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IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#201882#5155. Faster Than LightPlentyOfPenalty#WA 368ms122152kbC++204.3kb2023-10-05 17:20:502023-10-05 17:20:51

Judging History

你现在查看的是最新测评结果

  • [2023-10-05 17:20:51]
  • 评测
  • 测评结果:WA
  • 用时:368ms
  • 内存:122152kb
  • [2023-10-05 17:20:50]
  • 提交

answer

#include<bits/stdc++.h>
#define all(x) (x).begin(),(x).end()
using namespace std;
using V=long double;
const int N=2e5+9,T=10,L=1e9;
const V eps=1e-8;
int n;
int sgn(V x){
	if(fabsl(x)<eps)return 0;
	return x<0?-1:1;
}
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};}
};
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){
		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(sgn(hp[i].angle-hp[i-1].angle)!=0){
				hp[m++]=hp[i];
			}else if(sgn((hp[m-1].e-hp[m-1].s)^(hp[i].s-hp[m-1].s))>0){
				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&&sgn((hp[i].e-hp[i].s)^(p[ed]-hp[i].s))<0)ed--;
			while(st<ed&&sgn((hp[i].e-hp[i].s)^(p[st+1]-hp[i].s))<0)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&&sgn((hp[que[st]].e-hp[que[st]].s)^(p[ed]-hp[que[st]].s))<0)ed--;
		while(st<ed&&sgn((hp[que[ed]].e-hp[que[ed]].s)^(p[st+1]-hp[que[ed]].s))<0)st++;
		// debug();
		if(st+1>=ed)return false;
		return true;
	}
};
void check(){
	halfplanes sol;
	for(int i=1;i<=n;i++){
		// fprintf(stderr,"%d %d :: (%d,%d) -> (%d,%d)\n",i,1,1,a[i].y1-a[i].x1,0,a[i].y1);
		// fprintf(stderr,"%d %d :: (%d,%d) -> (%d,%d)\n",i,2,0,a[i].y2,1,a[i].y2-a[i].x2);
		// 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}));
	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].x1=/*1e9*/-a[i].x1;
		a[i].x2=/*1e9*/-a[i].x2;
		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: 1ms
memory: 3468kb

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: 3464kb

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: 3460kb

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: 3444kb

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: 3432kb

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: 3568kb

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: 3476kb

input:

3
0 0 1 1000000000
2 0 999999999 1
2 999999999 1000000000 1000000000

output:

possible

result:

ok single line: 'possible'

Test #8:

score: 0
Accepted
time: 358ms
memory: 121960kb

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:

impossible

result:

ok single line: 'impossible'

Test #9:

score: 0
Accepted
time: 349ms
memory: 121256kb

input:

199999
783545903 638444708 783545904 638444709
129510863 105527268 129510864 105527269
844145756 687822366 844145757 687822367
69111161 56312696 69111162 56312697
820438487 668505332 820438488 668505333
541037357 440845152 541037358 440845153
201057677 163824672 201057678 163824673
132372296 1078588...

output:

impossible

result:

ok single line: 'impossible'

Test #10:

score: 0
Accepted
time: 362ms
memory: 121956kb

input:

199999
90035476 60020102 90035477 60020103
482291029 321523804 482291030 321523805
943496815 628994328 943496816 628994329
278866936 185907742 278866937 185907743
310938589 207288844 310938590 207288845
203677765 135781628 203677766 135781629
368744134 245825874 368744135 245825875
559390024 3729231...

output:

impossible

result:

ok single line: 'impossible'

Test #11:

score: 0
Accepted
time: 346ms
memory: 120716kb

input:

199999
207687261 415417709 207687262 415417710
150460947 300965081 150460948 300965082
9349830 18742847 9349831 18742848
87879837 175802861 87879838 175802862
354035800 708114787 354035801 708114788
305159254 610361695 305159255 610361696
248609913 497263013 248609914 497263014
499646110 999335407 4...

output:

impossible

result:

ok single line: 'impossible'

Test #12:

score: 0
Accepted
time: 364ms
memory: 121760kb

input:

199999
79738802 97861382 79738803 97861383
614827422 754561052 614827423 754561053
517213290 634761890 517213291 634761891
788424494 967612004 788424495 967612005
613541698 752983118 613541699 752983119
698980304 857839589 698980305 857839590
487475098 598265018 487475099 598265019
733711836 9004646...

output:

impossible

result:

ok single line: 'impossible'

Test #13:

score: 0
Accepted
time: 362ms
memory: 120044kb

input:

199999
161399962 242105266 161399963 242105267
385751852 578633101 385751853 578633102
222705450 334063498 222705451 334063499
503730932 755601721 503730933 755601722
454037530 681061618 454037531 681061619
334605270 501913228 334605271 501913229
478675624 718018759 478675625 718018760
137316204 205...

output:

impossible

result:

ok single line: 'impossible'

Test #14:

score: 0
Accepted
time: 368ms
memory: 120744kb

input:

199999
222639792 110935680 222639793 110935683
931931336 465581452 931931337 465581455
35474718 17353143 35474719 17353146
206777070 103004319 206777071 103004322
914064786 456648177 914064787 456648180
301496196 150363882 301496197 150363885
515345552 257288560 515345553 257288563
500949336 2500904...

output:

impossible

result:

ok single line: 'impossible'

Test #15:

score: 0
Accepted
time: 347ms
memory: 121468kb

input:

199999
14166026 11542586 14166027 11542589
212205815 172908340 212205816 172908343
997392464 812690054 997392465 812690057
766610585 624645560 766610586 624645563
843092432 686964102 843092433 686964105
362333537 295234632 362333538 295234635
724513967 590344612 724513968 590344615
903878693 7364936...

output:

impossible

result:

ok single line: 'impossible'

Test #16:

score: 0
Accepted
time: 346ms
memory: 122080kb

input:

199999
259728590 173148768 259728591 173148771
221053226 147365192 221053227 147365195
899826680 599880828 899826681 599880831
847582532 565051396 847582533 565051399
258078974 172049024 258078975 172049027
369519293 246342570 369519294 246342573
214263539 142838734 214263540 142838737
737461550 491...

output:

impossible

result:

ok single line: 'impossible'

Test #17:

score: 0
Accepted
time: 332ms
memory: 120224kb

input:

199999
310634507 622037446 310634510 622037447
14947597 30663626 14947600 30663627
99728538 200225508 99728541 200225509
184650291 370069014 184650294 370069015
166422010 333612452 166422013 333612453
302228792 605226016 302228795 605226017
386996090 774760612 386996093 774760613
326681088 654130608...

output:

impossible

result:

ok single line: 'impossible'

Test #18:

score: 0
Accepted
time: 358ms
memory: 122152kb

input:

199999
799006978 980599598 799006981 980599599
101833006 124976996 101833009 124976997
491420512 603107117 491420515 603107118
529582438 649942208 529582441 649942209
453375406 556415396 453375409 556415397
591719612 726201467 591719615 726201468
775042202 951188282 775042205 951188283
218921560 268...

output:

impossible

result:

ok single line: 'impossible'

Test #19:

score: 0
Accepted
time: 351ms
memory: 120244kb

input:

199999
354595980 531899408 354595983 531899409
57294868 85947740 57294871 85947741
297914740 446877548 297914743 446877549
306592118 459893615 306592121 459893616
648745732 973124036 648745735 973124037
267426974 401145899 267426977 401145900
363073104 544615094 363073107 544615095
512209740 7683200...

output:

impossible

result:

ok single line: 'impossible'

Test #20:

score: -100
Wrong Answer
time: 324ms
memory: 120296kb

input:

200000
183486 13299 183487 13300
102571 78692 102572 78693
170699 23633 170700 23634
62500 111076 62501 111077
175314 19903 175315 19904
147075 42725 147076 42726
131050 55675 131051 55676
165234 28050 165235 28051
98541 81949 98542 81950
186747 10663 186748 10664
128558 57690 128559 57691
75090 100...

output:

impossible

result:

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