半平面交练习（计算几何）

四：半平面交

Rotating Scoreboard

/*Author : lifehappy
*/
#include <cstdio>
#include <cmath>
#include <cstring>
#include <algorithm>
#include <vector>
#include <iostream>using namespace std;const double pi = acos(-1.0);
const double eps = 1e-5;
const double inf = 1e100;int Sgn(double x) {return x < -eps ? -1 : x > eps;
}struct Vector {double x, y;bool operator < (Vector &a) const {return x < a.x;}void print() {printf("%f %f\n", x, y);}void read() {scanf("%lf %lf", &x, &y);}Vector(double _x = 0, double _y = 0) : x(_x), y(_y) {}double mod() {return sqrt(x * x + y * y);}double mod2() {return x * x + y * y;}Vector operator + (const Vector &a) {return Vector(x + a.x, y + a.y);}Vector operator - (const Vector &a) {return Vector(x - a.x, y - a.y);}double operator * (const Vector &a) {return x * a.x + y * a.y;}double operator ^ (const Vector &a) {return x * a.y - y * a.x;}Vector Rotate(double angle) {return Vector(x * cos(angle) - y * sin(angle), x * sin(angle) + y * cos(angle));}Vector operator << (const double &a) {return Vector(x * a, y * a);}Vector operator >> (const double &a) {return Vector(x / a, y / a);}bool operator == (const Vector & a) {return (Sgn(x - a.x) == 0) && (Sgn(y - a.y) == 0);}
};typedef Vector Point;double Dis_pp(Point a, Point b) {return sqrt((a - b) * (a - b));
}double Angle(Vector a, Vector b) {//[0, 2pi)double ans = atan2(a ^ b, a * b);return ans < 0 ? ans + 2 * pi : ans;// return atane(a ^ b, a * b);
}double To_lefttest(Point a, Point b, Point c) {return (b - a) ^(c - a);
}int Toleft_test(Point a, Point b, Point c) {return Sgn((b - a) ^ (c - a));
}struct Line {Point st, ed;Line(Point _st = Point(0, 0), Point _ed = Point(0, 0)) : st(_st), ed(_ed) {}bool operator < (const Line &t) {return st.x < t.st.x;}void read() {scanf("%lf %lf %lf %lf", &st.x, &st.y, &ed.x, &ed.y);}
};bool Parallel(Line a, Line b) {return Sgn((a.st - a.ed) ^ (b.st - b.ed)) == 0;
}bool Is_cross(Line a, Line b) {return Toleft_test(a.st, a.ed, b.st) * Toleft_test(a.st, a.ed, b.ed) <= 0 && Toleft_test(b.st, b.ed, a.st) * Toleft_test(b.st, b.ed, a.ed) <= 0;
}Point Cross_point(Line a, Line b) {if(!Is_cross(a, b)) {return Point(inf, inf);}else {double a1 = fabs(To_lefttest(a.st, a.ed, b.st)), a2 = fabs(To_lefttest(a.st, a.ed, b.ed));return ((b.st << a2) + (b.ed << a1)) >> (a1 + a2);}
}Point Intersect_point(Line a, Line b) {double a1 = a.st.y - a.ed.y, b1 = a.ed.x - a.st.x, c1 = a.st.x * a.ed.y - a.ed.x * a.st.y;double a2 = b.st.y - b.ed.y, b2 = b.ed.x - b.st.x, c2 = b.st.x * b.ed.y - b.ed.x * b.st.y;return Point((c1 * b2 - c2 * b1) / (a2 * b1 - a1 * b2), (a2 * c1 - a1 * c2) / (a1 * b2 - a2 * b1));
}Point Shadow(Line a, Point b) {Point dir = a.ed - a.st;return a.st + (dir << (((b - a.st) * dir) / dir.mod2()));
}Point Reflect(Line a, Point b) {return (Shadow(a, b) << 2) - b;
}bool inmid(double a, double b, double x) {if(a > b) swap(a, b);return Sgn(x - a) >= 0 && Sgn(b - x) >= 0;
}bool Point_in_line(Line a, Point b) {if(Toleft_test(a.st, a.ed, b) != 0) return false;return inmid(a.st.x, a.ed.x, b.x) && inmid(a.st.y, a.ed.y, b.y);
}double Dis_lp(Line a, Point b) {Point h = Shadow(a, b);if(Point_in_line(a, h)) {return Dis_pp(h, b);}return min(Dis_pp(a.st, b), Dis_pp(a.ed, b));
}// double Dis_ll(Line a, Line b) {//     if(Is_cross(a, b)) return 0;
//     return min({Dis_lp(a, b.st), Dis_lp(a, b.ed), Dis_lp(b, a.st), Dis_lp(b, a.ed)});
// }double Area(vector<Point> p, int n) {double ans = 0;for(int i = 0; i < n; i++) {ans += p[i] ^ p[(i + 1) % n];}return 0.5 * ans;
}double len(vector<Point> p, int n) {double ans = 0;for(int i = 0; i < n; i++) {ans += Dis_pp(p[i], p[(i + 1) % n]);}return ans;
}bool Is_convex(Point *a, int n) {bool flag[3] = {0, 0, 0};for(int i = 0; i < n; i++) {flag[Sgn(To_lefttest(a[i], a[(i + 1) % n], a[(i + 2) % n])) + 1] = true;if(flag[0] && flag[2]) return false;}return true;
}Point p0;bool cmp_graham(Point a, Point b) {int flag = Toleft_test(p0, a, b);return flag == 0 ? Dis_pp(p0, a) < Dis_pp(p0, b) : flag > 0;
}vector<Point> Graham(vector<Point> &a, int n) {p0 = a[0];for(int i = 0; i < n; i++) {if(a[i].y < p0.y || (a[i].y == p0.y && a[i].x < p0.x)) {p0 = a[i];}}vector<Point> ans;sort(a.begin(), a.end(), cmp_graham);if(n == 1) {ans.push_back(a[0]);return ans;}if(n == 2) {ans.push_back(a[0]);ans.push_back(a[1]);return ans;}ans.push_back(a[0]);ans.push_back(a[1]);int sz = 2;for(int i = 2; i < n; i++) {while(sz > 1 && To_lefttest(ans[sz - 2], ans[sz - 1], a[i]) <= 0) {ans.pop_back();sz--;}ans.push_back(a[i]);sz++;}return ans;
}bool cmp_andrew(Point a, Point b) {if(Sgn(a.x - b.x) == 0)    return a.y < b.y;return a.x < b.x;
}vector<Point> Andrew(vector<Point> &a, int n) {sort(a.begin(), a.end(), cmp_andrew);int p1 = 0, p2;vector<Point> ans;for(int i = 0; i < n; i++) {while(p1 > 1 && Toleft_test(ans[p1 - 2], ans[p1 - 1], a[i]) <= 0)   ans.pop_back(), p1--;ans.push_back(a[i]), p1++;}p2 = p1;for(int i = n - 2; i>= 0; i--) {while(p2 > p1 && Toleft_test(ans[p2 - 2], ans[p2 - 1], a[i]) <= 0)  ans.pop_back(), p2--;ans.push_back(a[i]), p2++;}// ans.pop_back();return ans;
}double Get_angle(Line a) {return atan2(a.ed.y - a.st.y, a.ed.x - a.st.x);
}bool cmp_Half_lane_intersection(Line a, Line b) {Vector va = a.ed - a.st, vb = b.ed - b.st;double A =  Get_angle(va), B = Get_angle(vb);if (Sgn(A - B) == 0) return Sgn(((va) ^ (b.ed - a.st))) != -1;return Sgn(A - B) == -1;
}bool On_right(Line a, Line b, Line c) {Point o = Intersect_point(b, c);if (Sgn((a.ed - a.st) ^ (o - a.st)) < 0) return true;return false;
}const int N = 1e3 + 10;Line que[N];bool Half_lane_intersection(vector<Line> &a) {sort(a.begin(), a.end(), cmp_Half_lane_intersection);int head = 0, tail = 0, cnt = 0, n = a.size();for(int i = 0; i < n - 1; i++) {if(Sgn(Get_angle(a[i]) - Get_angle(a[i + 1])) == 0) continue;a[cnt++] = a[i];}a[cnt++] = a[n - 1];for(int i = 0; i < cnt; i++) {while(tail - head > 1 && On_right(a[i], que[tail - 1], que[tail - 2])) tail--;while(tail - head > 1 && On_right(a[i], que[head], que[head + 1])) head++;que[tail++] = a[i];}while(tail - head > 1 && On_right(que[head], que[tail - 1], que[tail - 2])) tail--;while(tail - head > 1 && On_right(que[tail - 1], que[head], que[head + 1])) head++;if (tail - head < 3) return false;return true;
}int main() {// freopen("in.txt", "r", stdin);// freopen("out.txt", "w", stdout);// ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);int T;scanf("%d", &T);while(T--) {int n;scanf("%d", &n);vector<Point> res;for(int i = 0; i < n; i++) {Point ans;ans.read();res.push_back(ans);}double area = Area(res, n);vector<Line> a;if(area > 0) {for(int i = 0; i < n; i++) {a.push_back(Line(res[i], res[(i + 1) % n]));}}else {for(int i = n - 1; i >= 0; i--) {a.push_back(Line(res[(i + 1) % n], res[i]));}}if(Half_lane_intersection(a)) puts("YES");else puts("NO");}return 0;
}

How I Mathematician Wonder What You Are!

/*Author : lifehappy
*/
#include <cstdio>
#include <cmath>
#include <cstring>
#include <algorithm>
#include <vector>
#include <iostream>using namespace std;const double pi = acos(-1.0);
const double eps = 1e-5;
const double inf = 1e100;int Sgn(double x) {return x < -eps ? -1 : x > eps;
}struct Vector {double x, y;bool operator < (Vector &a) const {return x < a.x;}void print() {printf("%f %f\n", x, y);}void read() {scanf("%lf %lf", &x, &y);}Vector(double _x = 0, double _y = 0) : x(_x), y(_y) {}double mod() {return sqrt(x * x + y * y);}double mod2() {return x * x + y * y;}Vector operator + (const Vector &a) {return Vector(x + a.x, y + a.y);}Vector operator - (const Vector &a) {return Vector(x - a.x, y - a.y);}double operator * (const Vector &a) {return x * a.x + y * a.y;}double operator ^ (const Vector &a) {return x * a.y - y * a.x;}Vector Rotate(double angle) {return Vector(x * cos(angle) - y * sin(angle), x * sin(angle) + y * cos(angle));}Vector operator << (const double &a) {return Vector(x * a, y * a);}Vector operator >> (const double &a) {return Vector(x / a, y / a);}bool operator == (const Vector & a) {return (Sgn(x - a.x) == 0) && (Sgn(y - a.y) == 0);}
};typedef Vector Point;double Dis_pp(Point a, Point b) {return sqrt((a - b) * (a - b));
}double Angle(Vector a, Vector b) {//[0, 2pi)double ans = atan2(a ^ b, a * b);return ans < 0 ? ans + 2 * pi : ans;// return atane(a ^ b, a * b);
}double To_lefttest(Point a, Point b, Point c) {return (b - a) ^(c - a);
}int Toleft_test(Point a, Point b, Point c) {return Sgn((b - a) ^ (c - a));
}struct Line {Point st, ed;Line(Point _st = Point(0, 0), Point _ed = Point(0, 0)) : st(_st), ed(_ed) {}bool operator < (const Line &t) {return st.x < t.st.x;}void read() {scanf("%lf %lf %lf %lf", &st.x, &st.y, &ed.x, &ed.y);}
};bool Parallel(Line a, Line b) {return Sgn((a.st - a.ed) ^ (b.st - b.ed)) == 0;
}bool Is_cross(Line a, Line b) {return Toleft_test(a.st, a.ed, b.st) * Toleft_test(a.st, a.ed, b.ed) <= 0 && Toleft_test(b.st, b.ed, a.st) * Toleft_test(b.st, b.ed, a.ed) <= 0;
}Point Cross_point(Line a, Line b) {if(!Is_cross(a, b)) {return Point(inf, inf);}else {double a1 = fabs(To_lefttest(a.st, a.ed, b.st)), a2 = fabs(To_lefttest(a.st, a.ed, b.ed));return ((b.st << a2) + (b.ed << a1)) >> (a1 + a2);}
}Point Intersect_point(Line a, Line b) {double a1 = a.st.y - a.ed.y, b1 = a.ed.x - a.st.x, c1 = a.st.x * a.ed.y - a.ed.x * a.st.y;double a2 = b.st.y - b.ed.y, b2 = b.ed.x - b.st.x, c2 = b.st.x * b.ed.y - b.ed.x * b.st.y;return Point((c1 * b2 - c2 * b1) / (a2 * b1 - a1 * b2), (a2 * c1 - a1 * c2) / (a1 * b2 - a2 * b1));
}Point Shadow(Line a, Point b) {Point dir = a.ed - a.st;return a.st + (dir << (((b - a.st) * dir) / dir.mod2()));
}Point Reflect(Line a, Point b) {return (Shadow(a, b) << 2) - b;
}bool inmid(double a, double b, double x) {if(a > b) swap(a, b);return Sgn(x - a) >= 0 && Sgn(b - x) >= 0;
}bool Point_in_line(Line a, Point b) {if(Toleft_test(a.st, a.ed, b) != 0) return false;return inmid(a.st.x, a.ed.x, b.x) && inmid(a.st.y, a.ed.y, b.y);
}double Dis_lp(Line a, Point b) {Point h = Shadow(a, b);if(Point_in_line(a, h)) {return Dis_pp(h, b);}return min(Dis_pp(a.st, b), Dis_pp(a.ed, b));
}// double Dis_ll(Line a, Line b) {//     if(Is_cross(a, b)) return 0;
//     return min({Dis_lp(a, b.st), Dis_lp(a, b.ed), Dis_lp(b, a.st), Dis_lp(b, a.ed)});
// }double Area(vector<Point> p, int n) {double ans = 0;for(int i = 0; i < n; i++) {ans += p[i] ^ p[(i + 1) % n];}return 0.5 * ans;
}double len(vector<Point> p, int n) {double ans = 0;for(int i = 0; i < n; i++) {ans += Dis_pp(p[i], p[(i + 1) % n]);}return ans;
}bool Is_convex(Point *a, int n) {bool flag[3] = {0, 0, 0};for(int i = 0; i < n; i++) {flag[Sgn(To_lefttest(a[i], a[(i + 1) % n], a[(i + 2) % n])) + 1] = true;if(flag[0] && flag[2]) return false;}return true;
}Point p0;bool cmp_graham(Point a, Point b) {int flag = Toleft_test(p0, a, b);return flag == 0 ? Dis_pp(p0, a) < Dis_pp(p0, b) : flag > 0;
}vector<Point> Graham(vector<Point> &a, int n) {p0 = a[0];for(int i = 0; i < n; i++) {if(a[i].y < p0.y || (a[i].y == p0.y && a[i].x < p0.x)) {p0 = a[i];}}vector<Point> ans;sort(a.begin(), a.end(), cmp_graham);if(n == 1) {ans.push_back(a[0]);return ans;}if(n == 2) {ans.push_back(a[0]);ans.push_back(a[1]);return ans;}ans.push_back(a[0]);ans.push_back(a[1]);int sz = 2;for(int i = 2; i < n; i++) {while(sz > 1 && To_lefttest(ans[sz - 2], ans[sz - 1], a[i]) <= 0) {ans.pop_back();sz--;}ans.push_back(a[i]);sz++;}return ans;
}bool cmp_andrew(Point a, Point b) {if(Sgn(a.x - b.x) == 0)    return a.y < b.y;return a.x < b.x;
}vector<Point> Andrew(vector<Point> &a, int n) {sort(a.begin(), a.end(), cmp_andrew);int p1 = 0, p2;vector<Point> ans;for(int i = 0; i < n; i++) {while(p1 > 1 && Toleft_test(ans[p1 - 2], ans[p1 - 1], a[i]) <= 0)   ans.pop_back(), p1--;ans.push_back(a[i]), p1++;}p2 = p1;for(int i = n - 2; i>= 0; i--) {while(p2 > p1 && Toleft_test(ans[p2 - 2], ans[p2 - 1], a[i]) <= 0)  ans.pop_back(), p2--;ans.push_back(a[i]), p2++;}// ans.pop_back();return ans;
}double Get_angle(Line a) {return atan2(a.ed.y - a.st.y, a.ed.x - a.st.x);
}bool cmp_Half_lane_intersection(Line a, Line b) {Vector va = a.ed - a.st, vb = b.ed - b.st;double A =  Get_angle(va), B = Get_angle(vb);if (Sgn(A - B) == 0) return Sgn(((va) ^ (b.ed - a.st))) != -1;return Sgn(A - B) == -1;
}bool On_right(Line a, Line b, Line c) {Point o = Intersect_point(b, c);if (Sgn((a.ed - a.st) ^ (o - a.st)) < 0) return true;return false;
}const int N = 1e3 + 10;Line que[N];bool Half_lane_intersection(vector<Line> &a) {sort(a.begin(), a.end(), cmp_Half_lane_intersection);int head = 0, tail = 0, cnt = 0, n = a.size();for(int i = 0; i < n - 1; i++) {if(Sgn(Get_angle(a[i]) - Get_angle(a[i + 1])) == 0) continue;a[cnt++] = a[i];}a[cnt++] = a[n - 1];for(int i = 0; i < cnt; i++) {while(tail - head > 1 && On_right(a[i], que[tail - 1], que[tail - 2])) tail--;while(tail - head > 1 && On_right(a[i], que[head], que[head + 1])) head++;que[tail++] = a[i];}while(tail - head > 1 && On_right(que[head], que[tail - 1], que[tail - 2])) tail--;while(tail - head > 1 && On_right(que[tail - 1], que[head], que[head + 1])) head++;if (tail - head < 3) return false;return true;
}int main() {// freopen("in.txt", "r", stdin);// freopen("out.txt", "w", stdout);// ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);int n;while(scanf("%d", &n) && n) {vector<Point> res;for(int i = 0; i < n; i++) {Point ans;ans.read();res.push_back(ans);}double area = Area(res, n);vector<Line> a;if(area > 0) {for(int i = 0; i < n; i++) {a.push_back(Line(res[i], res[(i + 1) % n]));}}else {for(int i = n - 1; i >= 0; i--) {a.push_back(Line(res[(i + 1) % n], res[i]));}}if(Half_lane_intersection(a)) puts("1");else puts("0");}return 0;
}

Video Surveillance

/*Author : lifehappy
*/
#include <cstdio>
#include <cmath>
#include <cstring>
#include <algorithm>
#include <vector>
#include <iostream>using namespace std;const double pi = acos(-1.0);
const double eps = 1e-5;
const double inf = 1e100;int Sgn(double x) {return x < -eps ? -1 : x > eps;
}struct Vector {double x, y;bool operator < (Vector &a) const {return x < a.x;}void print() {printf("%f %f\n", x, y);}void read() {scanf("%lf %lf", &x, &y);}Vector(double _x = 0, double _y = 0) : x(_x), y(_y) {}double mod() {return sqrt(x * x + y * y);}double mod2() {return x * x + y * y;}Vector operator + (const Vector &a) {return Vector(x + a.x, y + a.y);}Vector operator - (const Vector &a) {return Vector(x - a.x, y - a.y);}double operator * (const Vector &a) {return x * a.x + y * a.y;}double operator ^ (const Vector &a) {return x * a.y - y * a.x;}Vector Rotate(double angle) {return Vector(x * cos(angle) - y * sin(angle), x * sin(angle) + y * cos(angle));}Vector operator << (const double &a) {return Vector(x * a, y * a);}Vector operator >> (const double &a) {return Vector(x / a, y / a);}bool operator == (const Vector & a) {return (Sgn(x - a.x) == 0) && (Sgn(y - a.y) == 0);}
};typedef Vector Point;double Dis_pp(Point a, Point b) {return sqrt((a - b) * (a - b));
}double Angle(Vector a, Vector b) {//[0, 2pi)double ans = atan2(a ^ b, a * b);return ans < 0 ? ans + 2 * pi : ans;// return atane(a ^ b, a * b);
}double To_lefttest(Point a, Point b, Point c) {return (b - a) ^(c - a);
}int Toleft_test(Point a, Point b, Point c) {return Sgn((b - a) ^ (c - a));
}struct Line {Point st, ed;Line(Point _st = Point(0, 0), Point _ed = Point(0, 0)) : st(_st), ed(_ed) {}bool operator < (const Line &t) {return st.x < t.st.x;}void read() {scanf("%lf %lf %lf %lf", &st.x, &st.y, &ed.x, &ed.y);}
};bool Parallel(Line a, Line b) {return Sgn((a.st - a.ed) ^ (b.st - b.ed)) == 0;
}bool Is_cross(Line a, Line b) {return Toleft_test(a.st, a.ed, b.st) * Toleft_test(a.st, a.ed, b.ed) <= 0 && Toleft_test(b.st, b.ed, a.st) * Toleft_test(b.st, b.ed, a.ed) <= 0;
}Point Cross_point(Line a, Line b) {if(!Is_cross(a, b)) {return Point(inf, inf);}else {double a1 = fabs(To_lefttest(a.st, a.ed, b.st)), a2 = fabs(To_lefttest(a.st, a.ed, b.ed));return ((b.st << a2) + (b.ed << a1)) >> (a1 + a2);}
}Point Intersect_point(Line a, Line b) {double a1 = a.st.y - a.ed.y, b1 = a.ed.x - a.st.x, c1 = a.st.x * a.ed.y - a.ed.x * a.st.y;double a2 = b.st.y - b.ed.y, b2 = b.ed.x - b.st.x, c2 = b.st.x * b.ed.y - b.ed.x * b.st.y;return Point((c1 * b2 - c2 * b1) / (a2 * b1 - a1 * b2), (a2 * c1 - a1 * c2) / (a1 * b2 - a2 * b1));
}Point Shadow(Line a, Point b) {Point dir = a.ed - a.st;return a.st + (dir << (((b - a.st) * dir) / dir.mod2()));
}Point Reflect(Line a, Point b) {return (Shadow(a, b) << 2) - b;
}bool inmid(double a, double b, double x) {if(a > b) swap(a, b);return Sgn(x - a) >= 0 && Sgn(b - x) >= 0;
}bool Point_in_line(Line a, Point b) {if(Toleft_test(a.st, a.ed, b) != 0) return false;return inmid(a.st.x, a.ed.x, b.x) && inmid(a.st.y, a.ed.y, b.y);
}double Dis_lp(Line a, Point b) {Point h = Shadow(a, b);if(Point_in_line(a, h)) {return Dis_pp(h, b);}return min(Dis_pp(a.st, b), Dis_pp(a.ed, b));
}// double Dis_ll(Line a, Line b) {//     if(Is_cross(a, b)) return 0;
//     return min({Dis_lp(a, b.st), Dis_lp(a, b.ed), Dis_lp(b, a.st), Dis_lp(b, a.ed)});
// }double Area(vector<Point> p, int n) {double ans = 0;for(int i = 0; i < n; i++) {ans += p[i] ^ p[(i + 1) % n];}return 0.5 * ans;
}double len(vector<Point> p, int n) {double ans = 0;for(int i = 0; i < n; i++) {ans += Dis_pp(p[i], p[(i + 1) % n]);}return ans;
}bool Is_convex(Point *a, int n) {bool flag[3] = {0, 0, 0};for(int i = 0; i < n; i++) {flag[Sgn(To_lefttest(a[i], a[(i + 1) % n], a[(i + 2) % n])) + 1] = true;if(flag[0] && flag[2]) return false;}return true;
}Point p0;bool cmp_graham(Point a, Point b) {int flag = Toleft_test(p0, a, b);return flag == 0 ? Dis_pp(p0, a) < Dis_pp(p0, b) : flag > 0;
}vector<Point> Graham(vector<Point> &a, int n) {p0 = a[0];for(int i = 0; i < n; i++) {if(a[i].y < p0.y || (a[i].y == p0.y && a[i].x < p0.x)) {p0 = a[i];}}vector<Point> ans;sort(a.begin(), a.end(), cmp_graham);if(n == 1) {ans.push_back(a[0]);return ans;}if(n == 2) {ans.push_back(a[0]);ans.push_back(a[1]);return ans;}ans.push_back(a[0]);ans.push_back(a[1]);int sz = 2;for(int i = 2; i < n; i++) {while(sz > 1 && To_lefttest(ans[sz - 2], ans[sz - 1], a[i]) <= 0) {ans.pop_back();sz--;}ans.push_back(a[i]);sz++;}return ans;
}bool cmp_andrew(Point a, Point b) {if(Sgn(a.x - b.x) == 0)    return a.y < b.y;return a.x < b.x;
}vector<Point> Andrew(vector<Point> &a, int n) {sort(a.begin(), a.end(), cmp_andrew);int p1 = 0, p2;vector<Point> ans;for(int i = 0; i < n; i++) {while(p1 > 1 && Toleft_test(ans[p1 - 2], ans[p1 - 1], a[i]) <= 0)   ans.pop_back(), p1--;ans.push_back(a[i]), p1++;}p2 = p1;for(int i = n - 2; i>= 0; i--) {while(p2 > p1 && Toleft_test(ans[p2 - 2], ans[p2 - 1], a[i]) <= 0)  ans.pop_back(), p2--;ans.push_back(a[i]), p2++;}// ans.pop_back();return ans;
}double Get_angle(Line a) {return atan2(a.ed.y - a.st.y, a.ed.x - a.st.x);
}bool cmp_Half_lane_intersection(Line a, Line b) {Vector va = a.ed - a.st, vb = b.ed - b.st;double A =  Get_angle(va), B = Get_angle(vb);if (Sgn(A - B) == 0) return Sgn(((va) ^ (b.ed - a.st))) != -1;return Sgn(A - B) == -1;
}bool On_right(Line a, Line b, Line c) {Point o = Intersect_point(b, c);if (Sgn((a.ed - a.st) ^ (o - a.st)) < 0) return true;return false;
}const int N = 1e3 + 10;Line que[N];bool Half_lane_intersection(vector<Line> &a) {sort(a.begin(), a.end(), cmp_Half_lane_intersection);int head = 0, tail = 0, cnt = 0, n = a.size();for(int i = 0; i < n - 1; i++) {if(Sgn(Get_angle(a[i]) - Get_angle(a[i + 1])) == 0) continue;a[cnt++] = a[i];}a[cnt++] = a[n - 1];for(int i = 0; i < cnt; i++) {while(tail - head > 1 && On_right(a[i], que[tail - 1], que[tail - 2])) tail--;while(tail - head > 1 && On_right(a[i], que[head], que[head + 1])) head++;que[tail++] = a[i];}while(tail - head > 1 && On_right(que[head], que[tail - 1], que[tail - 2])) tail--;while(tail - head > 1 && On_right(que[tail - 1], que[head], que[head + 1])) head++;if (tail - head < 3) return false;return true;
}int main() {// freopen("in.txt", "r", stdin);// freopen("out.txt", "w", stdout);// ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);int n, cas = 1;while(scanf("%d", &n) && n) {vector<Point> res;for(int i = 0; i < n; i++) {Point ans;ans.read();res.push_back(ans);}double area = Area(res, n);vector<Line> a;if(area > 0) {for(int i = 0; i < n; i++) {a.push_back(Line(res[i], res[(i + 1) % n]));}}else {for(int i = n - 1; i >= 0; i--) {a.push_back(Line(res[(i + 1) % n], res[i]));}}printf("Floor #%d\n", cas++);if(!Half_lane_intersection(a)) puts("Surveillance is impossible.");else puts("Surveillance is possible.");puts("");}return 0;
}

Art Gallery

/*Author : lifehappy
*/
#include <cstdio>
#include <cmath>
#include <cstring>
#include <algorithm>
#include <vector>
#include <iostream>using namespace std;const double pi = acos(-1.0);
const double eps = 1e-5;
const double inf = 1e100;int Sgn(double x) {return x < -eps ? -1 : x > eps;
}struct Vector {double x, y;bool operator < (Vector &a) const {return x < a.x;}void print() {printf("%f %f\n", x, y);}void read() {scanf("%lf %lf", &x, &y);}Vector(double _x = 0, double _y = 0) : x(_x), y(_y) {}double mod() {return sqrt(x * x + y * y);}double mod2() {return x * x + y * y;}Vector operator + (const Vector &a) {return Vector(x + a.x, y + a.y);}Vector operator - (const Vector &a) {return Vector(x - a.x, y - a.y);}double operator * (const Vector &a) {return x * a.x + y * a.y;}double operator ^ (const Vector &a) {return x * a.y - y * a.x;}Vector Rotate(double angle) {return Vector(x * cos(angle) - y * sin(angle), x * sin(angle) + y * cos(angle));}Vector operator << (const double &a) {return Vector(x * a, y * a);}Vector operator >> (const double &a) {return Vector(x / a, y / a);}bool operator == (const Vector & a) {return (Sgn(x - a.x) == 0) && (Sgn(y - a.y) == 0);}
};typedef Vector Point;double Dis_pp(Point a, Point b) {return sqrt((a - b) * (a - b));
}double Angle(Vector a, Vector b) {//[0, 2pi)double ans = atan2(a ^ b, a * b);return ans < 0 ? ans + 2 * pi : ans;// return atane(a ^ b, a * b);
}double To_lefttest(Point a, Point b, Point c) {return (b - a) ^(c - a);
}int Toleft_test(Point a, Point b, Point c) {return Sgn((b - a) ^ (c - a));
}struct Line {Point st, ed;Line(Point _st = Point(0, 0), Point _ed = Point(0, 0)) : st(_st), ed(_ed) {}bool operator < (const Line &t) {return st.x < t.st.x;}void read() {scanf("%lf %lf %lf %lf", &st.x, &st.y, &ed.x, &ed.y);}
};bool Parallel(Line a, Line b) {return Sgn((a.st - a.ed) ^ (b.st - b.ed)) == 0;
}bool Is_cross(Line a, Line b) {return Toleft_test(a.st, a.ed, b.st) * Toleft_test(a.st, a.ed, b.ed) <= 0 && Toleft_test(b.st, b.ed, a.st) * Toleft_test(b.st, b.ed, a.ed) <= 0;
}Point Cross_point(Line a, Line b) {if(!Is_cross(a, b)) {return Point(inf, inf);}else {double a1 = fabs(To_lefttest(a.st, a.ed, b.st)), a2 = fabs(To_lefttest(a.st, a.ed, b.ed));return ((b.st << a2) + (b.ed << a1)) >> (a1 + a2);}
}Point Intersect_point(Line a, Line b) {double a1 = a.st.y - a.ed.y, b1 = a.ed.x - a.st.x, c1 = a.st.x * a.ed.y - a.ed.x * a.st.y;double a2 = b.st.y - b.ed.y, b2 = b.ed.x - b.st.x, c2 = b.st.x * b.ed.y - b.ed.x * b.st.y;return Point((c1 * b2 - c2 * b1) / (a2 * b1 - a1 * b2), (a2 * c1 - a1 * c2) / (a1 * b2 - a2 * b1));
}Point Shadow(Line a, Point b) {Point dir = a.ed - a.st;return a.st + (dir << (((b - a.st) * dir) / dir.mod2()));
}Point Reflect(Line a, Point b) {return (Shadow(a, b) << 2) - b;
}bool inmid(double a, double b, double x) {if(a > b) swap(a, b);return Sgn(x - a) >= 0 && Sgn(b - x) >= 0;
}bool Point_in_line(Line a, Point b) {if(Toleft_test(a.st, a.ed, b) != 0) return false;return inmid(a.st.x, a.ed.x, b.x) && inmid(a.st.y, a.ed.y, b.y);
}double Dis_lp(Line a, Point b) {Point h = Shadow(a, b);if(Point_in_line(a, h)) {return Dis_pp(h, b);}return min(Dis_pp(a.st, b), Dis_pp(a.ed, b));
}// double Dis_ll(Line a, Line b) {//     if(Is_cross(a, b)) return 0;
//     return min({Dis_lp(a, b.st), Dis_lp(a, b.ed), Dis_lp(b, a.st), Dis_lp(b, a.ed)});
// }double Area(vector<Point> p, int n) {double ans = 0;for(int i = 0; i < n; i++) {ans += p[i] ^ p[(i + 1) % n];}return 0.5 * ans;
}double len(vector<Point> p, int n) {double ans = 0;for(int i = 0; i < n; i++) {ans += Dis_pp(p[i], p[(i + 1) % n]);}return ans;
}bool Is_convex(Point *a, int n) {bool flag[3] = {0, 0, 0};for(int i = 0; i < n; i++) {flag[Sgn(To_lefttest(a[i], a[(i + 1) % n], a[(i + 2) % n])) + 1] = true;if(flag[0] && flag[2]) return false;}return true;
}Point p0;bool cmp_graham(Point a, Point b) {int flag = Toleft_test(p0, a, b);return flag == 0 ? Dis_pp(p0, a) < Dis_pp(p0, b) : flag > 0;
}vector<Point> Graham(vector<Point> &a, int n) {p0 = a[0];for(int i = 0; i < n; i++) {if(a[i].y < p0.y || (a[i].y == p0.y && a[i].x < p0.x)) {p0 = a[i];}}vector<Point> ans;sort(a.begin(), a.end(), cmp_graham);if(n == 1) {ans.push_back(a[0]);return ans;}if(n == 2) {ans.push_back(a[0]);ans.push_back(a[1]);return ans;}ans.push_back(a[0]);ans.push_back(a[1]);int sz = 2;for(int i = 2; i < n; i++) {while(sz > 1 && To_lefttest(ans[sz - 2], ans[sz - 1], a[i]) <= 0) {ans.pop_back();sz--;}ans.push_back(a[i]);sz++;}return ans;
}bool cmp_andrew(Point a, Point b) {if(Sgn(a.x - b.x) == 0)    return a.y < b.y;return a.x < b.x;
}vector<Point> Andrew(vector<Point> &a, int n) {sort(a.begin(), a.end(), cmp_andrew);int p1 = 0, p2;vector<Point> ans;for(int i = 0; i < n; i++) {while(p1 > 1 && Toleft_test(ans[p1 - 2], ans[p1 - 1], a[i]) <= 0)   ans.pop_back(), p1--;ans.push_back(a[i]), p1++;}p2 = p1;for(int i = n - 2; i>= 0; i--) {while(p2 > p1 && Toleft_test(ans[p2 - 2], ans[p2 - 1], a[i]) <= 0)  ans.pop_back(), p2--;ans.push_back(a[i]), p2++;}// ans.pop_back();return ans;
}double Get_angle(Line a) {return atan2(a.ed.y - a.st.y, a.ed.x - a.st.x);
}bool Cmp_half_lane_intersection(Line a, Line b) {Vector va = a.ed - a.st, vb = b.ed - b.st;double A =  Get_angle(va), B = Get_angle(vb);if (Sgn(A - B) == 0) return Sgn(((va) ^ (b.ed - a.st))) != -1;return Sgn(A - B) == -1;
}bool On_right(Line a, Line b, Line c) {Point o = Intersect_point(b, c);if (Sgn((a.ed - a.st) ^ (o - a.st)) < 0) return true;return false;
}const int N = 1e4 + 10;Line que[N];double Half_lane_intersection(vector<Line> &a) {sort(a.begin(), a.end(), Cmp_half_lane_intersection);int head = 0, tail = 0, cnt = 0, n = a.size();for(int i = 0; i < n - 1; i++) {if(Sgn(Get_angle(a[i]) - Get_angle(a[i + 1])) == 0) continue;a[cnt++] = a[i];}a[cnt++] = a[n - 1];for(int i = 0; i < cnt; i++) {while(tail - head > 1 && On_right(a[i], que[tail - 1], que[tail - 2])) tail--;while(tail - head > 1 && On_right(a[i], que[head], que[head + 1])) head++;que[tail++] = a[i];}while(tail - head > 1 && On_right(que[head], que[tail - 1], que[tail - 2])) tail--;while(tail - head > 1 && On_right(que[tail - 1], que[head], que[head + 1])) head++;n = tail - head;if(n < 3) return 0;vector<Point> ans;for(int i = head; i < tail; i++) {ans.push_back(Intersect_point(que[i], que[(i + 1) % n + head]));}return Area(ans, ans.size());// if (tail - head < 3) return false;// return true;
}int main() {// freopen("in.txt", "r", stdin);// freopen("out.txt", "w", stdout);// ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);int T, n;scanf("%d", &T);while(T--) {scanf("%d", &n);vector<Point> res;for(int i = 0; i < n; i++) {Point ans;ans.read();res.push_back(ans);}double area = Area(res, n);vector<Line> a;if(area > 0) {for(int i = 0; i < n; i++) {a.push_back(Line(res[i], res[(i + 1) % n]));}}else {for(int i = n - 1; i >= 0; i--) {a.push_back(Line(res[(i + 1) % n], res[i]));}}printf("%.2f\n", Half_lane_intersection(a));}return 0;
}

Most Distant Point from the Sea

/*Author : lifehappy
*/
#include <cstdio>
#include <cmath>
#include <cstring>
#include <algorithm>
#include <vector>
#include <iostream>using namespace std;const double pi = acos(-1.0);
const double eps = 1e-5;
const double inf = 1e100;int Sgn(double x) {return x < -eps ? -1 : x > eps;
}struct Vector {double x, y;bool operator < (Vector &a) const {return x < a.x;}void print() {printf("%f %f\n", x, y);}void read() {scanf("%lf %lf", &x, &y);}Vector(double _x = 0, double _y = 0) : x(_x), y(_y) {}double mod() {return sqrt(x * x + y * y);}double mod2() {return x * x + y * y;}Vector operator + (const Vector &a) {return Vector(x + a.x, y + a.y);}Vector operator - (const Vector &a) {return Vector(x - a.x, y - a.y);}double operator * (const Vector &a) {return x * a.x + y * a.y;}double operator ^ (const Vector &a) {return x * a.y - y * a.x;}Vector Rotate(double angle) {return Vector(x * cos(angle) - y * sin(angle), x * sin(angle) + y * cos(angle));}Vector operator << (const double &a) {return Vector(x * a, y * a);}Vector operator >> (const double &a) {return Vector(x / a, y / a);}bool operator == (const Vector & a) {return (Sgn(x - a.x) == 0) && (Sgn(y - a.y) == 0);}
};typedef Vector Point;double Dis_pp(Point a, Point b) {return sqrt((a - b) * (a - b));
}double Angle(Vector a, Vector b) {//[0, 2pi)double ans = atan2(a ^ b, a * b);return ans < 0 ? ans + 2 * pi : ans;// return atane(a ^ b, a * b);
}double To_lefttest(Point a, Point b, Point c) {return (b - a) ^(c - a);
}int Toleft_test(Point a, Point b, Point c) {return Sgn((b - a) ^ (c - a));
}struct Line {Point st, ed;Line(Point _st = Point(0, 0), Point _ed = Point(0, 0)) : st(_st), ed(_ed) {}bool operator < (const Line &t) {return st.x < t.st.x;}void read() {scanf("%lf %lf %lf %lf", &st.x, &st.y, &ed.x, &ed.y);}
};bool Parallel(Line a, Line b) {return Sgn((a.st - a.ed) ^ (b.st - b.ed)) == 0;
}bool Is_cross(Line a, Line b) {return Toleft_test(a.st, a.ed, b.st) * Toleft_test(a.st, a.ed, b.ed) <= 0 && Toleft_test(b.st, b.ed, a.st) * Toleft_test(b.st, b.ed, a.ed) <= 0;
}Point Cross_point(Line a, Line b) {if(!Is_cross(a, b)) {return Point(inf, inf);}else {double a1 = fabs(To_lefttest(a.st, a.ed, b.st)), a2 = fabs(To_lefttest(a.st, a.ed, b.ed));return ((b.st << a2) + (b.ed << a1)) >> (a1 + a2);}
}Point Intersect_point(Line a, Line b) {double a1 = a.st.y - a.ed.y, b1 = a.ed.x - a.st.x, c1 = a.st.x * a.ed.y - a.ed.x * a.st.y;double a2 = b.st.y - b.ed.y, b2 = b.ed.x - b.st.x, c2 = b.st.x * b.ed.y - b.ed.x * b.st.y;return Point((c1 * b2 - c2 * b1) / (a2 * b1 - a1 * b2), (a2 * c1 - a1 * c2) / (a1 * b2 - a2 * b1));
}Point Shadow(Line a, Point b) {Point dir = a.ed - a.st;return a.st + (dir << (((b - a.st) * dir) / dir.mod2()));
}Point Reflect(Line a, Point b) {return (Shadow(a, b) << 2) - b;
}bool inmid(double a, double b, double x) {if(a > b) swap(a, b);return Sgn(x - a) >= 0 && Sgn(b - x) >= 0;
}bool Point_in_line(Line a, Point b) {if(Toleft_test(a.st, a.ed, b) != 0) return false;return inmid(a.st.x, a.ed.x, b.x) && inmid(a.st.y, a.ed.y, b.y);
}double Dis_lp(Line a, Point b) {Point h = Shadow(a, b);if(Point_in_line(a, h)) {return Dis_pp(h, b);}return min(Dis_pp(a.st, b), Dis_pp(a.ed, b));
}// double Dis_ll(Line a, Line b) {//     if(Is_cross(a, b)) return 0;
//     return min({Dis_lp(a, b.st), Dis_lp(a, b.ed), Dis_lp(b, a.st), Dis_lp(b, a.ed)});
// }double Area(vector<Point> p, int n) {double ans = 0;for(int i = 0; i < n; i++) {ans += p[i] ^ p[(i + 1) % n];}return 0.5 * ans;
}double len(vector<Point> p, int n) {double ans = 0;for(int i = 0; i < n; i++) {ans += Dis_pp(p[i], p[(i + 1) % n]);}return ans;
}bool Is_convex(Point *a, int n) {bool flag[3] = {0, 0, 0};for(int i = 0; i < n; i++) {flag[Sgn(To_lefttest(a[i], a[(i + 1) % n], a[(i + 2) % n])) + 1] = true;if(flag[0] && flag[2]) return false;}return true;
}Point p0;bool cmp_graham(Point a, Point b) {int flag = Toleft_test(p0, a, b);return flag == 0 ? Dis_pp(p0, a) < Dis_pp(p0, b) : flag > 0;
}vector<Point> Graham(vector<Point> &a, int n) {p0 = a[0];for(int i = 0; i < n; i++) {if(a[i].y < p0.y || (a[i].y == p0.y && a[i].x < p0.x)) {p0 = a[i];}}vector<Point> ans;sort(a.begin(), a.end(), cmp_graham);if(n == 1) {ans.push_back(a[0]);return ans;}if(n == 2) {ans.push_back(a[0]);ans.push_back(a[1]);return ans;}ans.push_back(a[0]);ans.push_back(a[1]);int sz = 2;for(int i = 2; i < n; i++) {while(sz > 1 && To_lefttest(ans[sz - 2], ans[sz - 1], a[i]) <= 0) {ans.pop_back();sz--;}ans.push_back(a[i]);sz++;}return ans;
}bool cmp_andrew(Point a, Point b) {if(Sgn(a.x - b.x) == 0)    return a.y < b.y;return a.x < b.x;
}vector<Point> Andrew(vector<Point> &a, int n) {sort(a.begin(), a.end(), cmp_andrew);int p1 = 0, p2;vector<Point> ans;for(int i = 0; i < n; i++) {while(p1 > 1 && Toleft_test(ans[p1 - 2], ans[p1 - 1], a[i]) <= 0)   ans.pop_back(), p1--;ans.push_back(a[i]), p1++;}p2 = p1;for(int i = n - 2; i>= 0; i--) {while(p2 > p1 && Toleft_test(ans[p2 - 2], ans[p2 - 1], a[i]) <= 0)  ans.pop_back(), p2--;ans.push_back(a[i]), p2++;}// ans.pop_back();return ans;
}double Get_angle(Line a) {return atan2(a.ed.y - a.st.y, a.ed.x - a.st.x);
}bool Cmp_half_lane_intersection(Line a, Line b) {Vector va = a.ed - a.st, vb = b.ed - b.st;double A =  Get_angle(va), B = Get_angle(vb);if (Sgn(A - B) == 0) return Sgn(((va) ^ (b.ed - a.st))) != -1;return Sgn(A - B) == -1;
}bool On_right(Line a, Line b, Line c) {Point o = Intersect_point(b, c);if (Sgn((a.ed - a.st) ^ (o - a.st)) < 0) return true;return false;
}const int N = 1e4 + 10;Line que[N];bool Half_lane_intersection(vector<Line> a, double x) {sort(a.begin(), a.end(), Cmp_half_lane_intersection);int head = 0, tail = 0, cnt = 0, n = a.size();for(int i = 0; i < n; i++) {Vector dir = a[i].ed - a[i].st;dir = dir.Rotate(pi / 2);double mod = dir.mod();dir.x /= mod, dir.y /= mod;a[i].st = a[i].st + (dir << x);a[i].ed = a[i].ed + (dir << x);}for(int i = 0; i < n - 1; i++) {if(Sgn(Get_angle(a[i]) - Get_angle(a[i + 1])) == 0) continue;a[cnt++] = a[i];}a[cnt++] = a[n - 1];for(int i = 0; i < cnt; i++) {while(tail - head > 1 && On_right(a[i], que[tail - 1], que[tail - 2])) tail--;while(tail - head > 1 && On_right(a[i], que[head], que[head + 1])) head++;que[tail++] = a[i];}while(tail - head > 1 && On_right(que[head], que[tail - 1], que[tail - 2])) tail--;while(tail - head > 1 && On_right(que[tail - 1], que[head], que[head + 1])) head++;// n = tail - head;// if(n < 3) return 0;// vector<Point> ans;// for(int i = head; i < tail; i++) {//     ans.push_back(Intersect_point(que[i], que[(i + 1) % n + head]));// }// return Area(ans, ans.size());if (tail - head < 3) return false;return true;
}int main() {// freopen("in.txt", "r", stdin);// freopen("out.txt", "w", stdout);// ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);int T, n;// scanf("%d", &T);while(scanf("%d", &n) && n) {// scanf("%d", &n);vector<Point> res;for(int i = 0; i < n; i++) {Point ans;ans.read();res.push_back(ans);}double area = Area(res, n);vector<Line> a;if(area > 0) {for(int i = 0; i < n; i++) {a.push_back(Line(res[i], res[(i + 1) % n]));}}else {for(int i = n - 1; i >= 0; i--) {a.push_back(Line(res[(i + 1) % n], res[i]));}}double l = 0, r = 10000;for(int i = 1; i <= 300; i++) {double mid = (l + r) / 2;if(Half_lane_intersection(a, mid)) l = mid;else r = mid;}printf("%.6f\n", l);}return 0;
}

Feng Shui (待调)

/*Author : lifehappy
*/
#include <cstdio>
#include <cmath>
#include <cstring>
#include <algorithm>
#include <vector>
#include <iostream>using namespace std;const double pi = acos(-1.0);
const double eps = 1e-5;
const double inf = 1e100;int Sgn(double x) {return x < -eps ? -1 : x > eps;
}struct Vector {double x, y;bool operator < (Vector &a) const {return x < a.x;}void print() {printf("%f %f\n", x, y);}void read() {scanf("%lf %lf", &x, &y);}Vector(double _x = 0, double _y = 0) : x(_x), y(_y) {}double mod() {return sqrt(x * x + y * y);}double mod2() {return x * x + y * y;}Vector operator + (const Vector &a) {return Vector(x + a.x, y + a.y);}Vector operator - (const Vector &a) {return Vector(x - a.x, y - a.y);}double operator * (const Vector &a) {return x * a.x + y * a.y;}double operator ^ (const Vector &a) {return x * a.y - y * a.x;}Vector Rotate(double angle) {return Vector(x * cos(angle) - y * sin(angle), x * sin(angle) + y * cos(angle));}Vector operator << (const double &a) {return Vector(x * a, y * a);}Vector operator >> (const double &a) {return Vector(x / a, y / a);}bool operator == (const Vector & a) {return (Sgn(x - a.x) == 0) && (Sgn(y - a.y) == 0);}
};typedef Vector Point;double Dis_pp(Point a, Point b) {return sqrt((a - b) * (a - b));
}double Angle(Vector a, Vector b) {//[0, 2pi)double ans = atan2(a ^ b, a * b);return ans < 0 ? ans + 2 * pi : ans;// return atane(a ^ b, a * b);
}double To_lefttest(Point a, Point b, Point c) {return (b - a) ^(c - a);
}int Toleft_test(Point a, Point b, Point c) {return Sgn((b - a) ^ (c - a));
}struct Line {Point st, ed;Line(Point _st = Point(0, 0), Point _ed = Point(0, 0)) : st(_st), ed(_ed) {}bool operator < (const Line &t) {return st.x < t.st.x;}void read() {scanf("%lf %lf %lf %lf", &st.x, &st.y, &ed.x, &ed.y);}
};bool Parallel(Line a, Line b) {return Sgn((a.st - a.ed) ^ (b.st - b.ed)) == 0;
}bool Is_cross(Line a, Line b) {return Toleft_test(a.st, a.ed, b.st) * Toleft_test(a.st, a.ed, b.ed) <= 0 && Toleft_test(b.st, b.ed, a.st) * Toleft_test(b.st, b.ed, a.ed) <= 0;
}Point Cross_point(Line a, Line b) {if(!Is_cross(a, b)) {return Point(inf, inf);}else {double a1 = fabs(To_lefttest(a.st, a.ed, b.st)), a2 = fabs(To_lefttest(a.st, a.ed, b.ed));return ((b.st << a2) + (b.ed << a1)) >> (a1 + a2);}
}Point Intersect_point(Line a, Line b) {double a1 = a.st.y - a.ed.y, b1 = a.ed.x - a.st.x, c1 = a.st.x * a.ed.y - a.ed.x * a.st.y;double a2 = b.st.y - b.ed.y, b2 = b.ed.x - b.st.x, c2 = b.st.x * b.ed.y - b.ed.x * b.st.y;return Point((c1 * b2 - c2 * b1) / (a2 * b1 - a1 * b2), (a2 * c1 - a1 * c2) / (a1 * b2 - a2 * b1));
}Point Shadow(Line a, Point b) {Point dir = a.ed - a.st;return a.st + (dir << (((b - a.st) * dir) / dir.mod2()));
}Point Reflect(Line a, Point b) {return (Shadow(a, b) << 2) - b;
}bool inmid(double a, double b, double x) {if(a > b) swap(a, b);return Sgn(x - a) >= 0 && Sgn(b - x) >= 0;
}bool Point_in_line(Line a, Point b) {if(Toleft_test(a.st, a.ed, b) != 0) return false;return inmid(a.st.x, a.ed.x, b.x) && inmid(a.st.y, a.ed.y, b.y);
}double Dis_lp(Line a, Point b) {Point h = Shadow(a, b);if(Point_in_line(a, h)) {return Dis_pp(h, b);}return min(Dis_pp(a.st, b), Dis_pp(a.ed, b));
}// double Dis_ll(Line a, Line b) {//     if(Is_cross(a, b)) return 0;
//     return min({Dis_lp(a, b.st), Dis_lp(a, b.ed), Dis_lp(b, a.st), Dis_lp(b, a.ed)});
// }double Area(vector<Point> p, int n) {double ans = 0;for(int i = 0; i < n; i++) {ans += p[i] ^ p[(i + 1) % n];}return 0.5 * ans;
}double len(vector<Point> p, int n) {double ans = 0;for(int i = 0; i < n; i++) {ans += Dis_pp(p[i], p[(i + 1) % n]);}return ans;
}bool Is_convex(Point *a, int n) {bool flag[3] = {0, 0, 0};for(int i = 0; i < n; i++) {flag[Sgn(To_lefttest(a[i], a[(i + 1) % n], a[(i + 2) % n])) + 1] = true;if(flag[0] && flag[2]) return false;}return true;
}Point p0;bool cmp_graham(Point a, Point b) {int flag = Toleft_test(p0, a, b);return flag == 0 ? Dis_pp(p0, a) < Dis_pp(p0, b) : flag > 0;
}vector<Point> Graham(vector<Point> &a, int n) {p0 = a[0];for(int i = 0; i < n; i++) {if(a[i].y < p0.y || (a[i].y == p0.y && a[i].x < p0.x)) {p0 = a[i];}}vector<Point> ans;sort(a.begin(), a.end(), cmp_graham);if(n == 1) {ans.push_back(a[0]);return ans;}if(n == 2) {ans.push_back(a[0]);ans.push_back(a[1]);return ans;}ans.push_back(a[0]);ans.push_back(a[1]);int sz = 2;for(int i = 2; i < n; i++) {while(sz > 1 && To_lefttest(ans[sz - 2], ans[sz - 1], a[i]) <= 0) {ans.pop_back();sz--;}ans.push_back(a[i]);sz++;}return ans;
}bool cmp_andrew(Point a, Point b) {if(Sgn(a.x - b.x) == 0)    return a.y < b.y;return a.x < b.x;
}vector<Point> Andrew(vector<Point> &a, int n) {sort(a.begin(), a.end(), cmp_andrew);int p1 = 0, p2;vector<Point> ans;for(int i = 0; i < n; i++) {while(p1 > 1 && Toleft_test(ans[p1 - 2], ans[p1 - 1], a[i]) <= 0)   ans.pop_back(), p1--;ans.push_back(a[i]), p1++;}p2 = p1;for(int i = n - 2; i>= 0; i--) {while(p2 > p1 && Toleft_test(ans[p2 - 2], ans[p2 - 1], a[i]) <= 0)  ans.pop_back(), p2--;ans.push_back(a[i]), p2++;}// ans.pop_back();return ans;
}double Get_angle(Line a) {return atan2(a.ed.y - a.st.y, a.ed.x - a.st.x);
}bool Cmp_half_lane_intersection(Line a, Line b) {Vector va = a.ed - a.st, vb = b.ed - b.st;double A =  Get_angle(va), B = Get_angle(vb);if (Sgn(A - B) == 0) return Sgn(((va) ^ (b.ed - a.st))) != -1;return Sgn(A - B) == -1;
}bool On_right(Line a, Line b, Line c) {Point o = Intersect_point(b, c);if (Sgn((a.ed - a.st) ^ (o - a.st)) < 0) return true;return false;
}const int N = 1e4 + 10;Line que[N];void Half_lane_intersection(vector<Line> a, double x) {sort(a.begin(), a.end(), Cmp_half_lane_intersection);int head = 0, tail = 0, cnt = 0, n = a.size();for(int i = 0; i < n; i++) {Vector dir = a[i].ed - a[i].st;dir = dir.Rotate(pi / 2);double mod = dir.mod();dir.x /= mod, dir.y /= mod;a[i].st = a[i].st + (dir << x);a[i].ed = a[i].ed + (dir << x);}for(int i = 0; i < n - 1; i++) {if(Sgn(Get_angle(a[i]) - Get_angle(a[i + 1])) == 0) continue;a[cnt++] = a[i];}a[cnt++] = a[n - 1];for(int i = 0; i < cnt; i++) {while(tail - head > 1 && On_right(a[i], que[tail - 1], que[tail - 2])) tail--;while(tail - head > 1 && On_right(a[i], que[head], que[head + 1])) head++;que[tail++] = a[i];}while(tail - head > 1 && On_right(que[head], que[tail - 1], que[tail - 2])) tail--;while(tail - head > 1 && On_right(que[tail - 1], que[head], que[head + 1])) head++;n = tail - head;// if(n < 3) return 0;vector<Point> ans;for(int i = head; i < tail; i++) {ans.push_back(Intersect_point(que[i], que[(i + 1) % n + head]));}double dis = -1;int fi = 0, se = 0;n = ans.size();for(int i = 0; i < n; i++) {for(int j = i + 1; j < n; j++) {double now = Dis_pp(ans[i], ans[j]);if(Sgn(now - dis) > 0) {fi = i, se = j;dis = now;}}}if(fabs(ans[fi].x) < eps) ans[fi].x = 0;if(fabs(ans[fi].y) < eps) ans[fi].y = 0;if(fabs(ans[se].x) < eps) ans[se].x = 0;if(fabs(ans[se].y) < eps) ans[se].y = 0;printf("%.4f %.4f %.4f %.4f\n", ans[fi].x, ans[fi].y, ans[se].x, ans[se].y);// return Area(ans, ans.size());// if (tail - head < 3) return false;// return true;
}int main() {// freopen("in.txt", "r", stdin);// freopen("out.txt", "w", stdout);// ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);int T, n;double r;// scanf("%d", &T);while(scanf("%d %lf", &n, &r) != EOF) {// scanf("%d", &n);vector<Point> res;for(int i = 0; i < n; i++) {Point ans;ans.read();res.push_back(ans);}double area = Area(res, n);vector<Line> a;if(area > 0) {for(int i = 0; i < n; i++) {a.push_back(Line(res[i], res[(i + 1) % n]));}}else {for(int i = n - 1; i >= 0; i--) {a.push_back(Line(res[(i + 1) % n], res[i]));}}Half_lane_intersection(a, r);}return 0;
}

Triathlon

Hotter Colder

Uyuw’s Concert(待修正)

/*Author : lifehappy
*/
#include <cstdio>
#include <cmath>
#include <cstring>
#include <algorithm>
#include <vector>
#include <iostream>using namespace std;#define double long doubleconst double pi = acos(-1.0);
const double eps = 1e-10;
const double inf = 1e100;int Sgn(double x) {return x < -eps ? -1 : x > eps;
}struct Vector {double x, y;bool operator < (Vector &a) const {return x < a.x;}void print() {printf("%f %f\n", x, y);}void read() {scanf("%lf %lf", &x, &y);}Vector(double _x = 0, double _y = 0) : x(_x), y(_y) {}double mod() {return sqrt(x * x + y * y);}double mod2() {return x * x + y * y;}Vector operator + (const Vector &a) {return Vector(x + a.x, y + a.y);}Vector operator - (const Vector &a) {return Vector(x - a.x, y - a.y);}double operator * (const Vector &a) {return x * a.x + y * a.y;}double operator ^ (const Vector &a) {return x * a.y - y * a.x;}Vector Rotate(double angle) {return Vector(x * cos(angle) - y * sin(angle), x * sin(angle) + y * cos(angle));}Vector operator << (const double &a) {return Vector(x * a, y * a);}Vector operator >> (const double &a) {return Vector(x / a, y / a);}bool operator == (const Vector & a) {return (Sgn(x - a.x) == 0) && (Sgn(y - a.y) == 0);}
};typedef Vector Point;double Dis_pp(Point a, Point b) {return sqrt((a - b) * (a - b));
}double Angle(Vector a, Vector b) {//[0, 2pi)double ans = atan2(a ^ b, a * b);return ans < 0 ? ans + 2 * pi : ans;// return atane(a ^ b, a * b);
}double To_lefttest(Point a, Point b, Point c) {return (b - a) ^(c - a);
}int Toleft_test(Point a, Point b, Point c) {return Sgn((b - a) ^ (c - a));
}struct Line {Point st, ed;Line(Point _st = Point(0, 0), Point _ed = Point(0, 0)) : st(_st), ed(_ed) {}bool operator < (const Line &t) {return st.x < t.st.x;}void read() {scanf("%lf %lf %lf %lf", &st.x, &st.y, &ed.x, &ed.y);}
};bool Parallel(Line a, Line b) {return Sgn((a.st - a.ed) ^ (b.st - b.ed)) == 0;
}bool Is_cross(Line a, Line b) {return Toleft_test(a.st, a.ed, b.st) * Toleft_test(a.st, a.ed, b.ed) <= 0 && Toleft_test(b.st, b.ed, a.st) * Toleft_test(b.st, b.ed, a.ed) <= 0;
}Point Cross_point(Line a, Line b) {if(!Is_cross(a, b)) {return Point(inf, inf);}else {double a1 = fabs(To_lefttest(a.st, a.ed, b.st)), a2 = fabs(To_lefttest(a.st, a.ed, b.ed));return ((b.st << a2) + (b.ed << a1)) >> (a1 + a2);}
}Point Intersect_point(Line a, Line b) {double a1 = a.st.y - a.ed.y, b1 = a.ed.x - a.st.x, c1 = a.st.x * a.ed.y - a.ed.x * a.st.y;double a2 = b.st.y - b.ed.y, b2 = b.ed.x - b.st.x, c2 = b.st.x * b.ed.y - b.ed.x * b.st.y;return Point((c1 * b2 - c2 * b1) / (a2 * b1 - a1 * b2), (a2 * c1 - a1 * c2) / (a1 * b2 - a2 * b1));
}Point Shadow(Line a, Point b) {Point dir = a.ed - a.st;return a.st + (dir << (((b - a.st) * dir) / dir.mod2()));
}Point Reflect(Line a, Point b) {return (Shadow(a, b) << 2) - b;
}bool inmid(double a, double b, double x) {if(a > b) swap(a, b);return Sgn(x - a) >= 0 && Sgn(b - x) >= 0;
}bool Point_in_line(Line a, Point b) {if(Toleft_test(a.st, a.ed, b) != 0) return false;return inmid(a.st.x, a.ed.x, b.x) && inmid(a.st.y, a.ed.y, b.y);
}double Dis_lp(Line a, Point b) {Point h = Shadow(a, b);if(Point_in_line(a, h)) {return Dis_pp(h, b);}return min(Dis_pp(a.st, b), Dis_pp(a.ed, b));
}// double Dis_ll(Line a, Line b) {//     if(Is_cross(a, b)) return 0;
//     return min({Dis_lp(a, b.st), Dis_lp(a, b.ed), Dis_lp(b, a.st), Dis_lp(b, a.ed)});
// }double Area(vector<Point> p, int n) {double ans = 0;for(int i = 0; i < n; i++) {ans += p[i] ^ p[(i + 1) % n];}return 0.5 * ans;
}double Len(vector<Point> p, int n) {double ans = 0;for(int i = 0; i < n; i++) {ans += Dis_pp(p[i], p[(i + 1) % n]);}return ans;
}bool Is_convex(Point *a, int n) {bool flag[3] = {0, 0, 0};for(int i = 0; i < n; i++) {flag[Sgn(To_lefttest(a[i], a[(i + 1) % n], a[(i + 2) % n])) + 1] = true;if(flag[0] && flag[2]) return false;}return true;
}Point p0;bool cmp_graham(Point a, Point b) {int flag = Toleft_test(p0, a, b);return flag == 0 ? Dis_pp(p0, a) < Dis_pp(p0, b) : flag > 0;
}vector<Point> Graham(vector<Point> &a, int n) {p0 = a[0];for(int i = 0; i < n; i++) {if(a[i].y < p0.y || (a[i].y == p0.y && a[i].x < p0.x)) {p0 = a[i];}}vector<Point> ans;sort(a.begin(), a.end(), cmp_graham);if(n == 1) {ans.push_back(a[0]);return ans;}if(n == 2) {ans.push_back(a[0]);ans.push_back(a[1]);return ans;}ans.push_back(a[0]);ans.push_back(a[1]);int sz = 2;for(int i = 2; i < n; i++) {while(sz > 1 && To_lefttest(ans[sz - 2], ans[sz - 1], a[i]) <= 0) {ans.pop_back();sz--;}ans.push_back(a[i]);sz++;}return ans;
}bool cmp_andrew(Point a, Point b) {if(Sgn(a.x - b.x) == 0)    return a.y < b.y;return a.x < b.x;
}vector<Point> Andrew(vector<Point> &a, int n) {sort(a.begin(), a.end(), cmp_andrew);int p1 = 0, p2;vector<Point> ans;for(int i = 0; i < n; i++) {while(p1 > 1 && Toleft_test(ans[p1 - 2], ans[p1 - 1], a[i]) <= 0)   ans.pop_back(), p1--;ans.push_back(a[i]), p1++;}p2 = p1;for(int i = n - 2; i>= 0; i--) {while(p2 > p1 && Toleft_test(ans[p2 - 2], ans[p2 - 1], a[i]) <= 0)  ans.pop_back(), p2--;ans.push_back(a[i]), p2++;}ans.pop_back();return ans;
}double Get_angle(Line a) {return atan2(a.ed.y - a.st.y, a.ed.x - a.st.x);
}bool Cmp_half_lane_intersection(Line a, Line b) {Vector va = a.ed - a.st, vb = b.ed - b.st;double A =  Get_angle(va), B = Get_angle(vb);if (Sgn(A - B) == 0) return Sgn(((va) ^ (b.ed - a.st))) != -1;return Sgn(A - B) == -1;
}bool On_right(Line a, Line b, Line c) {Point o = Intersect_point(b, c);if (Sgn((a.ed - a.st) ^ (o - a.st)) < 0) return true;return false;
}const int N = 2e4 + 10;Line que[N];// Line que[2];double Half_lane_intersection(vector<Line> &a) {sort(a.begin(), a.end(), Cmp_half_lane_intersection);int head = 0, tail = 0, cnt = 0, n = a.size();for(int i = 0; i < n - 1; i++) {if(Sgn(Get_angle(a[i]) - Get_angle(a[i + 1])) == 0) continue;a[cnt++] = a[i];}a[cnt++] = a[n - 1];for(int i = 0; i < cnt; i++) {while(tail - head > 1 && On_right(a[i], que[tail - 1], que[tail - 2])) tail--;while(tail - head > 1 && On_right(a[i], que[head], que[head + 1])) head++;que[tail++] = a[i];}while(tail - head > 1 && On_right(que[head], que[tail - 1], que[tail - 2])) tail--;while(tail - head > 1 && On_right(que[tail - 1], que[head], que[head + 1])) head++;n = tail - head;if(n < 3) return 0;vector<Point> ans;for(int i = head; i < tail; i++) {ans.push_back(Intersect_point(que[i], que[(i + 1) % n + head]));}return Area(ans, ans.size());// if (tail - head < 3) return false;// return true;
}int main() {// freopen("in.txt", "r", stdin);// freopen("out.txt", "w", stdout);// ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);int n;while(scanf("%d", &n) != EOF) {vector<Line> ans;for(int i = 1; i <= n; i++) {Line temp;temp.read();ans.push_back(temp);}ans.push_back(Line(Point(0, 0), Point(10000, 0)));ans.push_back(Line(Point(10000, 0), Point(10000, 10000)));ans.push_back(Line(Point(10000, 10000), Point(0, 10000)));ans.push_back(Line(Point(0, 1000), Point(0, 0)));printf("%.1lf\n", Half_lane_intersection(ans));}return 0;
}

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半平面交练习（计算几何）

四：半平面交

Rotating Scoreboard

How I Mathematician Wonder What You Are!

Video Surveillance

Art Gallery

Most Distant Point from the Sea

Feng Shui (待调)

Triathlon

Hotter Colder

Uyuw’s Concert(待修正)

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