From df25154fdad95e1a95acebbd64db90e63be61463 Mon Sep 17 00:00:00 2001
From: Fei Pan <pan-fei@outlook.com>
Date: Sat, 5 Oct 2024 22:24:10 +0800
Subject: [PATCH] luogu/P4250

---
 code/luogu/P4250.cpp | 127 +++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 127 insertions(+)
 create mode 100644 code/luogu/P4250.cpp

diff --git a/code/luogu/P4250.cpp b/code/luogu/P4250.cpp
new file mode 100644
index 0000000..8042a1b
--- /dev/null
+++ b/code/luogu/P4250.cpp
@@ -0,0 +1,127 @@
+#include <bits/stdc++.h>
+
+template <typename T>
+class HalfPlaneIntersection {
+    struct Point {
+        T x{0}, y{0};
+        friend T operator*(const Point &lhs, const Point &rhs) {
+            return lhs.x * rhs.y - lhs.y * rhs.x;
+        }
+    };
+    struct Line {
+        T a, b, c;
+        Point dir() const {
+            return Point{b, -a};
+        }
+        bool operator()(const Point &p) {
+            return a * p.x + b * p.y + c >= 0;
+        }
+        bool contains(const Line &other) const {
+            if (a * a > b * b) {
+                return c * fabsl(other.a) > other.c * fabsl(a);
+            }
+            return c * fabsl(other.b) > other.c * fabsl(b);
+        }
+    };
+    Point intersection(const Line &u, const Line &v) {
+        T denominator = u.a * v.b - v.a * u.b;
+        T x = -(u.c * v.b - v.c * u.b) / denominator;
+        T y = (u.c * v.a - v.c * u.a) / denominator;
+        return Point{x, y};
+    }
+
+public:
+    using line_t = Line;
+    using point_t = Point;
+    std::vector<Point> operator()(std::vector<Line> lines) {
+        std::sort(lines.begin(), lines.end(), [](const Line &u, const Line &v) {
+            return atan2(u.b, -u.a) > atan2(v.b, -v.a);
+        });
+        {
+            int j = -1;
+            for (int i = 0; i < lines.size(); ++i) {
+                if (j != -1 && lines[j].dir() * lines[i].dir() == 0) {
+                    if (lines[j].contains(lines[i])) {
+                        lines[j] = lines[i];
+                    }
+                } else {
+                    lines[++j] = lines[i];
+                }
+            }
+            lines.resize(j + 1);
+        }
+
+        std::vector<Line> q(lines.size());
+        std::vector<Point> c(lines.size());
+        int l = 0, r = 0;
+        q[0] = lines[0];
+        for (int i = 1; i < lines.size(); ++i) {
+            while (l < r && !lines[i](c[r])) {
+                --r;
+            }
+            while (l < r && !lines[i](c[l + 1])) {
+                ++l;
+            }
+            q[++r] = lines[i];
+            if (l < r) {
+                c[r] = intersection(q[r], q[r - 1]);
+            }
+        }
+        while (l < r && !q[l](c[r])) {
+            --r;
+        }
+        c[l] = intersection(q[l], q[r]);
+        return std::vector<Point>{c.begin() + l, c.begin() + r + 1};
+    }
+};
+
+using real = long double;
+using hpi = HalfPlaneIntersection<real>;
+using Line = hpi::line_t;
+using Point = hpi::point_t;
+
+Line operator-(const Line &lhs, const Line &rhs) {
+    return Line{lhs.a - rhs.a, lhs.b - rhs.b, lhs.c - rhs.c};
+}
+
+int main() {
+    std::ios::sync_with_stdio(false);
+    std::cin.tie(nullptr);
+
+    int n;
+    std::cin >> n;
+
+    std::vector<Point> p(n);
+    for (int i = 0; i < n; ++i) {
+        int x, y;
+        std::cin >> x >> y;
+        p[i].x = x;
+        p[i].y = y;
+    }
+
+    std::vector<Line> lines(n);
+    for (int i = 0; i < n; ++i) {
+        auto [x0, y0] = p[i];
+        auto [x1, y1] = p[(i + 1) % n];
+        lines[i] = Line{y0 - y1, x1 - x0, x0 * y1 - x1 * y0};
+    }
+
+    auto area = [](const std::vector<Point> &p) -> real {
+        real res = 0;
+        for (int i = 0; i < p.size(); ++i) {
+            auto [x0, y0] = p[i];
+            auto [x1, y1] = p[(i + 1) % p.size()];
+            res += x0 * y1 - x1 * y0;
+        }
+        return res / 2;
+    };
+
+    real S = area(hpi{}(lines));
+    for (int i = 1; i < n; ++i) {
+        lines.push_back(lines[i] - lines[0]);
+    }
+    real T = area(hpi{}(lines));
+
+    std::cout << std::fixed << std::setprecision(4);
+    std::cout << T / S << '\n';
+}