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IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#73076#5155. Faster Than LightSorting#WA 3ms7560kbC++2.9kb2023-01-21 22:14:002023-01-21 22:14:03

Judging History

你现在查看的是最新测评结果

  • [2023-08-10 23:21:45]
  • System Update: QOJ starts to keep a history of the judgings of all the submissions.
  • [2023-01-21 22:14:03]
  • 评测
  • 测评结果:WA
  • 用时:3ms
  • 内存:7560kb
  • [2023-01-21 22:14:00]
  • 提交

answer

#include <bits/stdc++.h>

using namespace std;

typedef long long ll;

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);}
    T cross(P p) const {return x * p.y - y * p.x;}
    T dot(P p) const {return x * p.x + y * p.y; }
    T cross(P a, P b) const {return (a - *this).cross(b - *this);}
};

const int N = 2e5 + 3;

int n;
ll x1[N], yedno[N], x2[N], y2[N];

#define all(x) (x).begin(), (x).end()

typedef Point<ll> P;
vector<P> convexHull(vector<P> pts) {
    if(pts.size() <= 1) return pts;
    sort(all(pts));
    vector<P> h((int)pts.size() + 1);
    int s = 0, t = 0;
    for(int it = 2; it--; s = --t, reverse(all(pts))){
        for(P p: pts){
            while(t >= s + 2 && h[t - 2].cross(h[t - 1], p) <= 0) t--;
            h[t++] = p;
        }
    }
    return {h.begin(), h.begin() + t - (t == 2 && h[0] == h[1])};
}

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

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

bool inHull(const vector<P> &l, P p, bool strict = true){
    int a = 1, b = (int)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;
}

bool check(const vector<Point<ll>> &in, const vector<Point<ll>> &out){
    vector<Point<ll>> ch = convexHull(in); 
    while(ch.size() > 2){
        int i = ch.size() - 3;
        if(ch[i].cross(ch[i + 1], ch[i + 2]) == 0){
            swap(ch[i + 1], ch[i + 2]);
            ch.pop_back();
        }
        else
            break;
    }

    for(auto p: out){
        if(inHull(ch, p, true))
            return false;
    }
    return true;
}


int main(){
    ios::sync_with_stdio(false);
    cin.tie(NULL);

    cin >> n;
    for(int i = 0; i < n; ++i)
        cin >> x1[i] >> yedno[i] >> x2[i] >> y2[i];

    if(n <= 2){
        cout << "possible\n";
        return 0;
    }

    vector<Point<ll>> in1, in2, out1, out2;
    for(int i = 0; i < n; ++i){
        in1.push_back(Point<ll>(x1[i], yedno[i]));
        in2.push_back(Point<ll>(x1[i], y2[i]));
        out1.push_back(Point<ll>(x2[i], y2[i]));
        out2.push_back(Point<ll>(x2[i], yedno[i]));
    }

    if(check(in1, out1) || check(in2, out2))
        cout << "possible\n";
    else
        cout << "impossible\n";
}
/*
3
1 1 2 2
2 2 3 3
3 3 4 4
*/

Details

Tip: Click on the bar to expand more detailed information

Test #1:

score: 100
Accepted
time: 2ms
memory: 7480kb

input:

5
1 3 3 4
2 2 4 3
4 1 5 3
5 2 7 3
6 3 8 4

output:

possible

result:

ok single line: 'possible'

Test #2:

score: 0
Accepted
time: 2ms
memory: 7472kb

input:

4
1 1 2 2
1 3 2 4
3 1 4 2
3 3 4 4

output:

impossible

result:

ok single line: 'impossible'

Test #3:

score: 0
Accepted
time: 3ms
memory: 7460kb

input:

3
1 1 2 2
1 3 2 4
3 3 4 4

output:

possible

result:

ok single line: 'possible'

Test #4:

score: -100
Wrong Answer
time: 3ms
memory: 7560kb

input:

5
0 0 1 999999999
0 999999999 999999999 1000000000
1 0 999999998 1
999999998 0 999999999 999999999
2 999999998 3 999999999

output:

possible

result:

wrong answer 1st lines differ - expected: 'impossible', found: 'possible'