uva10652 Board Wrapping（凸包）

最新推荐文章于 2020-11-24 16:51:08 发布

原创最新推荐文章于 2020-11-24 16:51:08 发布 · 280 阅读

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本文解析了UVA10652题目，该题要求计算多个旋转长方形被一个凸包覆盖时的面积比例。文章提供了完整的代码实现，包括长方形旋转、凸包构建及面积计算等关键步骤。

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uva10652

题目

就是给你几个长方形，并且要旋转一定角度，用一个凸包把它们包起来并且求长方形面积总和与凸包面积之比。

思路

模版题，多了个求凸包面积和向量的旋转。

代码

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
#define pi acos (-1)
using namespace std;
typedef long long ll;

const int maxn=3000;

int tot;

struct point
{
    double x, y;
    point (double _x = 0, double _y = 0) : x(_x), y(_y) {}
    point operator - (point a) const
    {
        return point (x-a.x, y-a.y);
    }
    point operator + (point a) const
    {
        return point (x+a.x, y+a.y);
    }
    bool operator < (const point &a) const
    {
        return x < a.x || (x == a.x && y < a.y);
    }
} p[maxn];

const double eps = 1e-10;
int dcmp (double x)
{
    if (fabs (x) < eps)
        return 0;
    else return x < 0 ? -1 : 1;
}
double cross (point a, point b)
{
    return a.x*b.y-a.y*b.x;
}
double dot (point a, point b)
{
    return a.x*b.x + a.y*b.y;
}
double AngleToRad (double x)
{
    return x*pi/180;
}
point rotate (point a, double rad)
{
    return point (a.x*cos (rad)-a.y*sin (rad), a.x*sin (rad)+a.y*cos (rad));
}

double ConvexPolygonArea (point *p, int n)
{
    double area = 0;
    for (int i = 1; i < n-1; i++)
        area += cross (p[i]-p[0], p[i+1]-p[0]);
    return area/2.0;
}

int n, m;
double l;
point ch[maxn];

int ConvexHull (int n)
{
    sort (p, p+n);
    int m = 0;
    for (int i = 0; i < n; i++)
    {
        while (m > 1 && cross (ch[m-1]-ch[m-2], p[i]-ch[m-1]) <= 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-1]) <= 0)
            m--;
        ch[m++] = p[i];
    }
    if (n > 1)
        m--;
    return m;
}

double dis (point a, point b)
{
    double xx = a.x-b.x, yy = a.y-b.y;
    return sqrt (xx*xx + yy*yy);
}

int main()
{
    int T;
    scanf("%d",&T);
    while(T--)
    {
        tot=0;
        double sum1=0,sum2=0;
        scanf("%d",&n);
        for(int i=0; i<n; i++)
        {
            double x,y,w,h,ang;
            scanf("%lf%lf%lf%lf%lf",&x,&y,&w,&h,&ang);
            ang=-AngleToRad(ang);
            sum1+=w*h;
            point from(x,y);
            p[tot++]=from+rotate(point(w/2.0,h/2.0),ang);
            p[tot++]=from+rotate(point(w/2.0,-h/2.0),ang);
            p[tot++]=from+rotate(point(-w/2.0,h/2.0),ang);
            p[tot++]=from+rotate(point(-w/2.0,-h/2.0),ang);
        }
        m=ConvexHull(tot);
        sum2=ConvexPolygonArea(ch,m);
        printf ("%.1f %\n", 100.0*sum1/sum2);
    }
    return 0;
}