uva 11168 凸包

void getLineGeneralEquation(const Point& p1, const Point& p2, double& a, double& b, double &c)
{
  a = p2.y - p1.y;
  b = p1.x - p2.x;
  c = -a * p1.x - b * p1.y;
}

把直线的两点式转化为一般式，恩，没什么要注意的。

#include <bits/stdc++.h>
using namespace std;
struct Point
{
	double x, y;
	Point(double x = 0, double y = 0): x(x), y(y) { }
};

typedef Point Vector;

Vector operator - (const Point& A, const Point& B)
{
	return Vector(A.x - B.x, A.y - B.y);
}

double Cross(const Vector& A, const Vector& B)
{
	return A.x * B.y - A.y * B.x;
}

bool operator < (const Point& p1, const Point& p2)
{
	return p1.x < p2.x || (p1.x == p2.x && p1.y < p2.y);
}

bool operator == (const Point& p1, const Point& p2)
{
	return p1.x == p2.x && p1.y == p2.y;
}
vector<Point> ConvexHull(vector<Point> p)
{
	// 预处理，删除重复点
	sort(p.begin(), p.end());
	p.erase(unique(p.begin(), p.end()), p.end());

	int n = p.size();
	int m = 0;
	vector<Point> ch(n + 1);
	for (int i = 0; i < n; i++)
	{
		while (m > 1 && Cross(ch[m - 1] - ch[m - 2], p[i] - ch[m - 2]) <= 0) m--;
		ch[m++] = p[i];
	}
	int k = m;
	for (int i = n - 2; i >= 0; i--)
	{
		while (m > k && Cross(ch[m - 1] - ch[m - 2], p[i] - ch[m - 2]) <= 0) m--;
		ch[m++] = p[i];
	}
	if (n > 1) m--;
	ch.resize(m);
	return ch;
}
void getLineGeneralEquation(const Point& p1, const Point& p2, double& a, double& b, double &c)
{
	a = p2.y - p1.y;
	b = p1.x - p2.x;
	c = -a * p1.x - b * p1.y;
}
int T, N, kase;
double x, y, A, B, C;
int main(int argc, char const *argv[])
{
	scanf("%d", &T);
	while (T--)
	{
		scanf("%d", &N);
		vector<Point>P;
		double sumx = 0, sumy = 0, ans = 1E9;
		for (int i = 0; i < N; i++)
		{
			scanf("%lf%lf", &x, &y);
			sumx += x, sumy += y;
			P.push_back(Point(x, y));
		}
		vector<Point>ch = ConvexHull(P);
		if (ch.size() <= 2) ans = 0;
		else for (int i = 0; i < ch.size(); i++)
			{
				getLineGeneralEquation(ch[i], ch[(i + 1) % ch.size()], A, B, C);
				ans = min(ans, fabs(A * sumx + B * sumy + C * N) / sqrt(A * A + B * B));
			}
		printf("Case #%d: %.3lf\n", ++kase, ans / N);
	}
	return 0;
}

所有点在该直线的同一侧，明显是直接利用凸包的边更优。所以枚举凸包的每一条边，然后求距离和。

把两点式转化为一般式后，不必循环啦，把所有的x和y分别加起来，带入方程就好了。