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IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#189242#5106. Islands from the Skybulijiojiodibuliduo#AC ✓112ms4364kbC++1711.8kb2023-09-27 03:02:062023-09-27 03:02:07

Judging History

你现在查看的是最新测评结果

  • [2023-09-27 03:02:07]
  • 评测
  • 测评结果:AC
  • 用时:112ms
  • 内存:4364kb
  • [2023-09-27 03:02:06]
  • 提交

answer

#include <bits/stdc++.h>
using namespace std;
#define rep(i,a,n) for (int i=a;i<n;i++)
#define per(i,a,n) for (int i=n-1;i>=a;i--)
#define pb push_back
#define eb emplace_back
#define mp make_pair
#define all(x) (x).begin(),(x).end()
#define fi first
#define se second
#define SZ(x) ((int)(x).size())
typedef vector<int> VI;
typedef basic_string<int> BI;
typedef long long ll;
typedef pair<int,int> PII;
typedef double db;
mt19937 mrand(random_device{}()); 
const ll mod=1000000007;
int rnd(int x) { return mrand() % x;}
ll powmod(ll a,ll b) {ll res=1;a%=mod; assert(b>=0); for(;b;b>>=1){if(b&1)res=res*a%mod;a=a*a%mod;}return res;}
ll gcd(ll a,ll b) { return b?gcd(b,a%b):a;}
// head

typedef double db;
const db EPS = 1e-9;
const db PI = acos(-1.0);
  
inline int sign(db a) { return a < -EPS ? -1 : a > EPS; }
  
inline int cmp(db a, db b){ return sign(a-b); }
  
struct P {
	db x, y;
	P() {}
	P(db _x, db _y) : x(_x), y(_y) {}
	P operator+(P p) { return {x + p.x, y + p.y}; }
	P operator-(P p) { return {x - p.x, y - p.y}; }
	P operator*(db d) { return {x * d, y * d}; }
	P operator/(db d) { return {x / d, y / d}; }
 
	bool operator<(P p) const { 
		int c = cmp(x, p.x);
		if (c) return c == -1;
		return cmp(y, p.y) == -1;
	}
 
	bool operator==(P o) const{
		return cmp(x,o.x) == 0 && cmp(y,o.y) == 0;
	}
 
	db dot(P p) { return x * p.x + y * p.y; }
	db det(P p) { return x * p.y - y * p.x; }
	 
	db distTo(P p) { return (*this-p).abs(); }
	db alpha() { return atan2(y, x); }
	void read() { cin>>x>>y; }
	void write() {cout<<"("<<x<<","<<y<<")"<<endl;}
	db abs() { return sqrt(abs2());}
	db abs2() { return x * x + y * y; }
	P rot90() { return P(-y,x);}
	P unit() { return *this/abs(); }
	int quad() const { return sign(y) == 1 || (sign(y) == 0 && sign(x) >= 0); }
	P rot(db an){ return {x*cos(an)-y*sin(an),x*sin(an) + y*cos(an)}; }
};
  
struct L{ //ps[0] -> ps[1]
	P ps[2];
	P dir_;
	P& operator[](int i) { return ps[i]; }
	P dir() { return dir_; }
	L (P a,P b) {
		ps[0]=a;
		ps[1]=b;
		dir_ = (ps[1]-ps[0]).unit();
	}
	bool include(P p) { return sign((dir_).det(p - ps[0])) > 0; }
	L push(){ // push eps outward
		const double eps = 1e-8;
		P delta = (ps[1] - ps[0]).rot90().unit() * eps;
		return {ps[0] + delta, ps[1] + delta};
	}
};

#define cross(p1,p2,p3) ((p2.x-p1.x)*(p3.y-p1.y)-(p3.x-p1.x)*(p2.y-p1.y))
#define crossOp(p1,p2,p3) sign(cross(p1,p2,p3))
  
bool chkLL(P p1, P p2, P q1, P q2) {
	db a1 = cross(q1, q2, p1), a2 = -cross(q1, q2, p2);
	return sign(a1+a2) != 0;
}
 
P isLL(P p1, P p2, P q1, P q2) {
	db a1 = cross(q1, q2, p1), a2 = -cross(q1, q2, p2);
	return (p1 * a2 + p2 * a1) / (a1 + a2);
}
  
P isLL(L l1,L l2){ return isLL(l1[0],l1[1],l2[0],l2[1]); }
  
bool intersect(db l1,db r1,db l2,db r2){
	if(l1>r1) swap(l1,r1); if(l2>r2) swap(l2,r2); 
	return !( cmp(r1,l2) == -1 || cmp(r2,l1) == -1 );
}
  
bool isSS(P p1, P p2, P q1, P q2){
	return intersect(p1.x,p2.x,q1.x,q2.x) && intersect(p1.y,p2.y,q1.y,q2.y) && 
	crossOp(p1,p2,q1) * crossOp(p1,p2,q2) <= 0 && crossOp(q1,q2,p1)
			* crossOp(q1,q2,p2) <= 0;
}
  
bool isSS_strict(P p1, P p2, P q1, P q2){
	return crossOp(p1,p2,q1) * crossOp(p1,p2,q2) < 0 && crossOp(q1,q2,p1)
			* crossOp(q1,q2,p2) < 0;
}
  
bool isMiddle(db a, db m, db b) {
	return sign(a - m) == 0 || sign(b - m) == 0 || (a < m != b < m);
}
  
bool isMiddle(P a, P m, P b) {
	return isMiddle(a.x, m.x, b.x) && isMiddle(a.y, m.y, b.y);
}
  
bool onSeg(P p1, P p2, P q){
	return crossOp(p1,p2,q) == 0 && isMiddle(p1, q, p2);
}
 
bool onSeg_strict(P p1, P p2, P q){
	return crossOp(p1,p2,q) == 0 && sign((q-p1).dot(p1-p2)) * sign((q-p2).dot(p1-p2)) < 0;
}
  
P proj(P p1, P p2, P q) {
	P dir = p2 - p1;
	return p1 + dir * (dir.dot(q - p1) / dir.abs2());
}
  
P reflect(P p1, P p2, P q){
	return proj(p1,p2,q) * 2 - q;
}
  
db nearest(P p1,P p2,P q){
	if (p1==p2) return p1.distTo(q);
	P h = proj(p1,p2,q);
	if(isMiddle(p1,h,p2))
		return q.distTo(h);
	return min(p1.distTo(q),p2.distTo(q));
}
  
db disSS(P p1, P p2, P q1, P q2){
	if(isSS(p1,p2,q1,q2)) return 0;
	return min(min(nearest(p1,p2,q1),nearest(p1,p2,q2)), min(nearest(q1,q2,p1),nearest(q1,q2,p2)));
}
  
db rad(P p1,P p2){
	return atan2l(p1.det(p2),p1.dot(p2));
}
  
db incircle(P p1, P p2, P p3){
	db A = p1.distTo(p2);
	db B = p2.distTo(p3);
	db C = p3.distTo(p1);
	return sqrtl(A*B*C/(A+B+C));
}
  
//polygon
  
db area(vector<P> ps){
	db ret = 0; rep(i,0,ps.size()) ret += ps[i].det(ps[(i+1)%ps.size()]); 
	return ret/2;
}
  
int contain(vector<P> ps, P p){ //2:inside,1:on_seg,0:outside
	int n = ps.size(), ret = 0; 
	rep(i,0,n){
		P u=ps[i],v=ps[(i+1)%n];
		if(onSeg(u,v,p)) return 1;
		if(cmp(u.y,v.y)<=0) swap(u,v);
		if(cmp(p.y,u.y) >0 || cmp(p.y,v.y) <= 0) continue;
		ret ^= crossOp(p,u,v) > 0;
	}
	return ret*2;
}
  
vector<P> convexHull(vector<P> ps) {
	int n = ps.size(); if(n <= 1) return ps;
	sort(ps.begin(), ps.end());
	vector<P> qs(n * 2); int k = 0;
	for (int i = 0; i < n; qs[k++] = ps[i++]) 
		while (k > 1 && crossOp(qs[k - 2], qs[k - 1], ps[i]) <= 0) --k;
	for (int i = n - 2, t = k; i >= 0; qs[k++] = ps[i--])
		while (k > t && crossOp(qs[k - 2], qs[k - 1], ps[i]) <= 0) --k;
	qs.resize(k - 1);
	return qs;
}
  
vector<P> convexHullNonStrict(vector<P> ps) {
	//caution: need to unique the Ps first
	int n = ps.size(); if(n <= 1) return ps;
	sort(ps.begin(), ps.end());
	vector<P> qs(n * 2); int k = 0;
	for (int i = 0; i < n; qs[k++] = ps[i++]) 
		while (k > 1 && crossOp(qs[k - 2], qs[k - 1], ps[i]) < 0) --k;
	for (int i = n - 2, t = k; i >= 0; qs[k++] = ps[i--])
		while (k > t && crossOp(qs[k - 2], qs[k - 1], ps[i]) < 0) --k;
	qs.resize(k - 1);
	return qs;
}
  
db convexDiameter(vector<P> ps){
	int n = ps.size(); if(n <= 1) return 0;
	int is = 0, js = 0; rep(k,1,n) is = ps[k]<ps[is]?k:is, js = ps[js] < ps[k]?k:js;
	int i = is, j = js;
	db ret = ps[i].distTo(ps[j]);
	do{
		if((ps[(i+1)%n]-ps[i]).det(ps[(j+1)%n]-ps[j]) >= 0)
			(++j)%=n;
		else
			(++i)%=n;
		ret = max(ret,ps[i].distTo(ps[j]));
	}while(i!=is || j!=js);
	return ret;
}
  
vector<P> convexCut(const vector<P>&ps, P q1, P q2) {
	vector<P> qs;
	int n = ps.size();
	rep(i,0,n){
		P p1 = ps[i], p2 = ps[(i+1)%n];
		int d1 = crossOp(q1,q2,p1), d2 = crossOp(q1,q2,p2);
		if(d1 >= 0) qs.pb(p1);
		if(d1 * d2 < 0) qs.pb(isLL(p1,p2,q1,q2));
	}
	return qs;
}
  
//min_dist
  
db min_dist(vector<P>&ps,int l,int r){
	if(r-l<=5){
		db ret = 1e100;
		rep(i,l,r) rep(j,l,i) ret = min(ret,ps[i].distTo(ps[j]));
		return ret;
	}
	int m = (l+r)>>1;
	db ret = min(min_dist(ps,l,m),min_dist(ps,m,r));
	vector<P> qs; rep(i,l,r) if(abs(ps[i].x-ps[m].x)<= ret) qs.pb(ps[i]);
	sort(qs.begin(), qs.end(),[](P a,P b) -> bool {return a.y<b.y; });
	rep(i,1,qs.size()) for(int j=i-1;j>=0&&qs[j].y>=qs[i].y-ret;--j)
		ret = min(ret,qs[i].distTo(qs[j]));
	return ret;
}
  
int type(P o1,db r1,P o2,db r2){
	db d = o1.distTo(o2);
	if(cmp(d,r1+r2) == 1) return 4;
	if(cmp(d,r1+r2) == 0) return 3;
	if(cmp(d,abs(r1-r2)) == 1) return 2;
	if(cmp(d,abs(r1-r2)) == 0) return 1;
	return 0;
}
  
vector<P> isCL(P o,db r,P p1,P p2){
	if (cmp(abs((o-p1).det(p2-p1)/p1.distTo(p2)),r)>0) return {};
	db x = (p1-o).dot(p2-p1), y = (p2-p1).abs2(), d = x * x - y * ((p1-o).abs2() - r*r);
	d = max(d,(db)0.0); P m = p1 - (p2-p1)*(x/y), dr = (p2-p1)*(sqrt(d)/y);
	return {m-dr,m+dr}; //along dir: p1->p2
}
  
vector<P> isCC(P o1, db r1, P o2, db r2) { //need to check whether two circles are the same
	db d = o1.distTo(o2); 
	if (cmp(d, r1 + r2) == 1) return {};
	if (cmp(d,abs(r1-r2))==-1) return {};
	d = min(d, r1 + r2);
	db y = (r1 * r1 + d * d - r2 * r2) / (2 * d), x = sqrt(r1 * r1 - y * y);
	P dr = (o2 - o1).unit();
	P q1 = o1 + dr * y, q2 = dr.rot90() * x;
	return {q1-q2,q1+q2};//along circle 1
}
  
vector<P> tanCP(P o, db r, P p) {
	db x = (p - o).abs2(), d = x - r * r;
	if (sign(d) <= 0) return {}; // on circle => no tangent
	P q1 = o + (p - o) * (r * r / x);
	P q2 = (p - o).rot90() * (r * sqrt(d) / x);
	return {q1-q2,q1+q2}; //counter clock-wise
}
  
// extanCC, intanCC : -r2, tanCP : r2 = 0
vector<pair<P, P>> tanCC(P o1, db r1, P o2, db r2) {
	P d = o2 - o1;
	db dr = r1 - r2, d2 = d.abs2(), h2 = d2 - dr * dr;
	if (sign(d2) == 0|| sign(h2) < 0) return {};
	h2 = max(0.0, h2);
	vector<pair<P, P>> ret;
	for (db sign : {-1, 1}) {
		P v = (d * dr + d.rot90() * sqrt(h2) * sign) / d2;
		ret.push_back({o1 + v * r1, o2 + v * r2});
	}
	if (sign(h2) == 0) ret.pop_back();
	return ret;
}
  
db areaCT(db r, P p1, P p2){
	vector<P> is = isCL(P(0,0),r,p1,p2);
	if(is.empty()) return r*r*rad(p1,p2)/2;
	bool b1 = cmp(p1.abs2(),r*r) == 1, b2 = cmp(p2.abs2(), r*r) == 1;
	if(b1 && b2){
		P md=(is[0]+is[1])/2;
		if(sign((p1-md).dot(p2-md)) <= 0) 
			return r*r*(rad(p1,is[0]) + rad(is[1],p2))/2 + is[0].det(is[1])/2;
		else return r*r*rad(p1,p2)/2;
	}
	if(b1) return (r*r*rad(p1,is[0]) + is[0].det(p2))/2;
	if(b2) return (p1.det(is[1]) + r*r*rad(is[1],p2))/2;
	return p1.det(p2)/2;
}
  
bool parallel(L l0, L l1) { return sign( l0.dir().det( l1.dir() ) ) == 0; }
  
bool sameDir(L l0, L l1) { return parallel(l0, l1) && sign(l0.dir().dot(l1.dir()) ) == 1; }
  
bool cmp (P a,  P b) {
	if (a.quad() != b.quad()) {
		return a.quad() < b.quad();
	} else {
		return sign( a.det(b) ) > 0;
	}
}
  
bool operator < (L l0, L l1) {
	if (sameDir(l0, l1)) {
		return l1.include(l0[0]);
	} else {
		return cmp( l0.dir(), l1.dir() );
	}
}
  
bool check(L u, L v, L w) { 
	return w.include(isLL(u,v)); 
}
  
vector<P> halfPlaneIS(vector<L> &l) {
	sort(l.begin(), l.end());
	deque<L> q;
	for (int i = 0; i < (int)l.size(); ++i) {
		if (i && sameDir(l[i], l[i - 1])) continue;
		while (q.size() > 1 && !check(q[q.size() - 2], q[q.size() - 1], l[i])) q.pop_back();
		while (q.size() > 1 && !check(q[1], q[0], l[i])) q.pop_front();
		q.push_back(l[i]);
	}
	while (q.size() > 2 && !check(q[q.size() - 2], q[q.size() - 1], q[0])) q.pop_back();
	while (q.size() > 2 && !check(q[1], q[0], q[q.size() - 1])) q.pop_front();
	vector<P> ret;
	for (int i = 0; i < (int)q.size(); ++i) ret.push_back(isLL(q[i], q[(i + 1) % q.size()]));
	return ret;
}
 
P inCenter(P A, P B, P C) {
	double a = (B - C).abs(), b = (C - A).abs(), c = (A - B).abs();
	return (A * a + B * b + C * c) / (a + b + c);
}
 
P circumCenter(P a, P b, P c) { 
	P bb = b - a, cc = c - a;
	double db = bb.abs2(), dc = cc.abs2(), d = 2 * bb.det(cc);
	return a - P(bb.y * dc - cc.y * db, cc.x * db - bb.x * dc) / d;
}
 
P othroCenter(P a, P b, P c) { 
	P ba = b - a, ca = c - a, bc = b - c;
	double Y = ba.y * ca.y * bc.y,
	A = ca.x * ba.y - ba.x * ca.y,
	x0 = (Y + ca.x * ba.y * b.x - ba.x * ca.y * c.x) / A,
	y0 = -ba.x * (x0 - c.x) / ba.y + ca.y;
	return {x0, y0};
}


const int N=111;
int n,m;
vector<vector<P>> pol;
P p[N],p1[N],p2[N],dir[N];
int pz[N],qz[N];
int main() {
	scanf("%d%d",&n,&m);
	rep(i,0,n) {
		int n0;
		scanf("%d",&n0);
		rep(j,0,n0) {
			int x,y;
			scanf("%d%d",&x,&y);
			p[j]=P(x,y);
		}
		pol.pb(vector<P>(p,p+n0));
	}
	shuffle(all(pol),mrand);
	rep(i,0,m) {
		int px,py,qx,qy;
		scanf("%d%d%d%d%d%d",&px,&py,&pz[i],
			&qx,&qy,&qz[i]);
		p1[i]=P(px,py);
		p2[i]=P(qx,qy);
		dir[i]=(p2[i]-p1[i]).unit().rot90();
	}
	auto check=[&](db ang,vector<P> po) {
		rep(i,0,m) {
			vector<P> reg{p1[i]-dir[i]*pz[i]*tan(ang),
				p2[i]-dir[i]*qz[i]*tan(ang),p2[i]+dir[i]*qz[i]*tan(ang),
				p1[i]+dir[i]*pz[i]*tan(ang)};
			bool ins=1;
			for (auto p:po) ins&=contain(reg,p)>=1;
			if (ins) return true;
		}
		return false;
	};
	db ans=0;
	for (auto po:pol) {
		if (!check(ans,po)) {
			db L=ans,R=PI/2;
			rep(i,0,100) {
				db md=(L+R)*0.5;
				if (!check(md,po)) L=md; else R=md;
				if (cmp(L,PI/2)>=0) {
					puts("impossible");
					return 0;
				}
			}
			ans=L;
		}
	}
	printf("%.10f\n",ans/PI*180);
}

Details

Tip: Click on the bar to expand more detailed information

Test #1:

score: 100
Accepted
time: 1ms
memory: 4084kb

input:

1 1
3
-5 0
5 0
0 5
-10 10 10 10 10 10

output:

44.9999999999

result:

ok 

Test #2:

score: 0
Accepted
time: 0ms
memory: 4088kb

input:

1 1
3
-5 0
5 0
0 5
-10 0 10 10 0 10

output:

26.5650511725

result:

ok 

Test #3:

score: 0
Accepted
time: 1ms
memory: 4064kb

input:

1 1
3
-5 0
5 0
0 5
0 10 10 10 0 10

output:

46.6861433415

result:

ok 

Test #4:

score: 0
Accepted
time: 1ms
memory: 4160kb

input:

1 1
3
-5 0
5 0
0 5
0 10 5 10 0 10

output:

59.4910411336

result:

ok 

Test #5:

score: 0
Accepted
time: 1ms
memory: 4028kb

input:

1 1
3
-5 0
5 0
0 5
0 10 20 -10 0 10

output:

31.2196984472

result:

ok 

Test #6:

score: 0
Accepted
time: 0ms
memory: 4068kb

input:

1 3
3
-5 0
5 0
0 5
-10 0 25 10 0 20
-5 10 10 10 -5 20
-4 1 100 5 10 100

output:

12.5288077090

result:

ok 

Test #7:

score: 0
Accepted
time: 0ms
memory: 4032kb

input:

1 2
4
0 0
20 0
20 40
0 40
-10 30 30 30 30 30
-10 10 30 30 10 30

output:

44.9999999990

result:

ok 

Test #8:

score: 0
Accepted
time: 1ms
memory: 3968kb

input:

1 4
4
0 0
20 0
20 40
0 40
-10 30 30 30 30 30
-10 20 30 30 20 30
-10 10 30 30 10 30
10 -10 30 10 50 30

output:

18.4349488229

result:

ok 

Test #9:

score: 0
Accepted
time: 2ms
memory: 4152kb

input:

1 2
4
0 0
40 0
40 40
0 40
10 10 10 20 20 20
30 10 10 10 30 20

output:

impossible

result:

ok 

Test #10:

score: 0
Accepted
time: 2ms
memory: 4096kb

input:

1 3
4
0 0
20 0
20 40
0 40
-10 30 30 15 30 30
5 30 30 30 30 30
1 50 30 21 50 30

output:

impossible

result:

ok 

Test #11:

score: 0
Accepted
time: 0ms
memory: 3996kb

input:

1 1
4
0 0
40 0
40 40
0 40
-100 -100 20 100 100 10

output:

63.6657521531

result:

ok 

Test #12:

score: 0
Accepted
time: 1ms
memory: 4084kb

input:

1 4
4
-10 -10
10 -10
10 10
-10 10
-100 0 10 100 0 10
0 100 10 0 -100 10
50 50 15 -50 -50 15
-50 50 15 50 -50 15

output:

43.3138566583

result:

ok 

Test #13:

score: 0
Accepted
time: 28ms
memory: 4032kb

input:

1 100
100
822286 0
856789 53904
986567 124632
629039 119995
732157 187986
691605 224716
728650 288493
591087 278144
801573 440668
425257 269876
614456 446428
424157 350893
645680 606334
406524 432904
545628 659551
359831 495265
367048 578376
251435 457360
319990 680014
336526 849968
214009 658652
23...

output:

53.7906384311

result:

ok 

Test #14:

score: 0
Accepted
time: 5ms
memory: 4340kb

input:

100 1
100
461002 481444
460618 481480
460584 481512
460833 481595
460670 481605
460545 481607
460942 481801
460526 481672
460912 481923
460765 481903
460505 481781
460430 481766
460589 481959
460593 482032
460477 481972
460440 481994
460510 482183
460285 481888
460387 482179
460246 481963
460303 482...

output:

impossible

result:

ok 

Test #15:

score: 0
Accepted
time: 5ms
memory: 4364kb

input:

100 1
100
461002 481444
460618 481480
460584 481512
460833 481595
460670 481605
460545 481607
460942 481801
460526 481672
460912 481923
460765 481903
460505 481781
460430 481766
460589 481959
460593 482032
460477 481972
460440 481994
460510 482183
460285 481888
460387 482179
460246 481963
460303 482...

output:

33.6907956097

result:

ok 

Test #16:

score: 0
Accepted
time: 4ms
memory: 4176kb

input:

100 1
100
461002 481444
460618 481480
460584 481512
460833 481595
460670 481605
460545 481607
460942 481801
460526 481672
460912 481923
460765 481903
460505 481781
460430 481766
460589 481959
460593 482032
460477 481972
460440 481994
460510 482183
460285 481888
460387 482179
460246 481963
460303 482...

output:

66.4027966421

result:

ok 

Test #17:

score: 0
Accepted
time: 112ms
memory: 4364kb

input:

100 100
100
461002 481444
460618 481480
460584 481512
460833 481595
460670 481605
460545 481607
460942 481801
460526 481672
460912 481923
460765 481903
460505 481781
460430 481766
460589 481959
460593 482032
460477 481972
460440 481994
460510 482183
460285 481888
460387 482179
460246 481963
460303 4...

output:

4.1890016471

result:

ok 

Test #18:

score: 0
Accepted
time: 23ms
memory: 4336kb

input:

100 11
100
461002 481444
460618 481480
460584 481512
460833 481595
460670 481605
460545 481607
460942 481801
460526 481672
460912 481923
460765 481903
460505 481781
460430 481766
460589 481959
460593 482032
460477 481972
460440 481994
460510 482183
460285 481888
460387 482179
460246 481963
460303 48...

output:

32.4119284772

result:

ok 

Test #19:

score: 0
Accepted
time: 79ms
memory: 4328kb

input:

100 90
100
461002 481444
460618 481480
460584 481512
460833 481595
460670 481605
460545 481607
460942 481801
460526 481672
460912 481923
460765 481903
460505 481781
460430 481766
460589 481959
460593 482032
460477 481972
460440 481994
460510 482183
460285 481888
460387 482179
460246 481963
460303 48...

output:

5.5754489360

result:

ok 

Extra Test:

score: 0
Extra Test Passed