POJ 1265 Area (Pick定理&多边形面积)

http://poj.org/problem?id=1265

定理证明见Matrix67——最酷的证明：Pick定理另类证法

注意dx和dy是机器人下一步移动的方向，所以位置要累加。

完整代码：

/*0ms,372KB*/

#include<cstdio>
#include<cstdlib>
const int mx = 105;

struct point
{
	double x, y;
	point(double x = 0.0, double y = 0.0): x(x), y(y) {}
	void read() const
	{
		scanf("%lf%lf", &x, &y);
	}
};

point a[mx];
int n;

///oa x ob
inline double cross_product(point& a, point& b)
{
	return a.x * b.y - a.y * b.x;
}

///求多边形面积。以原点为向量起点。注意ans[]要是顺时针顺序
double area()
{
	double sum = 0.0;
	a[n] = a[0];
	for (int i = 0; i < n; ++i) sum += cross_product(a[i], a[i + 1]);
	return sum / 2.0;
}

int gcd(int a, int b)
{
	return b ? gcd(b, a % b) : a;
}

int borderpoint()
{
	int cnt = 0;
	a[n] = a[0];
	for (int i = 0; i < n; ++i)
		cnt += gcd(abs((int)(a[i].x - a[i + 1].x)), abs((int)(a[i].y - a[i + 1].y)));
	return cnt;
}

int main()
{
	int t, i, B;
	double A;
	scanf("%d", &t);
	for (int k = 1; k <= t; ++k)
	{
		scanf("%d", &n);
		for (i = 1; i < n; ++i)
		{
			a[i].read();
			a[i].x += a[i - 1].x;
			a[i].y += a[i - 1].y;
		}
		scanf("%*d%*d");
		A = area();
		B = borderpoint();
		printf("Scenario #%d:\n%d %d %.1f\n\n", k, (int)A + 1 - B / 2, B, A);
	}
	return 0;
}