例题4.6 包装木板 UVa10652

1.题目描述：点击打开链接

2.解题思路：本题是凸包的一道简单的应用，只需要事先把输入的矩形的顶点放入顶点集P中，然后对该顶点集求凸包，并计算这个凸包的面积即可。

3.代码：

#include<iostream>
#include<algorithm>
#include<cassert>
#include<string>
#include<sstream>
#include<set>
#include<bitset>
#include<vector>
#include<stack>
#include<map>
#include<queue>
#include<deque>
#include<cstdlib>
#include<cstdio>
#include<cstring>
#include<cmath>
#include<ctime>
#include<cctype>
#include<complex>
#include<functional>
#pragma comment(linker, "/STACK:1024000000,1024000000")

using namespace std;

#define rep(i,n) for(int i=0;i<(n);i++)
#define me(s) memset(s,0,sizeof(s))
#define pb push_back
#define lid (id<<1)
#define rid (id<<1|1)
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int> P;

const double PI = acos(-1.0);
double torad(double deg) { return deg/180 * PI; }

struct Point {
double x, y;
Point(double x=0, double y=0):x(x),y(y) { }
};

typedef Point Vector;

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

Vector Rotate(const Vector& A, double rad) {
return Vector(A.x*cos(rad)-A.y*sin(rad), A.x*sin(rad)+A.y*cos(rad));
}

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;
}

// 点集凸包
// 如果不希望在凸包的边上有输入点，把两个 <= 改成 <
// 如果不介意点集被修改，可以改成传递引用
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;
}

// 多边形的有向面积
double PolygonArea(vector<Point> p) {
double area = 0;
int n = p.size();
for(int i = 1; i < n-1; i++)
area += Cross(p[i]-p[0], p[i+1]-p[0]);
return area/2;
}

int main() {
int T;
scanf("%d", &T);
while(T--) {
int n;
double area1 = 0;
scanf("%d", &n);
vector<Point> P;
for(int i = 0; i < n; i++) {
double x, y, w, h, j, ang;
scanf("%lf%lf%lf%lf%lf", &x, &y, &w, &h, &j);
Point o(x,y);
ang = -torad(j);
P.push_back(o + Rotate(Vector(-w/2,-h/2), ang));
P.push_back(o + Rotate(Vector(w/2,-h/2), ang));
P.push_back(o + Rotate(Vector(-w/2,h/2), ang));
P.push_back(o + Rotate(Vector(w/2,h/2), ang));
area1 += w*h;
}
double area2 = PolygonArea(ConvexHull(P));
printf("%.1lf %%\n", area1*100/area2);
}
return 0;
}