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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
#746167#7906. Almost ConvexmobbbRE 0ms3612kbC++206.6kb2024-11-14 13:40:282024-11-14 13:40:29

Judging History

你现在查看的是最新测评结果

  • [2024-11-14 13:40:29]
  • 评测
  • 测评结果:RE
  • 用时:0ms
  • 内存:3612kb
  • [2024-11-14 13:40:28]
  • 提交

answer

#include <bits/stdc++.h>

#define ll long long 

#define db ll
constexpr db EPS = 0;
int sign(db a){ return a < -EPS ? -1 : a > EPS; }
int cmp(db a,db b) {return sign(a - b);}
struct P {
	db x,y;
	P() {}
	P(db _x,db _y) : x(_x),y(_y){}
	P operator+(P p) {return {x + p.x,y + p.y};}
	P operator-(P p) {return {x - p.x,y - p.y};}
	P operator*(db d) {return {x * d,y * d};}
	P operator/(db d) {return {x / d,y / d};}
	
	bool operator < (P p) const{
		int c = cmp(x,p.x);
		if (c) return c == -1;
		return cmp(y , p.y) == -1;
	}

	bool operator == (P o) const{
		return cmp(x,o.x) == 0 && cmp(y,o.y) == 0;
	}
	db dot(P p){return x * p.x + y * p.y;}
	// a * b == |a| * |b| * cos<a,b>  ,大于0为锐角小于0为钝角等于0为直角
	db det(P p){return {x * p.y - y * p.x};} 
	// a * b == |a| * |b| * sin<a,b> == - (b * a) ,a逆时针转多少度可以转到b
	// 大于0 b在a的逆时针方向,等于0共线,小于0 b在a的顺时针方向
	void read(){std::cin >> x >> y;}
	void print(){std::cout << x << " " << y  << "\n";}
	db distTo(P p) {return (*this - p).abs();}
	db alpha() {return atan2l(y,x);}
	db abs() {return sqrtl(abs2());}
	db abs2() {return x * x + y * y;}
	P rot90() {return P(-y,x);} // 逆时针旋转90度
	int quad(){return sign(y) == 1 || (sign(y) == 0 && sign(x) == 1);}
	P unit() {return *this / abs();}
	P rot(db an){return {x * cosl(an) - y * sinl(an),x * sinl(an) + y * cosl(an)};}
};
#define cross(p1,p2,p3) ((p2.x - p1.x) * (p3.y - p1.y) - (p2.y - p1.y) * (p3.x - p1.x))
#define crossOp(p1,p2,p3) sign(cross(p1,p2,p3)) // 以p1为起点去考虑<p1,p2> <p1,p3> 
// 大于0 p3在p2的逆时针方向,小于0在顺时针,等于0共线

// 两个直线是否相交
bool chkLL(P p1,P p2,P q1,P q2){
	db a1 = cross(q1,q2,p1),a2 = -cross(q1,q2,p2);
	return sign(a1 + a2) != 0;
}
// 求两直线交点
P isLL(P p1,P p2,P q1,P q2){
	db a1 = cross(q1,q2,p1),a2 = -cross(q1,q2,p2);
	return (p1 * a2 + p2 * a1) / (a1 + a2);
}
// 判断区间 [l1,r1] ,[l2,r2] 是否相交
bool intersect(db l1,db r1,db l2,db r2){
	if (l1 > r1) std::swap(l1,r1);if (l2 > r2) std::swap(l2,r2);
	return !(cmp(r1,l2) == -1 || cmp(r2,l1) == -1);
}
// 两线段是否相交
bool isSS(P p1,P p2,P q1,P q2){
	return intersect(p1.x,p2.x,q1.x,q2.x) && intersect(p1.y,p2.y,q1.y,q2.y) && 
	crossOp(p1,p2,q1) * crossOp(p1,p2,q2) <= 0 && crossOp(q1,q2,p1) * crossOp(q1,q2,p2) <= 0;
}
// 两线段是否严格相交
bool isSS_strict(P p1,P p2,P q1,P q2){
	return crossOp(p1,p2,q1) * crossOp(p1,p2,q2) < 0 && crossOp(q1,q2,p1) * crossOp(q1,q2,p2) < 0;
}
// m 在不在a和b之间
bool isMiddle(db a,db m,db b){
	return sign(a - m) == 0 || sign(b - m) == 0 || (a < m != b < m);
}
// 点m 在不在a和b之间
bool isMiddle(P a,P m,P b){
	return isMiddle(a.x,m.x,b.x) && isMiddle(a.y,m.y,b.y);
}
// 点q在线段上
bool onSeg(P p1,P p2, P q){
	return crossOp(p1,p2,q) == 0 && isMiddle(p1,q,p2);
}
// 点q严格在线段上
bool onSeg_strict(P p1,P p2,P q){
	return crossOp(p1,p2,q) == 0 && sign((q - p1).dot(p1 - p2)) * sign((q - p2).dot(p1 - p2));
}
// 求 q 到 p1p2的投影
P proj(P p1,P p2,P q){
	P dir = p2 - p1;
	return p1 + dir * (dir.dot(q - p1) / dir.abs2());
}
// 求 q以直线p1p2为轴的反射
P refect(P p1,P p2,P q){
	return proj(p1,p2,q) * 2 - q;
}
// 求q到线段p1p2的最短距离
db nearest(P p1,P p2,P q){
	if (p1 == p2) return p1.distTo(q);
	P h = proj(p1,p2,q);
	if (isMiddle(p1,h,p2)){
		return q.distTo(h);
	}
	return std::min(p1.distTo(q),p2.distTo(q));
}
// 求线段p1p2 与线段q1q2的距离
db disSS(P p1,P p2,P q1,P q2){
	if(isSS(p1,p2,q2,q2)) return 0;
	return std::min({nearest(p1,p2,q1),nearest(p1,p2,q2),nearest(q1,q2,p1),nearest(q1,q2,p2)});
}
// 极角排序
// sort(p.begin(), p.end(), [&](P a, P b){
// 	int qa = a.quad(),qb = b.quad();
// 	if (qa != qb) return qa < qb;
// 	return sign(a.det(b)) > 0;
// })
std::vector<P> convexHull(std::vector<P> ps){ // need unique , <= strict , < strict
	int n = ps.size();
	if (n <= 1) return ps;
	std::sort(ps.begin(),ps.end());
	std::vector<P> qs(n * 2);
	int k = 0;
	for (int i = 0;i < n;qs[k++] = ps[i++]){
		while (k > 1 && crossOp(qs[k - 2],qs[k - 1],ps[i]) <= 0){
			k--;
		}
	}
	for (int i = n - 2,t = k;i >= 0;qs[k++] = ps[i--]){
		while (k > t && crossOp(qs[k - 2],qs[k - 1],ps[i]) <= 0){
			k--;
		}
	}
	qs.resize(k - 1);
	return qs;
}

db area(std::vector<P> ps){
	db ans = 0;
	for (int i = 0;i < ps.size();i++){
		ans += ps[i].det(ps[(i + 1) % (ps.size())]);
	}
	ans /= 2;
	return ans;
}

bool check(std::vector<P> p){
	int n = p.size();

	bool ok = true;
	double angle = 0;
	for (int i = 0; i < n; i++){
		P L = p[(i - 1 + n) % n] - p[i];
		P R = p[(i + 1) % n] - p[i];
		if (L.det(R) >= 0 || L == P(0, 0) || R == P(0, 0)){
			ok = false;
		}
		L = p[i] - p[(i - 1 + n) % n];
	}
	if (ok){
		return true;
	}	
	ok = true;
	for (int i = 0; i < n; i++){
		P L = p[(i - 1 + n) % n] - p[i];
		P R = p[(i + 1) % n] - p[i];
		if (L.det(R) <= 0 || L == P(0, 0) || R == P(0, 0)){
			ok = false;
		}
	}
	if (ok){
		return true;
	}else{
		return false;
	}
}

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

	int n;

	std::cin >> n;
	std::vector<P> p(n);

	for (int i = 0; i < n; i++){
		p[i].read();
	}
	sort(p.begin(), p.end(), [&](P a, P b){
		int qa = a.quad(),qb = b.quad();
		if (qa != qb) return qa < qb;
		return sign(a.det(b)) > 0;
	});
	auto Hull = convexHull(p);
	std::map<P, int> cnt;
	for (int i = 0; i < Hull.size(); i++){
		cnt[Hull[i]] = 1;
	}
	sort(Hull.begin(), Hull.end(), [&](P a, P b){
		a = a - Hull[0], b = b - Hull[0];
		int qa = a.quad(),qb = b.quad();
		if (qa != qb) return qa < qb;
		return sign(a.det(b)) > 0;
	});
	assert(check(Hull));
	std::vector<P> inside;
	for (int i = 0; i < n; i++){
		if (cnt.find(p[i]) == cnt.end()){
			inside.push_back(p[i]);
		}	
	}
	auto select = convexHull(inside);

	int m = Hull.size(), k = inside.size();
	int ans = 1;
	for (int i = 0; i < m; i++){
		P p1 = Hull[i], p2 = Hull[(i + 1) % m];
		std::vector<P> cur(2 * k);
		int begin = 0, end = -1;
		for (int j = 0; j < k; j++){
			P l = p1 - select[j], r = p2 - select[j];
			// P pre = select[(j - 1 + k) % k] - select[j], next = select[(j + 1) % k] - select[j];
			// if (l.det(pre) > 0 && r.det(pre) < 0){
			// 	continue;
			// }
			// if (l.det(next) > 0 && r.det(next) < 0){
			// 	continue;
			// }
			bool ok = true;
			for (int x = 0; x < k; x++){
				P tmp = select[x] - select[j];
				if (l.det(tmp) > 0 && r.det(tmp) < 0){
					ok = false;
				}
			}
			if (ok){
				ans++;
			}
		}
	}
	std::cout << ans << '\n';

	return 0;
}

详细

Test #1:

score: 100
Accepted
time: 0ms
memory: 3548kb

input:

7
1 4
4 0
2 3
3 1
3 5
0 0
2 4

output:

9

result:

ok 1 number(s): "9"

Test #2:

score: 0
Accepted
time: 0ms
memory: 3480kb

input:

5
4 0
0 0
2 1
3 3
3 1

output:

5

result:

ok 1 number(s): "5"

Test #3:

score: 0
Accepted
time: 0ms
memory: 3476kb

input:

3
0 0
3 0
0 3

output:

1

result:

ok 1 number(s): "1"

Test #4:

score: 0
Accepted
time: 0ms
memory: 3612kb

input:

6
0 0
3 0
3 2
0 2
1 1
2 1

output:

7

result:

ok 1 number(s): "7"

Test #5:

score: 0
Accepted
time: 0ms
memory: 3564kb

input:

4
0 0
0 3
3 0
3 3

output:

1

result:

ok 1 number(s): "1"

Test #6:

score: -100
Runtime Error

input:

2000
86166 617851
383354 -277127
844986 386868
-577988 453392
-341125 -386775
-543914 -210860
-429613 606701
-343534 893727
841399 339305
446761 -327040
-218558 -907983
787284 361823
950395 287044
-351577 -843823
-198755 138512
-306560 -483261
-487474 -857400
885637 -240518
-297576 603522
-748283 33...

output:


result: