QOJ.ac

QOJ

ID题目提交者结果用时内存语言文件大小提交时间测评时间
#380272#5106. Islands from the SkyUFRJ#AC ✓296ms4600kbC++204.6kb2024-04-06 23:17:272024-04-06 23:17:27

Judging History

你现在查看的是最新测评结果

  • [2024-04-06 23:17:27]
  • 评测
  • 测评结果:AC
  • 用时:296ms
  • 内存:4600kb
  • [2024-04-06 23:17:27]
  • 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 += inHull(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;
}

詳細信息

Test #1:

score: 100
Accepted
time: 1ms
memory: 4184kb

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: 0ms
memory: 4364kb

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: 0ms
memory: 4228kb

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: 0ms
memory: 4376kb

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: 0ms
memory: 4224kb

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: 0ms
memory: 4352kb

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: 0ms
memory: 4228kb

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: 0ms
memory: 4408kb

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: 0ms
memory: 4172kb

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: 0ms
memory: 4248kb

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: 4364kb

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: 0ms
memory: 4196kb

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: 9ms
memory: 4376kb

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: 0ms
memory: 4368kb

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: 4484kb

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: 17ms
memory: 4600kb

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: 296ms
memory: 4440kb

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: 40ms
memory: 4560kb

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: 247ms
memory: 4592kb

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