
vector<id> al[10005];

priority_queue<dii,vector<dii>,greater<dii> > pq;

bool inter(vec i,vec j,vec a,vec b){
	//i.x + j.x*L1 = a.x + b.x*L2
	//i.y + j.y*L1 = a.y + b.y*L2
	
	//j.x * L1 - b.x * L2 = a.x - i.x
	//j.y * L1 - b.y * L2 = a.y - i.y
	
	//check that L1,L2 in [0,1]
	
	vector<double> v = {
		a.x - i.x,
		a.y - i.y
	};
	
	vector<vector<double> > mat = {
		{j.x,-b.x},
		{j.y,-b.y}
	};
	
	double det=mat[0][0]*mat[1][1]-mat[0][1]*mat[1][0];
	if (abs(det)<=1e-9) return false;
	
	vector<vector<double> > imat = {
		{mat[1][1],-mat[0][1]},
		{-mat[1][0],mat[0][0]}
	};
	rep(x,0,2) rep(y,0,2) imat[x][y]/=det;
	
	rep(x,0,2){
		double res=0;
		rep(y,0,2){
			res+=imat[x][y]*v[y];
		}
		if (res<0 || 1<res) return false;
	}
	return true;
}

bool ok(vec i,vec j){
	vector<vec> v={  {-k+2*EPS,-k+EPS},{-k+EPS,k-2*EPS},{k-2*EPS,k-EPS},{k-EPS,-k+2*EPS} };
	vector<vec> v2={ {-k+2*EPS,k-EPS},{k-EPS,k-2*EPS},{k-2*EPS,-k+EPS},{-k+EPS,-k+2*EPS} };
	
	rep(x,0,4){
		if (inter(i,sub(j,i),v[x],sub(v2[x],v[x]))) return false;
	}
	return true;
}

signed main(){
	cin.tie(0);
	cout.tie(0);
	cin.sync_with_stdio(false);
	
	cin>>n>>k;
	rep(x,0,n) rep(y,0,4) cin>>arr[x][y];
	rep(x,0,4) rep(y,0,4){
		if (x==3 || (x && (x+y)%2==0)) arr[n+x][y]=-k;
		else arr[n+x][y]=k;
	}
	n+=4;
	
	//rep(x,0,n){
		//rep(y,0,4) cout<<arr[x][y]<<" "; cout<<endl;
	//}
	
	rep(x,0,n) p.pub({(double)arr[x][0],(double)arr[x][1]});
	rep(x,0,n) p.pub({(double)arr[x][2],(double)arr[x][3]});
	rep(x,0,n){
		al[x].pub({x+n,0});
		al[x+n].pub({x,0});
	}
	
	double ans=8*k;
	
	rep(x,0,n) rep(y,x+1,n){
		vec temp[4];
		vec temp2[4];
		
		double best=1e18;
		int idx=-1;
		
		rep(z,0,4){
			if (z>=2) swap(x,y);
			
			if (z%2==0) temp2[z]=p[x];
			else temp2[z]=p[x+n];
			
			vec base=p[y];
			vec dir=sub(p[y+n],p[y]);
			
			double lo=0,hi=1;
			rep(x,0,70){
				double mi1=lo+(hi-lo)/3,mi2=lo+2*(hi-lo)/3;
				
				if (dist(add(base,mul(mi1,dir)),temp2[z])<dist(add(base,mul(mi2,dir)),temp2[z])){
					hi=mi2;
				}
				else{
					lo=mi1;
				}
			}
			
			temp[z]=add(base,mul(lo,dir));
			double curr=dist(temp2[z],temp[z]);
			if (curr<best){
				best=curr;
				idx=z;
			}
			
			if (z>=2) swap(x,y);
		}
		
		if (ok(temp[idx],temp2[idx])){
			//cout<<x<<" "<<y<<" "<<best<<" "<<idx<<endl;
			//cout<<temp[idx].x<<" "<<temp[idx].y<<endl;
			//cout<<temp2[idx].x<<" "<<temp2[idx].y<<endl;
			//rep(z,0,4) cout<<arr[x][z]<<" "; cout<<endl;
			//rep(z,0,4) cout<<arr[y][z]<<" "; cout<<endl;
			//cout<<endl;
			
			//cout<<"cunny"<<endl;
			int IDX1=sz(p),IDX2;
			p.pub(temp[idx]);
			
			if (idx==0) IDX2=x;
			if (idx==1) IDX2=x+n;
			if (idx==2) IDX2=y;
			if (idx==3) IDX2=y+n;
			
			//cout<<temp2[idx].x<<" "<<temp2[idx].y<<endl;
			//cout<<p[IDX2].x<<" "<<p[IDX2].y<<endl;
			
			al[IDX1].pub({IDX2,best});
			al[IDX2].pub({IDX1,best});
			
			if (idx<2) IDX2=y;
			else IDX2=x;
			al[IDX1].pub({IDX2,0});
			al[IDX2].pub({IDX1,0});
		}
	}
	
	rep(x,0,sz(p)){
		angle.pub(atan2(p[x].x,p[x].y)+TAU/2);
		//cout<<x<<" "<<p[x].x<<" "<<p[x].y<<" "<<angle[x]<<endl;
	}
	
	rep(x,0,n){
		rep(y,0,10005) rep(z,0,5) w[y][z]=1e18;
		
		w[x][2]=0;
		pq.push({w[x][2],ii(x,2)});
		
		while (!pq.empty()){
			double weight;
			ii u;
			tie(weight,u)=pq.top(),pq.pop();
			if (w[u.fi][u.se]!=weight) continue;
			
			double angle1=diff(angle[x],angle[u.fi])+TAU*u.se;
			
			for (auto [it,w2]:al[u.fi]){
				int it2=count(angle1+diff(angle[u.fi],angle[it])-diff(angle[x],angle[it]));
				if (it2<0 || 4<it2) continue;
				if (w[it][it2]>weight+w2){
					w[it][it2]=weight+w2;
					pq.push({w[it][it2],ii(it,it2)});
				}
			}
		}
		
		//cout<<x<<" "<<w[x][3]<<endl;
		ans=min(ans,w[x][3]);
	}
	
	cout<<fixed<<setprecision(12)<<ans<<endl;
}

Subtask #1
18.0 / 18.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 852 KB Output is correct
2 Correct 1 ms 956 KB Output is correct
3 Correct 1 ms 852 KB Output is correct
4 Correct 1 ms 852 KB Output is correct
5 Correct 1 ms 852 KB Output is correct
6 Correct 1 ms 960 KB Output is correct
7 Correct 1 ms 852 KB Output is correct
8 Correct 1 ms 864 KB Output is correct
9 Correct 1 ms 852 KB Output is correct
10 Correct 1 ms 852 KB Output is correct
11 Correct 1 ms 964 KB Output is correct
12 Correct 1 ms 852 KB Output is correct
13 Correct 1 ms 852 KB Output is correct
14 Correct 1 ms 852 KB Output is correct
15 Correct 1 ms 852 KB Output is correct
16 Correct 1 ms 964 KB Output is correct
17 Correct 1 ms 852 KB Output is correct
18 Correct 1 ms 852 KB Output is correct
19 Correct 1 ms 852 KB Output is correct
20 Correct 1 ms 852 KB Output is correct

Subtask #2
33.0 / 33.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 852 KB Output is correct
2 Correct 1 ms 956 KB Output is correct
3 Correct 1 ms 852 KB Output is correct
4 Correct 1 ms 852 KB Output is correct
5 Correct 1 ms 852 KB Output is correct
6 Correct 1 ms 960 KB Output is correct
7 Correct 1 ms 852 KB Output is correct
8 Correct 1 ms 864 KB Output is correct
9 Correct 1 ms 852 KB Output is correct
10 Correct 1 ms 852 KB Output is correct
11 Correct 1 ms 964 KB Output is correct
12 Correct 1 ms 852 KB Output is correct
13 Correct 1 ms 852 KB Output is correct
14 Correct 1 ms 852 KB Output is correct
15 Correct 1 ms 852 KB Output is correct
16 Correct 1 ms 964 KB Output is correct
17 Correct 1 ms 852 KB Output is correct
18 Correct 1 ms 852 KB Output is correct
19 Correct 1 ms 852 KB Output is correct
20 Correct 1 ms 852 KB Output is correct
21 Correct 1 ms 956 KB Output is correct
22 Correct 2 ms 852 KB Output is correct
23 Correct 2 ms 852 KB Output is correct
24 Correct 2 ms 852 KB Output is correct
25 Correct 2 ms 852 KB Output is correct
26 Correct 2 ms 960 KB Output is correct
27 Correct 1 ms 852 KB Output is correct
28 Correct 2 ms 852 KB Output is correct
29 Correct 2 ms 852 KB Output is correct
30 Correct 2 ms 852 KB Output is correct
31 Correct 3 ms 864 KB Output is correct
32 Correct 2 ms 964 KB Output is correct
33 Correct 2 ms 960 KB Output is correct
34 Correct 2 ms 852 KB Output is correct
35 Correct 2 ms 852 KB Output is correct
36 Correct 2 ms 860 KB Output is correct
37 Correct 2 ms 852 KB Output is correct
38 Correct 1 ms 852 KB Output is correct
39 Correct 2 ms 852 KB Output is correct
40 Correct 1 ms 868 KB Output is correct
41 Correct 1 ms 860 KB Output is correct
42 Correct 1 ms 852 KB Output is correct
43 Correct 1 ms 972 KB Output is correct

Subtask #3
0 / 49.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 852 KB Output is correct
2 Correct 1 ms 956 KB Output is correct
3 Correct 1 ms 852 KB Output is correct
4 Correct 1 ms 852 KB Output is correct
5 Correct 1 ms 852 KB Output is correct
6 Correct 1 ms 960 KB Output is correct
7 Correct 1 ms 852 KB Output is correct
8 Correct 1 ms 864 KB Output is correct
9 Correct 1 ms 852 KB Output is correct
10 Correct 1 ms 852 KB Output is correct
11 Correct 1 ms 964 KB Output is correct
12 Correct 1 ms 852 KB Output is correct
13 Correct 1 ms 852 KB Output is correct
14 Correct 1 ms 852 KB Output is correct
15 Correct 1 ms 852 KB Output is correct
16 Correct 1 ms 964 KB Output is correct
17 Correct 1 ms 852 KB Output is correct
18 Correct 1 ms 852 KB Output is correct
19 Correct 1 ms 852 KB Output is correct
20 Correct 1 ms 852 KB Output is correct
21 Correct 1 ms 956 KB Output is correct
22 Correct 2 ms 852 KB Output is correct
23 Correct 2 ms 852 KB Output is correct
24 Correct 2 ms 852 KB Output is correct
25 Correct 2 ms 852 KB Output is correct
26 Correct 2 ms 960 KB Output is correct
27 Correct 1 ms 852 KB Output is correct
28 Correct 2 ms 852 KB Output is correct
29 Correct 2 ms 852 KB Output is correct
30 Correct 2 ms 852 KB Output is correct
31 Correct 3 ms 864 KB Output is correct
32 Correct 2 ms 964 KB Output is correct
33 Correct 2 ms 960 KB Output is correct
34 Correct 2 ms 852 KB Output is correct
35 Correct 2 ms 852 KB Output is correct
36 Correct 2 ms 860 KB Output is correct
37 Correct 2 ms 852 KB Output is correct
38 Correct 1 ms 852 KB Output is correct
39 Correct 2 ms 852 KB Output is correct
40 Correct 1 ms 868 KB Output is correct
41 Correct 1 ms 860 KB Output is correct
42 Correct 1 ms 852 KB Output is correct
43 Correct 1 ms 972 KB Output is correct
44 Correct 925 ms 2088 KB Output is correct
45 Correct 691 ms 2048 KB Output is correct
46 Correct 582 ms 1700 KB Output is correct
47 Correct 404 ms 1508 KB Output is correct
48 Correct 903 ms 2096 KB Output is correct
49 Correct 761 ms 1968 KB Output is correct
50 Correct 572 ms 1640 KB Output is correct
51 Correct 413 ms 1416 KB Output is correct
52 Correct 572 ms 1640 KB Output is correct
53 Correct 546 ms 1652 KB Output is correct
54 Correct 607 ms 1708 KB Output is correct
55 Correct 626 ms 1892 KB Output is correct
56 Correct 650 ms 1956 KB Output is correct
57 Correct 533 ms 1584 KB Output is correct
58 Correct 534 ms 1648 KB Output is correct
59 Correct 551 ms 1672 KB Output is correct
60 Correct 558 ms 1676 KB Output is correct
61 Correct 649 ms 1880 KB Output is correct
62 Correct 3 ms 960 KB Output is correct
63 Correct 3 ms 980 KB Output is correct
64 Correct 527 ms 1824 KB Output is correct
65 Correct 544 ms 1716 KB Output is correct
66 Correct 369 ms 1376 KB Output is correct
67 Incorrect 773 ms 2100 KB Output isn't correct
68 Halted 0 ms 0 KB -