QOJ.ac
QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#201946 | #5155. Faster Than Light | PlentyOfPenalty# | WA | 270ms | 88460kb | C++20 | 4.7kb | 2023-10-05 17:50:20 | 2023-10-05 17:50:21 |
Judging History
answer
#include<bits/stdc++.h>
#define all(x) (x).begin(),(x).end()
using namespace std;
using V=long double;
const int N=2e5+9;
const V eps=1e-9,T=10,L=1e9+T*T;
int n;
int sgn(V x){
if(fabsl(x)<eps)return 0;
return x<0?-1:1;
}
bool mem_equal(V x,V y){
return fabsl(x-y)<eps*max(fabsl(x),fabsl(y));
}
bool mem_less(V x,V y){
if(mem_equal(x,y))return false;
return x<y;
}
bool mem_greater(V x,V y){
if(mem_equal(x,y))return false;
return x>y;
}
struct point{
V x,y;
friend V operator^(const point &a,const point &b){return a.x*b.y-a.y*b.x;}
friend V operator*(const point &a,const point &b){return a.x*b.x+a.y*b.y;}
friend inline point operator+(const point &a,const point &b){return {a.x+b.x,a.y+b.y};}
friend inline point operator-(const point &a,const point &b){return {a.x-b.x,a.y-b.y};}
};
bool check_less(const point &a,const point &b){
return mem_less(a.x*b.y,a.y*b.x);
}
bool check_greater(const point &a,const point &b){
return mem_greater(a.x*b.y,a.y*b.x);
}
struct line{
point s,e;
V angle;
line(){}
int x,y;
line(point s,point e,int _x=-1,int _y=-1):s(s),e(e){
x=_x,y=_y;
angle=atan2l(e.y-s.y,e.x-s.x);
}
inline bool operator<(const line &rhs)const{
return angle<rhs.angle;
}
point crosspoint(const line &v){
V a1=(v.e-v.s)^(s-v.s);
V a2=(v.e-v.s)^(e-v.s);
return point{
(s.x*a2-e.x*a1)/(a2-a1),
(s.y*a2-e.y*a1)/(a2-a1)
};
}
bool parallel(const line &v){
point a=e-s;
point b=v.e-v.s;
return mem_equal(a.x*b.y,a.y*b.x);
// return sgn((e-s)^(v.e-v.s))==0;
}
};
struct rectangle{
int x1,y1,x2,y2;
}a[N];
void FOUND(){
cout<<"possible"<<endl;
exit(0);
}
struct halfplanes{
int n=0,st,ed;
vector<line> hp;
vector<point> p;
vector<int> que;
void push(const line &x){
if(hp.size()<n+5){
p.resize(n+5);
hp.resize(n+5);
que.resize(n+5);
}
hp[n++]=x;
}
void unique(){
int m=1;
for(int i=1;i<n;i++){
if(!mem_equal(hp[i].angle,hp[i-1].angle)){
hp[m++]=hp[i];
}else if(check_greater(hp[m-1].e-hp[m-1].s,hp[i].s-hp[m-1].s)){
hp[m-1]=hp[i];
}
}
n=m;
}
void debug(){
fprintf(stderr,"st=%d ed=%d\n",st,ed);
for(int i=st;i<=ed;i++)fprintf(stderr,"que[%d]=%d :: %d %d\n",i,que[i],hp[que[i]].x,hp[que[i]].y);
}
bool solve(){
sort(hp.begin(),hp.begin()+n);
// for(int i=0;i<n;i++)fprintf(stderr,"hp[%d]::%d %d::(%d,%d)->(%d,%d)\n",i,hp[i].x,hp[i].y,(int)hp[i].s.x,(int)hp[i].s.y,(int)hp[i].e.x,(int)hp[i].e.y);
unique();
que[st=0]=0;
que[ed=1]=1;
p[1]=hp[0].crosspoint(hp[1]);
for(int i=2;i<n;i++){
while(st<ed&&check_less(hp[i].e-hp[i].s,p[ed]-hp[i].s))ed--;
while(st<ed&&check_less(hp[i].e-hp[i].s,p[st+1]-hp[i].s))st++;
que[++ed]=i;
if(hp[i].parallel(hp[que[ed-1]]))return false;
p[ed]=hp[i].crosspoint(hp[que[ed-1]]);
// debug();
}
while(st<ed&&check_less(hp[que[st]].e-hp[que[st]].s,p[ed]-hp[que[st]].s))ed--;
while(st<ed&&check_less(hp[que[ed]].e-hp[que[ed]].s,p[st+1]-hp[que[ed]].s))st++;
// debug();
if(st+1>=ed)return false;
return true;
}
};
void check(){
halfplanes sol;
for(int i=1;i<=n;i++){
// fprintf(stderr,"a[%d] :: %d %d %d %d\n",i,a[i].x1,a[i].y1,a[i].x2,a[i].y2);
sol.push(line({1,(V)(a[i].y1-a[i].x1)},{0,(V)a[i].y1},i,1));
sol.push(line({0,(V)a[i].y2},{1,(V)(a[i].y2-a[i].x2)},i,2));
}
// sol.push(line({0,-T},{L,0}));
// sol.push(line({L-T,0},{L,L}));
// sol.push(line({L,L-T},{0,L}));
// sol.push(line({-T,L},{0,0}));
sol.push(line({-L,-L-T},{L,-L}));
sol.push(line({L-T,-L},{L,L}));
sol.push(line({L,L-T},{-L,L}));
sol.push(line({-L-T,L},{-L,-L}));
if(sol.solve())FOUND();
}
void basic_check(vector<pair<int,int>> &a){
vector<int> val;
for(auto &it:a){
val.push_back(it.first);
val.push_back(it.second);
}
sort(all(val));
val.erase(unique(all(val)),val.end());
vector<int> ins(val.size()),del(val.size());
for(auto &it:a){
it.first=lower_bound(all(val),it.first)-val.begin();
it.second=lower_bound(all(val),it.second)-val.begin();
ins[it.first]++;
del[it.second]++;
}
int cur=0;
for(int i=0;i<val.size();i++){
cur+=ins[i];
if(cur==n)FOUND();
cur-=del[i];
}
}
int main(){
#ifdef memset0
freopen("F.in","r",stdin);
#endif
ios::sync_with_stdio(0),cin.tie(0);
cin>>n;
vector<pair<int,int>> allx,ally;
for(int i=1;i<=n;i++){
cin>>a[i].x1>>a[i].y1>>a[i].x2>>a[i].y2;
// a[i].x1+=T>>1;
// a[i].y1+=T>>1;
// a[i].x2+=T>>1;
// a[i].y2+=T>>1;
allx.emplace_back(a[i].x1,a[i].x2);
ally.emplace_back(a[i].y1,a[i].y2);
swap(a[i].y1,a[i].y2);
}
basic_check(allx);
basic_check(ally);
check();
for(int i=1;i<=n;i++){
a[i].y1=1e9-a[i].y1;
a[i].y2=1e9-a[i].y2;
swap(a[i].y1,a[i].y2);
}
check();
cout<<"impossible"<<endl;
}
Details
Tip: Click on the bar to expand more detailed information
Test #1:
score: 100
Accepted
time: 0ms
memory: 3848kb
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: 0ms
memory: 3660kb
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: 0ms
memory: 3848kb
input:
3 1 1 2 2 1 3 2 4 3 3 4 4
output:
possible
result:
ok single line: 'possible'
Test #4:
score: 0
Accepted
time: 0ms
memory: 3564kb
input:
5 0 0 1 999999999 0 999999999 999999999 1000000000 1 0 999999998 1 999999998 0 999999999 999999999 2 999999998 3 999999999
output:
impossible
result:
ok single line: 'impossible'
Test #5:
score: 0
Accepted
time: 0ms
memory: 3824kb
input:
4 0 1 1 1000000000 1 0 999999999 1 999999999 0 1000000000 999999999 2 999999999 999999999 1000000000
output:
possible
result:
ok single line: 'possible'
Test #6:
score: 0
Accepted
time: 0ms
memory: 3784kb
input:
3 0 0 1 1000000000 2 0 999999999 1 2 999999999 999999999 1000000000
output:
impossible
result:
ok single line: 'impossible'
Test #7:
score: 0
Accepted
time: 0ms
memory: 3828kb
input:
3 0 0 1 1000000000 2 0 999999999 1 2 999999999 1000000000 1000000000
output:
possible
result:
ok single line: 'possible'
Test #8:
score: -100
Wrong Answer
time: 270ms
memory: 88460kb
input:
199999 433914929 216935871 433914930 216935872 621822279 310889546 621822280 310889547 395914333 197935573 395914334 197935574 582775641 291366227 582775642 291366228 658726133 329341473 658726134 329341474 71689261 35823037 71689262 35823038 453260967 226608890 453260968 226608891 249802825 1248798...
output:
possible
result:
wrong answer 1st lines differ - expected: 'impossible', found: 'possible'