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답안 #447966

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
447966 2021-07-28T10:18:54 Z Jasiekstrz Geometrija (COCI21_geometrija) C++17
110 / 110
 175 ms 564 KB 
#include<bits/stdc++.h>
#define fi first
#define se second
using namespace std;
const int N=1e3;
struct Point
{
	long long x,y;
};
Point operator-(Point a,Point b)
{
	return {a.x-b.x,a.y-b.y};
}
long long operator*(Point a,Point b)
{
	return a.x*b.y-a.y*b.x;
}
int sgn(long long x)
{
	return (x<0 ? -1:1);
}
int ilo(Point a,Point b,Point c)
{
	return sgn((a-c)*(b-c));
}
bool cross(Point a,Point b,Point c,Point d)
{
	return (ilo(c,b,a)!=ilo(d,b,a) && ilo(a,d,c)!=ilo(b,d,c));
}
bool inside(Point p,Point a,Point b,Point c)
{
	int val=sgn((p-a)*(b-a));
	if(sgn((p-b)*(c-b))==val && sgn((p-c)*(a-c))==val)
		return true;
	return false;
}
Point tab[N+10];
vector<int> hull;
bool onhull[N+10];
bool vis[N+10];
bool cross_all(Point a,Point b,int n)
{
	vector<Point> t[2];
	for(int i=1;i<=n;i++)
	{
		long long tmp=(tab[i]-b)*(a-b);
		if(tmp>0)
			t[1].push_back(tab[i]);
		else if(tmp<0)
			t[0].push_back(tab[i]);
	}
	vector<Point> sa=t[0],sb=t[0];
	sort(sa.begin(),sa.end(),[&a](Point p,Point q){ return (p-a)*(q-a)<0; });
	sort(sb.begin(),sb.end(),[&b](Point p,Point q){ return (p-b)*(q-b)<0; });
	for(auto v:t[1])
	{
		int cnt=t[0].size();

		int bg=0,en=sb.size();
		while(bg<en)
		{
			int mid=(bg+en+1)/2;
			if((b-v)*(sb[mid-1]-b)>0)
				bg=mid;
			else
				en=mid-1;
		}
		cnt-=bg;

		bg=0,en=sa.size();
		while(bg<en)
		{
			int mid=(bg+en+1)/2;
			if((a-v)*(sa[sa.size()-mid]-a)<0)
				bg=mid;
			else
				en=mid-1;
		}
		cnt-=bg;

		if(cnt>0)
			return true;
	}
	return false;
}
int main()
{
	ios_base::sync_with_stdio(false);
	cin.tie(NULL);
	cout.tie(NULL);
	int n,ans=0;
	cin>>n;
	for(int i=1;i<=n;i++)
		cin>>tab[i].x>>tab[i].y;
	sort(tab+1,tab+n+1,[](Point a,Point b){ return a.x<b.x; });

	auto pop_bad=[](int x)
	{
		while(hull.size()>1 && 
				(tab[x]-tab[hull[hull.size()-2]])*(tab[hull.back()]-tab[hull[hull.size()-2]])<0)
			hull.pop_back();
		hull.push_back(x);
		return;
	};
	for(int i=1;i<=n;i++)
		pop_bad(i);
	for(int i=n-1;i>=1;i--)
		pop_bad(i);
	hull.pop_back();
	for(auto v:hull)
		onhull[v]=true;
	//for(auto v:hull)
	//	cerr<<tab[v].x<<" "<<tab[v].y<<"\n";

	for(int i=1;i<=n;i++)
	{
		if(onhull[i])
			continue;
		int a=1,b,c;
		for(b=1,c=2;sgn((tab[hull[b]]-tab[a])*(tab[i]-tab[a]))==
				sgn((tab[hull[c]]-tab[a])*(tab[i]-tab[a]));b++,c++);
		b=hull[b];
		c=hull[c];
		for(int j=1;j<=n;j++)
		{
			if(j==i || j==a || j==b || j==c || !inside(tab[j],tab[a],tab[b],tab[c]))
				continue;
			if(inside(tab[i],tab[a],tab[b],tab[j]))
				c=j;
			else if(inside(tab[i],tab[a],tab[j],tab[c]))
				b=j;
			else if(inside(tab[i],tab[j],tab[b],tab[c]))
				a=j;
		}
		for(int j:{a,b,c})
		{
			//cerr<<tab[i].x<<","<<tab[i].y<<" "<<tab[j].x<<","<<tab[j].y<<"\n";
			if(!vis[j] && !cross_all(tab[i],tab[j],n))
				ans++;
		}
		vis[i]=true;
		//cerr<<tab[i].x<<" "<<tab[i].y<<" "<<ans<<"\n";
	}
	cout<<ans+hull.size()<<"\n";
	return 0;
}

Subtask #1
20.0 / 20.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 332 KB Output is correct
2 Correct 1 ms 332 KB Output is correct
3 Correct 1 ms 332 KB Output is correct
4 Correct 1 ms 332 KB Output is correct
5 Correct 1 ms 332 KB Output is correct
6 Correct 1 ms 204 KB Output is correct
7 Correct 1 ms 332 KB Output is correct
8 Correct 1 ms 332 KB Output is correct
9 Correct 1 ms 332 KB Output is correct
10 Correct 1 ms 332 KB Output is correct
11 Correct 1 ms 204 KB Output is correct

Subtask #2
30.0 / 30.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 332 KB Output is correct
2 Correct 1 ms 332 KB Output is correct
3 Correct 1 ms 332 KB Output is correct
4 Correct 1 ms 332 KB Output is correct
5 Correct 1 ms 332 KB Output is correct
6 Correct 1 ms 204 KB Output is correct
7 Correct 1 ms 332 KB Output is correct
8 Correct 1 ms 332 KB Output is correct
9 Correct 1 ms 332 KB Output is correct
10 Correct 1 ms 332 KB Output is correct
11 Correct 1 ms 204 KB Output is correct
12 Correct 5 ms 332 KB Output is correct
13 Correct 4 ms 332 KB Output is correct
14 Correct 4 ms 376 KB Output is correct
15 Correct 3 ms 332 KB Output is correct
16 Correct 1 ms 204 KB Output is correct
17 Correct 5 ms 332 KB Output is correct
18 Correct 5 ms 396 KB Output is correct
19 Correct 4 ms 380 KB Output is correct
20 Correct 5 ms 332 KB Output is correct
21 Correct 6 ms 332 KB Output is correct
22 Correct 4 ms 396 KB Output is correct
23 Correct 5 ms 392 KB Output is correct

Subtask #3
60.0 / 60.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 332 KB Output is correct
2 Correct 1 ms 332 KB Output is correct
3 Correct 1 ms 332 KB Output is correct
4 Correct 1 ms 332 KB Output is correct
5 Correct 1 ms 332 KB Output is correct
6 Correct 1 ms 204 KB Output is correct
7 Correct 1 ms 332 KB Output is correct
8 Correct 1 ms 332 KB Output is correct
9 Correct 1 ms 332 KB Output is correct
10 Correct 1 ms 332 KB Output is correct
11 Correct 1 ms 204 KB Output is correct
12 Correct 5 ms 332 KB Output is correct
13 Correct 4 ms 332 KB Output is correct
14 Correct 4 ms 376 KB Output is correct
15 Correct 3 ms 332 KB Output is correct
16 Correct 1 ms 204 KB Output is correct
17 Correct 5 ms 332 KB Output is correct
18 Correct 5 ms 396 KB Output is correct
19 Correct 4 ms 380 KB Output is correct
20 Correct 5 ms 332 KB Output is correct
21 Correct 6 ms 332 KB Output is correct
22 Correct 4 ms 396 KB Output is correct
23 Correct 5 ms 392 KB Output is correct
24 Correct 113 ms 332 KB Output is correct
25 Correct 110 ms 428 KB Output is correct
26 Correct 113 ms 416 KB Output is correct
27 Correct 112 ms 564 KB Output is correct
28 Correct 110 ms 432 KB Output is correct
29 Correct 80 ms 508 KB Output is correct
30 Correct 82 ms 544 KB Output is correct
31 Correct 1 ms 332 KB Output is correct
32 Correct 1 ms 332 KB Output is correct
33 Correct 91 ms 392 KB Output is correct
34 Correct 98 ms 436 KB Output is correct
35 Correct 101 ms 452 KB Output is correct
36 Correct 106 ms 448 KB Output is correct
37 Correct 175 ms 400 KB Output is correct
38 Correct 167 ms 416 KB Output is correct
39 Correct 102 ms 452 KB Output is correct
40 Correct 107 ms 456 KB Output is correct
41 Correct 104 ms 468 KB Output is correct
42 Correct 115 ms 452 KB Output is correct