题目大意是
有一些点，然后我们要用一个六角星形将任意这些点连成的直线覆盖。 并且这些点构成的凸包面积必须满足小于某个值
六角星形的中心点和半径已经给定了。
就是一个判定问题了。
首先要判断所有点是否都在六角星形内
我们观察这个形状，发现是两个三角形组成的图形。
那么只需判断某个点是否在某个三角形内即可
这里就用到叉积就行了。
然后对所有点求个凸包。
求个面积
然后看这些凸包的边是否在六角星形内
观察图形，可以发现其由12个短线段构成边界
那么看边是否在六角星形内。只需判断某个边是否与这些边界规范相交即可
代码如下。
#include <iostream>
#include <cstdio>
#include <cstring>
#include <string>
#include <algorithm>
#include <cstdlib>
#include <cmath>
#include <map>
#include <sstream>
#include <queue>
#include <vector>
#define MAXN 111111
#define MAXM 211111
#define eps 1e-8
#define INF 1000000001
using namespace std;
int dblcmp(double d)
{if (fabs(d) < eps) return 0;return d > eps ? 1 : -1;
}struct point
{double x, y;point(){}point(double _x, double _y):x(_x), y(_y){};void input(){scanf("%lf%lf",&x, &y);}double dot(point p){return x * p.x + y * p.y;}double distance(point p){return hypot(x - p.x, y - p.y);}point sub(point p){return point(x - p.x, y - p.y);}double det(point p){return x * p.y - y * p.x;}bool operator < (point a)const{return dblcmp(a.x - x) == 0 ? dblcmp(y - a.y) < 0 : x < a.x;}}p[MAXN], hg[15];
struct line
{point a, b;line(){}line(point _a, point _b){ a = _a; b = _b;}int segcrossseg(line v){int d1 = dblcmp(b.sub(a).det(v.a.sub(a)));int d2 = dblcmp(b.sub(a).det(v.b.sub(a)));int d3 = dblcmp(v.b.sub(v.a).det(a.sub(v.a)));int d4 = dblcmp(v.b.sub(v.a).det(b.sub(v.a)));if ((d1 ^ d2) == -2 && (d3 ^ d4) == -2) return 2;return (d1 == 0 && dblcmp(v.a.sub(a).dot(v.a.sub(b))) <=0 ||d2 == 0 && dblcmp(v.b.sub(a).dot(v.b.sub(b))) <=0 ||d3 == 0 && dblcmp(a.sub(v.a).dot(a.sub(v.b))) <= 0 ||d4 == 0 && dblcmp(b.sub(v.a).dot(b.sub(v.b))) <= 0);}}seg[13], tri[2][3];
struct polygon
{int n;point p[MAXN];line l[MAXN];double area;void input(){for(int i = 0; i < n; i++) p[i].input();}void getline(){for(int i = 0; i < n; i++)l[i] = line(p[i], p[(i + 1) % n]);}void getarea(){area = 0;int a = 1, b = 2;while(b <= n - 1){area += p[a].sub(p[0]).det(p[b].sub(p[0]));a++;b++;}area = fabs(area) / 2;}
}convex;
bool conpoint(point p[],int n)
{for (int i = 1; i < n; i++)if (dblcmp(p[i].x - p[0].x) != 0 ||dblcmp(p[i].y - p[0].y) != 0)return false;return true;
}
bool conline(point p[],int n)
{for (int i = 2; i < n; i++)if (dblcmp(p[1].sub(p[0]).det(p[i].sub(p[0]))) != 0) return false;return true;
}
void getconvex(point p[], int n, point res[], int& resn)
{resn = 0;if (conpoint(p, n)){res[resn++] = p[0];return;}sort(p, p + n);if (conline(p,n)){res[resn++] = p[0];res[resn++] = p[n - 1];return;}for (int i = 0; i < n;)if (resn < 2 || dblcmp(res[resn - 1].sub(res[resn - 2]).det(p[i].sub(res[resn - 1]))) > 0)res[resn++] = p[i++];else --resn;int top = resn - 1;for (int i = n - 2; i >= 0;)if (resn < top + 2 || dblcmp(res[resn - 1].sub(res[resn - 2]).det(p[i].sub(res[resn - 1]))) > 0)res[resn++] = p[i--];else --resn;resn--;
}
int n;
bool intriangle(point x)
{int tmp = 2;for(int i = 0; i < 2; i++){for(int j = 0; j < 3; j++)if(dblcmp(tri[i][j].a.sub(x).det(tri[i][j].b.sub(x))) > 0){tmp--;break;}}return tmp > 0;
}
int main()
{double sx, sy, S, R;while(scanf("%lf%lf", &sx, &sy) != EOF){scanf("%d", &n);for(int i = 0; i < n; i++) p[i].input();getconvex(p, n, convex.p, convex.n);convex.getline();convex.getarea();scanf("%lf%lf", &R, &S);double sthree = sqrt(3.0);hg[0] = point(sx, sy + sthree * R);hg[1] = point(sx + R / 2, sy + sthree * R / 2);hg[2] = point(sx + R * 3.0 / 2, sy + sthree * R / 2);hg[3] = point(sx + R, sy);hg[4] = point(sx + R * 3.0 / 2, sy - sthree * R / 2);hg[5] = point(sx + R / 2, sy - sthree * R / 2);hg[6] = point(sx, sy - sthree * R);hg[7] = point(sx - R / 2, sy - sthree * R / 2);hg[8] = point(sx - R * 3.0 / 2, sy - sthree * R / 2);hg[9] = point(sx - R, sy);hg[10] = point(sx - R * 3.0 / 2, sy + sthree * R / 2);hg[11] = point(sx - R / 2, sy + sthree * R / 2);tri[0][0] = line(hg[0], hg[4]);tri[0][1] = line(hg[4], hg[8]);tri[0][2] = line(hg[8], hg[0]);tri[1][0] = line(hg[2], hg[6]);tri[1][1] = line(hg[6], hg[10]);tri[1][2] = line(hg[10], hg[2]);for(int i = 0; i < 12; i++) seg[i] = line(hg[i], hg[(i + 1) % 12]);int flag = 1;for(int i = 0; i < n; i++){if(!intriangle(p[i])){flag = 0;break;}}for(int i = 0; i < 12; i++){if(flag == 0) break;for(int j = 0; j < convex.n; j++)if(seg[i].segcrossseg(convex.l[j]) == 2){flag = 0;break;}}if(flag){if(dblcmp(3.0 * sthree * R * R - convex.area - S) > 0) puts("Succeeded.");else puts("Failed.");}else puts("Failed.");}return 0;
}