Codeforces Round #172 (Div. 2) Rectangle Puzzle

You are given two rectangles on a plane. The centers of both rectangles are located in the origin of coordinates (meaning the center of the rectangle’s symmetry). The first rectangle’s sides are parallel to the coordinate axes: the length of the side that is parallel to the Oxaxis, equals w, the length of the side that is parallel to the Oy axis, equals h. The second rectangle can be obtained by rotating the first rectangle relative to the origin of coordinates by angle α.

Your task is to find the area of the region which belongs to both given rectangles. This region is shaded in the picture.

The first line contains three integers w, h, α (1 ≤ w, h ≤ 10⁶; 0 ≤ α ≤ 180). Angle α is given in degrees.

In a single line print a real number — the area of the region which belongs to both given rectangles.

The answer will be considered correct if its relative or absolute error doesn’t exceed 10^- 6.

The second sample has been drawn on the picture above.

#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <iomanip>

using namespace std;

const double PI=acos(-1);

int main()
{
    double w,h,a;
    double ans;
    cin>>w>>h>>a;

    cout<<setiosflags(ios::fixed)<<setprecision(8);
    if(a>90)a=180-a;
    a*=PI/180;

    if(fabs(a/PI*180-90)<1e-5)
    {
        //ans=w*h;
        if(w>h)ans=h*h;
        else ans=w*w;
        cout<<ans;
    }
    else if(a>=atan(2*h/w) && w>h/sin(a)+h/tan(a))
    {
        ans=h*h/sin(a);
        cout<<ans;
    }
    else if(a>=atan(2*w/h) && h>w/sin(a)+w/tan(a))
    {
        ans=w*w/sin(a);
        cout<<ans;
    }
    else
    {
        ans=w*h;


        /*
        double a11=1.0/sin(a)/cos(a)+tan(a)-1.0/tan(a),
        a12=2/cos(a),
        a21=2/cos(a),
        a22=1.0/sin(a)/cos(a)+tan(a)-1.0/tan(a),
        b1=w/cos(a)+h*tan(a)-w,
        b2=w*tan(a)+h/cos(a)-h;
        double x1=(b1*a22-b2*a12)/(a11*a22-a12*a21),x2=(a11*b2-a21*b1)/(a11*a22-a12*a21);
        ans-=x2*x2/tan(a)+(w-x2-x1/sin(a))*(w-x2-x1/sin(a))*tan(a);
        */
        ans=(sin(a/2)*h*h - 2*cos(a/2)*h*w + sin(a/2)*w*w)/(2*cos(a/2) - 4*cos(a/2)*cos(a/2)*cos(a/2));
        cout<<ans;
    }
    //system("pause");
}

本文链接：Codeforces Round #172 (Div. 2) Rectangle Puzzle

转载声明：本站文章若无特别说明，皆为原创，转载请注明来源：Rexdf，谢谢！^^