QOJ.ac
QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#189242 | #5106. Islands from the Sky | bulijiojiodibuliduo# | AC ✓ | 112ms | 4364kb | C++17 | 11.8kb | 2023-09-27 03:02:06 | 2023-09-27 03:02:07 |
Judging History
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