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QOJ

IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#380638#5106. Islands from the SkyUFRJAC ✓445ms4704kbC++144.6kb2024-04-07 07:25:362024-04-07 07:25:40

Judging History

你现在查看的是最新测评结果

  • [2024-04-07 07:25:40]
  • 评测
  • 测评结果:AC
  • 用时:445ms
  • 内存:4704kb
  • [2024-04-07 07:25:36]
  • 提交

answer

#include "bits/stdc++.h"

using namespace std;
using lint = int64_t;

#define PI acos(-1.0)

template<class T> int sgn(T x) { return (x > 0) - (x < 0); }
template<class T>
struct Point {
    typedef Point P;
    T x, y;
    explicit Point(T x = 0, T y = 0) : x(x), y(y) { }
    bool operator<(P p) const { return tie(x, y) < tie(p.x, p.y); }
    bool operator==(P p) const { return tie(x, y) == tie(p.x, p.y); }
    P operator+(P p) const { return P(x+p.x, y+p.y); }
    P operator-(P p) const { return P(x-p.x, y-p.y); }
    P operator*(T d) const { return P(x*d, y*d); }
    P operator/(T d) const { return P(x/d, y/d); }
    T dot(P p) const { return x*p.x + y*p.y; }
    T cross(P p) const { return x*p.y - y*p.x; }
    T cross(P a, P b) const { return (a-*this).cross(b-*this); }
    T dist2() const {return x*x + y*y; }
    T dist() const {return sqrt((double) dist2()); }
    double angle() const { return atan2(y, x); }
};

using P = Point<double>;

double segDist(P &s, P &e, P &p) {
    if(s == e) return (p-s).dist();
    auto d = (e-s).dist2(), t = min(d, max(.0, (p-s).dot(e-s)));
    return ((p-s)*d-(e-s)*t).dist() / d;
}

template<class P> bool onSegment(P s, P e, P p) {
    return p.cross(s, e) == 0 && (s - p).dot(e - p) <= 0;
}

template<class P>
bool inPolygon(vector<P> &p, P a, bool strict = true) {
    int cnt = 0, n = p.size();
    for(int i = 0; i < n; ++i) {
        P q = p[(i+1) % n ];
        if(onSegment(p[i], q, a)) return !strict;
        cnt ^= ((a.y < p[i].y) - (a.y < q.y)) * a.cross(p[i], q) > 0;
    }
    return cnt;
}

template<class P> 
int sideOf(P s, P e, P p) { return sgn(s.cross(e, p)); }

template<class P>
int sideOf(const P &s, const P &e, const P &p, double eps) {
    auto a = (e-s).cross(p-s);
    double l = (e-s).dist() * eps;
    return (a > l) - (a < -l);
}

bool inHull(const vector<P> &l, P p, bool strict = true) {
    int a = 1, b = l.size() - 1, r = !strict;
    if(l.size() < 3) return r && onSegment(l[0], l.back(), p);
    if(sideOf(l[0], l[a], l[b]) > 0) swap(a, b);
    if(sideOf(l[0], l[a], p) >= r || sideOf(l[0], l[b], p) <= -r)
        return false;
    while(abs(a - b) > 1) {
        int c = (a + b) / 2;
        (sideOf(l[0], l[c], p) > 0 ? b : a) = c;
    }
    return sgn(l[a].cross(l[b], p)) < r;
}

int n, m;
vector<vector<P>> islands;
vector<pair<tuple<int,int,int>, tuple<int,int,int>>> airplanes;


bool test_angle(double angle) {
    vector<vector<P>> traps;

    int x1, x2, y1, y2, z1, z2;
    for(auto [from, to] : airplanes) {
        tie(x1, y1, z1) = from;
        tie(x2, y2, z2) = to;

        double dist1 = tan(angle * PI / 180) * z1;
        double dist2 = tan(angle * PI / 180) * z2;

        P s = P(x1, y1);
        P e = P(x2, y2);
        P aux = (e - s)/ (e - s).dist();
        P dir = P(-aux.y, aux.x);

        // cout << angle << " " << dist1 << " " << dist2 << endl;
        vector<P> poly = {s + dir * dist1, s - dir * dist1, e - dir * dist2, e + dir * dist2};
        // cout << "Poly: " << endl;
        // for(auto &i : poly) {
        //     cout << i.x << " " << i.y << endl;
        // }
        traps.push_back(poly);
    }

    vector<bool>w(n);

    // cout << "Angle: " << angle << endl;
    for(int i=0;i<n;i++){
        for(auto& poly : traps){
            int cnt = 0;
            for(auto& pnt : islands[i]){
                cnt += inPolygon(poly, pnt);
                // cout << i << " " << pnt.x << " " << pnt.y << " " << inHull(poly, pnt) << endl;
            }
            if(cnt == (int) islands[i].size()){
                w[i] = true;
                break;
            }
        }
    }

    bool ok = true;
    for(int i = 0; i < n; i++) {
        // cout << w[i] << " ";
        ok &= w[i];
    }
    return ok;
}

int main() {
    cin.tie(nullptr)->sync_with_stdio(false);

    cin >> n >> m;
    islands.resize(n);
    for(int i = 0, isize, x, y; i < n; i++) {
        cin >> isize;
        for(int j = 0; j < isize; j++) {
            cin >> x >> y;
            islands[i].push_back(P(x, y));
        }
    }

    for(int i = 0, x1, x2, y1, y2, z1, z2; i < m; i++) {
        cin >> x1 >> y1 >> z1;
        cin >> x2 >> y2 >> z2;
        airplanes.push_back({{x1, y1, z1}, {x2, y2, z2}});
    }

    double lo = 0, hi = 90;

    if(!test_angle(hi - 1e-7)){
        cout << "impossible\n";
        return 0; 
    }

    for(int i = 0; i < 100; i++) {
        double mid = (lo + hi) / 2;
        bool ok = test_angle(mid);

        if(ok) hi = mid;
        else lo = mid;
    }

    cout << fixed << setprecision(10) << lo << "\n";
    return 0;
}

Details

Tip: Click on the bar to expand more detailed information

Test #1:

score: 100
Accepted
time: 1ms
memory: 4412kb

input:

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

output:

45.0000000000

result:

ok 

Test #2:

score: 0
Accepted
time: 1ms
memory: 4272kb

input:

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

output:

26.5650511771

result:

ok 

Test #3:

score: 0
Accepted
time: 1ms
memory: 4436kb

input:

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

output:

46.6861433417

result:

ok 

Test #4:

score: 0
Accepted
time: 1ms
memory: 4412kb

input:

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

output:

59.4910411338

result:

ok 

Test #5:

score: 0
Accepted
time: 1ms
memory: 4400kb

input:

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

output:

31.2196984474

result:

ok 

Test #6:

score: 0
Accepted
time: 1ms
memory: 4400kb

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:

12.5288077092

result:

ok 

Test #7:

score: 0
Accepted
time: 1ms
memory: 4244kb

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:

45.0000000000

result:

ok 

Test #8:

score: 0
Accepted
time: 1ms
memory: 4212kb

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: 1ms
memory: 3920kb

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: 1ms
memory: 4020kb

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: 1ms
memory: 4404kb

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: 4408kb

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: 12ms
memory: 4496kb

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: 2ms
memory: 4164kb

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: 17ms
memory: 4648kb

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: 18ms
memory: 4556kb

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: 445ms
memory: 4704kb

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: 45ms
memory: 4532kb

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: 368ms
memory: 4632kb

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