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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 |
---|---|---|---|---|---|---|---|---|---|
#73085 | #5155. Faster Than Light | Sorting# | WA | 2ms | 7568kb | C++ | 4.8kb | 2023-01-21 23:50:07 | 2023-01-21 23:56:56 |
Judging History
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);}
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);}
};
struct Angle{
ll x, y;
ll t;
Angle(ll x, ll y, ll t = 0): x(x), y(y), t(t){}
Angle(Point<ll> p): x(p.x), y(p.y), t(0){}
int half() const {
assert(x || y);
return y < 0 || (y == 0 && x < 0);
}
};
bool operator<(Angle a, Angle b){
return make_tuple(a.t, a.half(), a.y * b. x) <
make_tuple(b.t, b.half(), a.x * b.y);
}
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 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> vector<P> segInter(P a, P b, P c, P d){
auto oa = c.cross(d, a), ob = c.cross(d, b),
oc = a.cross(b, c), od = a.cross(b, d);
if(sgn(oa) * sgn(ob) < 0 && sgn(oc) * sgn(od) < 0)
return {(a * ob - b * oa) / (ob - oa)};
set<P> s;
if(ons)
}*/
bool check(const vector<Point<ll>> &in, vector<Point<ll>> out){
vector<Point<ll>> ch1 = convexHull(in);
for(auto &p: out)
p = Point<ll>{-p.x, -p.y};
vector<Point<ll>> ch2 = convexHull(out);
// for(auto [x, y]: ch1)
// cout << x << "," << y << " ";
// cout << endl;
// cout << "Ch2 ";
// for(auto [x, y]: ch2)
// cout << x << "," << y << " ";
// cout << endl;
assert(ch1.size() != 2 && ch2.size() != 2);
ch1.push_back(ch1[0]);
ch2.push_back(ch2[0]);
int i = 1, j = 1;
vector<Point<ll>> v;
v.push_back(ch1[0] + ch2[0]);
while(i < ch1.size() && j < ch2.size()){
Angle a1(ch1[i] - ch1[i - 1]);
Angle a2(ch2[j] - ch2[j - 1]);
if(a1 < a2){
v.push_back(v.back() + ch1[i] - ch1[i - 1]);
++i;
}
else{
v.push_back(v.back() + ch2[j] - ch2[j - 1]);
++j;
}
}
while(i < ch1.size()){
v.push_back(v.back() + ch1[i] - ch1[i - 1]);
++i;
}
while(j < ch2.size()){
v.push_back(v.back() + ch2[j] - ch2[j - 1]);
++j;
}
v.pop_back();
// cout << "v: ";
// for(auto [x, y]: v)
// cout << x << "," << y << " ";
// cout << endl;
return !inPolygon(v, Point<ll>(0, 0), 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
*/
詳細信息
Test #1:
score: 100
Accepted
time: 2ms
memory: 7568kb
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: 7468kb
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: 2ms
memory: 7472kb
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: 0ms
memory: 7456kb
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'