Board Wrapping

最新推荐文章于 2020-10-02 21:15:08 发布

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位于加拿大不列颠哥伦比亚省的这家小型锯木厂发明了一种新型的板材干燥包装方法，通过固定板材于特殊模具中，使干燥过程更加高效。然而，空间是一个问题，板材不能过于紧密排列，以免干燥速度过慢，同时需要充分利用干燥室空间。

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The small sawmill in Mission, British Columbia, has developed a brand new way of packaging boards for drying. By fixating the boards in special moulds, the board can dry efficiently in a drying room.

Space is an issue though. The boards cannot be too close, because then the drying will be too slow. On the other hand, one wants to use the drying room efficiently.

Looking at it from a 2-D perspective, your task is to calculate the fraction between the space occupied by the boards to the total space occupied by the mould. Now, the mould is surrounded by an aluminium frame of negligible thickness, following the hull of the boards' corners tightly. The space occupied by the mould would thus be the interior of the frame.

Input

On the first line of input there is one integer, N <= 50, giving the number of test cases (moulds) in the input. After this line, N test cases follow. Each test case starts with a line containing one integer n, 1< n <= 600, which is the number of boards in the mould. Then n lines follow, each with five floating point numbers x, y, w, h, j where 0 <= x, y, w, h <=10000 and –90° < j <=90°. The x and y are the coordinates of the center of the board and w and h are the width and height of the board, respectively. j is the angle between the height axis of the board to the y-axis in degrees, positive clockwise. That is, if j = 0, the projection of the board on the x-axis would be w. Of course, the boards cannot intersect.

Output

For every test case, output one line containing the fraction of the space occupied by the boards to the total space in percent. Your output should have one decimal digit and be followed by a space and a percent sign (%).

Sample Input Output for Sample Input

4 7.5 6 3 0

8 11.5 6 3 0

9.5 6 6 3 90

4.5 3 4.4721 2.2361 26.565

64.3 %

#include<iostream>
#include<cstdio>
#include<cmath>
#include<algorithm>
using namespace std;

const double Pi=acos(-1.0);
const double eps=1e-6;
int dcmp(double x)
{
	if(fabs(x)<eps) return 0;
	else return x>0 ? 1:-1;
}

struct point{
	double x,y;
	point() {}
	point(double x,double y):x(x),y(y) {}
	point operator +(const point &b) const {return point(x+b.x,y+b.y);}
	point operator -(const point &b) const {return point(x-b.x,y-b.y);}
	point operator *(const double &b) const {return point(x*b,y*b);}
	point operator /(const double &b) const {return point(x/b,y/b);}
	bool operator <(const point &b) const {return dcmp(x-b.x)<0||(dcmp(x-b.x)==0&&dcmp(y-b.y)<0);}
}a[2410],b[2410];

double det(const point &a,const point &b) {return a.x*b.y-a.y*b.x;}

point Rotate(point p,double A)
{
	return point(p.x*cos(A)-p.y*sin(A),p.x*sin(A)+p.y*cos(A));
}

int main()
{
	int t;
	scanf("%d",&t);
	while(t--) {
		int n,k=0;
		scanf("%d",&n);
		double w,h,rad,sum=0.0,sum1=0.0;
		point s;
		for(int i=0;i<n;i++) {
			scanf("%lf%lf%lf%lf%lf",&s.x,&s.y,&w,&h,&rad);
			sum+=w*h;
			point p1=point(s.x-w/2.0,s.y-h/2.0),p2=point(s.x-w/2.0,s.y+h/2.0);
			point p3=point(s.x+w/2.0,s.y-h/2.0),p4=point(s.x+w/2.0,s.y+h/2.0);
			rad=rad/180*Pi;
			a[k++]=s+Rotate(p1-s,-rad);
			a[k++]=s+Rotate(p2-s,-rad);
			a[k++]=s+Rotate(p3-s,-rad);
			a[k++]=s+Rotate(p4-s,-rad);
		}
		sort(a,a+k);
		int j=0;
		for(int i=0;i<k;i++) {
			while(j>1&&dcmp(det(b[j-1]-b[j-2],a[i]-b[j-2]))<=0) j--;
			b[j++]=a[i];
		}
		int tmp=j;
		for(int i=k-2;i>=0;i--) {
			while(j>tmp&&dcmp(det(b[j-1]-b[j-2],a[i]-b[j-2]))<=0) j--;
			b[j++]=a[i];
		}
		for(int i=0;i<j-1;i++) sum1+=det(b[i],b[i+1]);
		sum1/=2.0;
		sum=sum/sum1*100.0;
		printf("%.1lf %%\n",sum);
	}
	return 0;
}

The small sawmill in Mission, British Columbia, has developed a brand new way of packaging boards for drying. By fixating the boards in special moulds, the board can dry efficiently in a drying room.

Space is an issue though. The boards cannot be too close, because then the drying will be too slow. On the other hand, one wants to use the drying room efficiently.